Other Free Encyclopedias » Science Encyclopedia » Science & Philosophy: Categorical judgement to Chimaera

Chi-Square Test

chd table syndrome expected

The chi-square test (KHGR2) is the most commonly used method for comparing frequencies or proportions. It is a statistical test used to determine if observed data deviate from those expected under a particular hypothesis. The chi-square test is also referred to as a test of a measure of fit or "goodness of fit" between data. Typically, the hypothesis tested is whether or not two samples are different enough in a particular characteristic to be considered members of different populations. Chi-square analysis belongs to the family of univariate analysis, i.e., those tests that evaluate the possible effect of one variable (often called the independent variable) upon an outcome (often called the dependent variable).

The chi-square analysis is used to test the null hypothesis (H0), which is the hypothesis that states there is no significant difference between expected and observed data. Investigators either accept or reject H0, after comparing the value of chi-square to a probability distribution. Chi-square values with low probability lead to the rejection of H0 and it is assumed that a factor other than chance creates a large deviation between expected and observed results. As with all non-parametric tests (that do not require normal distribution curves), chi-square tests only evaluate a single variable, thus they do not take into account the interaction among more than one variable upon the outcome.

A chi-square analysis is best illustrated using an example in which data from a population is categorized with respect to two qualitative variables. Table 1 shows a sample of patients categorized with respect to two qualitative variables, namely, congenital heart defect (CHD; present or absent) and karyotype (trisomy 21, also called Down syndrome, or trisomy 13, also called Patau syndrome). The classification table used in a chi-square analysis is called a contingency table and this is its simplest form (2 x 2). The data in a contingency table are often defined as row (r) and column (c) variables.

In general, a chi-square analysis evaluates whether or not variables within a contingency table are independent, or that there is no association between them. In this example, independence would mean that the proportion of individuals affected by CHD is not dependent on karyotype; thus, the proportion of patients with CHD would be similar for both Down and Patau syndrome patients. Dependence, or association, would mean that the proportion of individuals affected by CHD is dependent on kayotype, so that CHD would be more commonly found in patients with one of the two karyotypes examined.

Table 1 shows a 2 x 2 contingency table for a chi-square test—CHD (congenital heart defects) found in patients with Down and Patau syndromes

Figure 1. Chi-square distributions for 1, 3, and 5 degrees of freedom. The shaded region in each of the distributions indicates the upper 5% of the distribution. Illustration by Argosy. The Gale Group.


Chi-square is the sum of the squared difference between observed and expected data, divided by the expected data in all possible categories:


Χ2 = (O11 - E11)2 / E11 + (O12 - E12)2 / E 12 + (O21 - E21)2/ E21 + (O22E22)2 / E22, where O11 represents the observed number of subjects in column 1, row 1, and so on. A summary is shown in Table 2.


The observed frequency is simply the actual number of observations in a cell. In other words, O11 for CHD in the Down-syndrome-affected individuals is 24. Likewise, the observed frequency of CHD in the Patau-syndrome-affected patients is 20 (O12). Because the null hypothesis assumes that the two variables are independent

TABLE 1.
    Karyotype  
    Down syndrome Patau syndrome Total
Congenital Heart Defects CHD present 24 20 44
  CHD absent 36 5 41
  Total 60 25 85

TABLE 2.
    Karyotype  
    Down syndrome Patau syndrome Total
Congenital Heart Defects CHD present O11 O12 r1
  CHD absent O21 O22 r2
  Total c1 c2 N

TABLE 3.
Observed (o) Expected (e) o-e (o-e)2 (o-e)2/e
24 31.1 -7.1 50.41 1.62
20 12.9 7.1 50.41 3.91
36 28.9 7.1 50.41 1.74
5 12.1 -7.1 50.41 4.17
85 85.0     Χ2=11.44


of each other, expected frequencies are calculated using the multiplication rule of probability. The multiplication rule says that the probability of the occurrence of two independent events X and Y is the product of the individual probabilities of X and Y. In this case, the expected probability that a patient has both Down syndrome and CHD is the product of the probability that a patient has Down syndrome (60/85 = 0.706) and the probability that a patient has CHD (44/85 = 0.518), or 0.706 x 0.518 = 0.366. The expected frequency of patients with both Down syndrome and CHD is the product of the expected probability and the total population studied, or 0.366 x 85 = 31.1.

Table 3 presents observed and expected frequencies and Χ2 for data in Table 1.

Before the chi-square value can be evaluated, the degrees of freedom for the data set must be determined. Degrees of freedom are the number of independent variables in the data set. In a contingency table, the degrees of freedom are calculated as the product of the number of rows minus 1 and the number of columns minus 1, or (r-1)(c-1). In this example, (2-1)(2-1) = 1; thus, there is just one degree of freedom.

Once the degrees of freedom are determined, the value of Χ2 is compared with the appropriate chi-square distribution, which can be found in tables in most statistical analyses texts. A relative standard serves as the basis for accepting or rejecting the hypothesis. In biological research, the relative standard is usually p = 0.05, where p is the probability that the deviation of the observed frequencies from the expected frequencies is due to chance alone. If p is less than or equal to 0.05, then the null hypothesis is rejected and the data are not independent of each other. For one degree of freedom, the critical value associated with p = 0.05 for Χ2 is 3.84. Chi-square values higher than this critical value are associated with a statistically low probability that H0 is true. Because the chi-square value is 11.44, much greater than 3.84, the hypothesis that the proportion of trisomy-13-affected patients with CHD does not differ significantly from the corresponding proportion for trisomy-21-affected patients is rejected. Instead, it is very likely that there is a dependence of CHD on karyotype.

Figure 1 shows chi-square distributions for 1, 3, and 5 degrees of freedom. The shaded region in each of the distributions indicates the upper 5% of the distribution. The critical value associated with p = 0.05 is indicated. Notice that as the degrees of freedom increases, the chi-square value required to reject the null hypothesis increases.

Because a chi-square test is a univariate test; it does not consider relationships among multiple variables at the same time. Therefore, dependencies detected by chi-square analyses may be unrealistic or non-causal. There may be other unseen factors that make the variables appear to be associated. However, if properly used, the test is a very useful tool for the evaluation of associations and can be used as a preliminary analysis of more complex statistical evaluations.

Resources

Books

Grant, Gregory R., and Warren J. Ewens. Statistical Methods in Bioinformatics. New York: Springer Verlag, 2001.

Nikulin, Mikhail S., and Priscilla E. Greenwood. A Guide to Chi-Square Testing. New York: Wiley-Interscience, 1996.

Other

Rice University. Rice Virtual Lab in Statistics. "Chi Square Test of Deviations." (cited November 20, 2002). <http;://www. ruf.rice.edu/~lane/stat_sim/chisq_theor/>.


Antonio Farina

[back] Chestnut - The Sweet Chestnut, The American Chestnut - Other chestnuts

User Comments

Your email address will be altered so spam harvesting bots can't read it easily.
Hide my email completely instead?

Cancel or

Vote down Vote up

over 6 years ago

This article is good, and would like to used it for my work. Can you please elaborate on it please?

Vote down Vote up

3 days ago

I'm a bit confused on why you calculate joint probability of patient having both Down and Patau syndrome, since it is impossible in real life (and hence in dataset)? As I understand the Chi-Square test, you would calculate that 60/85 = 70.6 % have Down syndrome, and the rest 29.4 % have Patau syndrome. So you would expect people with CHD to have the same 71-29 split as you would expect people without CHD to have? And then, based from this calculate the test statistic.
Could you help me with this understanding please?

Vote down Vote up

7 months ago

This http://www.horloges-rolex.nl/ is http://www.toms-outlet.net/ the http://www.uggboots.net.co/ Chairman http://www.jordanretro.org/ Mao's http://www.montres-pascher.fr/ revolution http://www.adidas.com.se/ in http://www.nike-airmax.us.com/ China http://www.raybans-sunglasses.cc/ into http://www.ugg-uggboots.net/ the http://www.cheap-raybanoutlet.com/ war http://texans.nfljersey.us.com/ of http://www.prada-shoes.com.co/ liberation, the http://www.coco-chanels.us.org/ KMT http://patriots.nfljersey.us.com/ and http://www.replica-watches.com.co/ the http://www.beats-headphone.com.co/ CPC http://www.nikeair-max.es/ military http://www.jordan-shoes.com.co/ situation http://www.vans-shoes.co.uk/ in the http://www.salomon-schuhe.com.de/ transition phase, http://www.michael-kors.net.co/ in http://www.rayban-eyeglasses.com/ the http://www.newbalance-outlet.org/ war http://www.coachhandbags2016.us.com/ Kongzong http://titans.nfljersey.us.com/ occasion, http://nets.nbajersey.us.com/ the http://www.oakleysunglasses-canada.ca/ smoke http://packers.nfljersey.us.com/ of http://www.chanelhandbags.net.in/ the http://www.levisjeans.com.co/ battlefield, http://nuggets.nbajersey.us.com/ the http://www.mcm-handbags.org/ warble http://www.abercrombie-hollister.nl/ of http://www.ghdshairstraightener.org.uk/ a http://steelers.nfljersey.us.com/ seven http://www.nike-rosherun.nl/ verses. http://www.canada-goosesjackets.us.com/ Poem, http://www.tomsshoes-outlet.us.com/ with http://www.soccer-shoes.us.com/ great http://www.cheap-michaelkors.com/ courage http://www.cheap-oakleyglasses.com/ and http://www.nike-schuhe.com.de/ strategists mind, http://mcmbackpack.co-om.com/ sing a http://pelicans.nbajersey.us.com/ great http://www.abercrombie-and-fitch.us.com/ strategist, http://www.chi-flatiron.us.com/ strategist, chest http://www.the-northface.com.co/ hidden http://www.burberry-outletsale.net/ commander http://heat.nbajersey.us.com/ million http://www.air-max.com.de/ soldiers, http://www.pandorajewellery.com.au/ all-powerful, http://bulls.nbajersey.us.com/ deep http://coachoutlet.euro-us.net/ feelings http://www.christianlouboutin-shoes.ca/ male http://www.adidas-superstar.nl/ ancient http://www.abercrombiefitchs.us.com/ and http://www.kate-spade.gb.net/ modern historical http://www.yogapantscanada.ca/ figures http://cavaliers.nbajersey.us.com/ emotional http://www.omega-watches.us.com/ world.The http://pistons.nbajersey.us.com/ first http://www.giuseppe-zanotti.net/ joint http://www.salvatoreferragamo.in.net/ and http://bucks.nbajersey.us.com/ jaw http://www.toms-outlets.us.com/ joint http://www.cheaprayban.com.co/ poetry http://www.jordanrelease-dates.us.com/ mainly http://www.pandora.com.de/ scenery, http://trailblazers.nbajersey.us.com/ what http://www.burberryoutlet-sale.in.net/ scene http://www.mcmbags.us.com/ it? http://giants.nfljersey.us.com/ Neither http://northfaceoutlet.co-om.com/ lambasted http://bengals.nfljersey.us.com/ smoke, http://www.polooutlets-store.com/ nor http://www.longchamps.us.com/ is http://www.nikeair--max.fr/ it http://www.calvin-kleins.cc/ "Battlefield yellow" http://www.adidas.org.es/ and http://www.beatsbydrdrephone.com/ bridges, http://hawks.nbajersey.us.com/ but http://www.vibram-fivefingers.us.com/ in http://www.ralphlauren-au.com/ time http://www.air-max-schoenen.nl/ and http://www.supra-shoes.org/ space http://www.abercrombie-andfitch.ca/ come http://www.babyliss-pro.us.com/ together, http://www.michael-korshandbags.us.org/ the http://www.ugg-boots.ca/ grand http://www.rayban-pascher.fr/ universe, http://www.oakley-outlet.cc/ the http://www.ugg-australia.com.de/ vast http://www.oakleyoutlet.fr/ expanse of http://panthers.nfljersey.us.com/ wide-angle http://bears.nfljersey.us.com/ start, http://49ers.nfljersey.us.com/ lays http://www.omegarelojes.es/ out http://www.polos-outlet.com/ a http://www.thenorth-faces.co.uk/ school http://www.hermes-outlet.com.co/ of http://www.cheap-raybansoutlet.net/ both http://www.thejoreseproject.com/ heroic http://www.cheapmichaelkors.us.org/ desolate http://www.ralphlauren-outlet.ca/ scene, http://dolphins.nfljersey.us.com/ cheerful http://www.rolex-watches.cc/ and http://www.burberry-outlet.net.co/ lofty http://www.asicsgels.de/ sentiments http://lakers.nbajersey.us.com/ and http://www.rosherun.co.uk/ aspirations http://www.tommy-hilfiger-online-shop.de/ of http://www.mcm-bags.us.com/ the http://www.cheapjerseys.us.org/ situation, http://www.thomas-sabo.com.de/ in http://www.airjordans.us/ the http://www.cheap-jordans.net/ narrative http://www.tiffanyandco-au.com/ and http://www.chiflatiron.net.co/ lyrical, http://www.michaelkors.com.se/ and http://www.ferragamoshoes.in.net/ express http://www.gucci-taschen-outlet.de/ their http://www.burberry-handbagsoutlet.com.co/ arms. "Autumn http://coach-outlet.tumblr.com/ cross http://www.mk-outletonline.us/ the river on http://www.michael-korsoutlet.cc/ the" praise http://www.oakleyonline.us.com/ both http://supra.shoesoutlet.cc/ from http://www.oakley--sunglasses.com.au/ a http://www.cheap-baseballbats.us/ strategic extension http://www.swarovskicrystals.us.com/ into combat http://www.soccer-shoesoutlet.com/ operations http://www.michaelkorsoutletonline.net.co/ outside http://mavericks.nbajersey.us.com/ of http://www.toryburch-sandals.in.net/ me http://seahawks.nfljersey.us.com/ changes http://www.lauren-ralph.co.uk/ in http://falcons.nfljersey.us.com/ the http://www.ugg-boots-australia.com.au/ strategic http://www.pradaoutlet.com.co/ situation http://www.raybans-wayfarers.net/ of http://www.designerhandbagsoutlet.net.co/ the PLA, but http://www.beats-by-dre.com.co/ also http://www.rolex-watches.us.com/ expressed http://www.toms-shoes.net.co/ Liu http://www.katespadeoutlet.gb.net/ and http://www.michael-kors-taschen.com.de/ Deng http://www.giuseppezanotti.com.co/ forced http://www.prada-handbags.com.co/ the Yellow http://www.nike-shoescanada.ca/ River, http://www.hollisteronlineshop.com.de/ thousands http://www.nike-huarache.nl/ of http://www.ralphlaurenepolo.com/ miles into http://www.converses-outlet.com/ Dabie http://www.ralphs-laurenoutlet.co.uk/ Mountains magnificent http://timberwolves.nbajersey.us.com/ momentum http://www.airyeezy.us.com/ of http://www.swarovskijewelry.com.co/ praise. http://grizzlies.nbajersey.us.com/ "Ono http://www.beatsbydre.com.co/ into http://www.michaelkors.co.nl/ the http://colts.nfljersey.us.com/ sky," http://www.michaelkorsbags.com.co/ I http://www.montblanc-penssale.com/ heighten http://www.michael-kors-outlet-online.us.org/ the http://www.coco-chanel.com.de/ PLA http://www.burberry-handbagssale.in.net/ prosperity http://www.converse.com.de/ and http://www.michael-korsbags.co.uk/ growth http://www.christian--louboutin.in.net/ from http://www.tiffany-und-co.de/ the http://www.michaelkorsoutlet.ar.com/ majestic http://www.timberlandshoes.net.co/ momentum. http://www.pradahandbags.net.co/ All http://www.bottegaveneta-bagsoutlet.com/ of http://www.juicycoutureoutlet.net.co/ this http://www.burberry-outletcanada.ca/ is http://www.rayban.com.de/ in http://www.burberryoutletonline.cc/ "clear http://www.hollisterclothes.us.com/ river", http://www.marc-jacobsonsale.com/ "Ono", http://www.michael-kors-australia.com.au/ "Dome" http://www.toms--outlet.com.co/ among http://www.instylers.us.com/ sings. http://www.hermesbirkin-bag.net/ This http://www.gucci-outletstore.com/ magnificent http://www.toryburchsale.com.co/ heroic http://www.nikerosherun.us/ momentum, http://www.converse.net.co/ is forceful http://www.timberland-boots.in.net/ in http://www.longchamphandbagsoutlet.net/ the http://www.toryburchoutlet-sale.us.com/ vast http://celtics.nbajersey.us.com/ space http://www.insanity-workout.us.com/ of the http://www.nikefree5.net/ grand show http://www.scarpe-hoganoutlets.it/ out.Jaw-linked http://www.timberlands-paschere.fr/ "with http://www.nfljersey.us.com/ the http://www.nike-shoesoutlet.us/ people http://www.swarovski-online-shop.de/ to http://browns.nfljersey.us.com/ make http://www.converse-shoes.net/ good, http://www.ugg-bootsclearance.com/ green http://www.ugg-boots.us.org/ cloud http://www.raybans-glasses.com/ near http://www.uggsoutlet.com.co/ the http://airhuarache.shoesoutlet.cc/ moon" http://www.coachoutletstore.net.co/ is http://www.nike-roshe-run.de/ also http://www.tommyhilfiger.net.co/ optimistic http://www.zxcoachoutlet.com/ and http://rockets.nbajersey.us.com/ confident http://www.longchamp.com.de/ spirit http://www.celine-bags.org/ of http://www.tocoachoutlet.com/ the http://spurs.nbajersey.us.com/ situation and http://www.cheapjerseys.com.co/ outlook http://www.burberryhandbagsoutlet.com/ for. http://www.oakleysunglasses-outlet.net/ One http://www.airmax-90.org/ of http://www.reebok.com.de/ the http://www.cheap-nike-shoes.net/ "green http://www.the-northfacejackets.us.com/ cloud near http://www.vans-schuhe.com.de/ the http://www.michael-kors-outlet.us.org/ moon" http://wizards.nbajersey.us.com/ is http://www.cheap-omegawatches.com/ a http://www.abercrombie-fitchs.cc/ flash http://www.uggs-onsale.net/ in http://www.asics-outlet.us.com/ the http://www.toms-shoes.com.co/ pan, http://www.hermesbags.jp.net/ the http://www.abercrombie-kid.us.com/ natural http://www.rayban-sunglassesoutlet.org.uk/ landscape http://www.christian-louboutinshoes.com.co/ of http://www.oakley-sunglasses.mex.com/ the http://www.oakley-glasses2016.com/ moon http://www.poloralphlaurenoutlet.net.co/ out http://www.nikestore.com.de/ of http://www.ralphlaurenonlineshop.de/ sight http://www.timberlandbootsoutlet.us.com/ of http://www.ray-bans.cc/ the http://www.burberry-outletstore.net/ thick http://www.cheap-rolexwatches.co.uk/ clouds, http://www.hollisterclothingstore.org/ is http://www.michaeljordan.com.de/ extremely http://www.co-aol.com/ brilliant, http://www.fashion-clothes.us.com/ brilliant, wonderful, http://www.cheapthomassabos.co.uk/ of http://www.nfl-jersey.us.com/ course, http://www.oakleysoutletonline.cc/ is http://www.gucci-shoesoutlet.net/ the http://raiders.nfljersey.us.com/ vision of http://www.hollister-abercrombie.com.se/ the http://www.coach-factory.in.net/ revolutionary http://www.barbour-jacketsoutlet.com/ war http://www.oakleyoutlet.it/ optimistic http://www.handbagsoutlet.net.co/ outlook.Neck http://www.newoutletonlinemall.com/ joint, http://www.tomsoutlet-online.net/ went http://www.christianlouboutinshoes.jp.net/ on http://www.nikestore.us/ to http://www.uggboots.com.de/ reach http://www.basketballshoes.com.co/ the emotional depths of hearts, "the http://www.tiffanyandco-ca.ca/ hometown http://www.nike-factorys.us/ of http://www.soft-ballbats.com/ Hong http://broncos.nfljersey.us.com/ tone" http://www.rolexwatchesforsale.us.com/ - http://www.hogan.com.de/ absolutely; http://www.oakley.org.es/ "the letter http://rams.nfljersey.us.com/ his wife http://www.thenorthfacejackets.fr/ and http://www.michaelkorsbags.us.org/ children" http://www.adidas-schuhe-online.de/ - http://www.coachblackfriday.com/ does http://www.prada.com.de/ not http://www.nike-air-force.de/ pass, http://www.vans-shoes.net/ apparently http://www.ralphlauren-polos.com.co/ nervous, intense, day http://www.mmoncler-outlet.com/ and http://www.guccishoes-outlet.net/ night http://www.ralphlaurenpolos.in.net/ Kongzong http://www.airhuarache.co.uk/ war, http://www.newbalance-shoes.org/ to http://www.truereligion-outlet.us.org/ attend http://www.weddingdresses-sale.com/ to http://www.eyeglass-outlet.net/ his http://www.coach-factoryyoutletonline.net/ wife http://www.longchamp-bags.us.com/ and http://chiefs.nfljersey.us.com/ children, http://www.nike-schoenen.co.nl/ but http://76ers.nbajersey.us.com/ on http://cowboys.nfljersey.us.com/ the http://www.michaelkors.so/ "hometown http://www.michaelkorsoutletonline-sale.us.com/ Hong tone http://www.gucci-handbags.in.net/ - http://www.swarovski-australia.com.au/ his http://www.hollisters-canada.ca/ wife http://www.pulseras-pandora.com.es/ and http://www.coach-outletonline.net.co/ children http://www.nikeskoes.dk/ believe" http://www.cheapshoes.com.co/ or unlimited http://www.nike-roshe-run.com.es/ expect. http://www.burberrybagsoutlet.net/ In http://www.michaelkors-canadaoutlet.ca/ the http://www.tory-burchshoesoutlet.net/ TV http://www.nike-air-max.com.se/ series http://www.michael-kors.com.es/ "liberation", http://www.uhren-shop.com.de/ in http://www.coach-outletonline.ca/ the http://www.nbajersey.us.com/ side http://www.marc-jacobs.us.com/ of http://airmax.shoesoutlet.cc/ Chairman http://eagles.nfljersey.us.com/ Mao, http://www.ok-em.com/ Zhou http://www.jimmy-chooshoes.com/ Enlai http://www.longchampoutlet.com.co/ was http://www.the-northface.net.co/ the http://chargers.nfljersey.us.com/ first http://www.ralphlaurenoutlet-online.us.com/ Lu http://www.weddingdressesuk.org.uk/ Xun's http://www.guccishoes.com.co/ "not http://www.air-huarache.co.uk/ really http://ravens.nfljersey.us.com/ ruthless http://www.ralphlaurenoutlet.us.com/ hero" http://www.airmax-2015.org/ to http://www.guccishoes-uk.org.uk/ give http://www.coachoutletstore-online.com.co/ a http://www.polos-ralphlauren.us.com/ comment, http://www.oakley-glassesoutlet.net/ it http://www.p90xworkout.us.com/ is http://www.uggsaustralia.com.co/ very http://www.nike-maxfr.com/ appropriate.Tail-linked http://www.mcm-backpacks.com/ "Man http://monsterbeats.co-om.com/ Yu http://www.tnf-jackets.us.com/ frequency Alice http://bills.nfljersey.us.com/ Wang, http://www.tiffanyand-co.us/ Veuve http://www.burberry-2016.uk/ playing http://www.newbalancecanada.ca/ Border http://airmax.misblackfriday.com/ Town." http://www.jimmy-choos.com/ The http://www.longchamp-handbagsoutlet.us.com/ "Alice http://www.truereligionjeans.net.co/ Wang," http://www.pandora-charms.org.uk/ the http://www.maccosmetics.gr.com/ term, http://suns.nbajersey.us.com/ the http://www.iphone-cases.net.co/ performance of http://www.adidas-superstar.de/ this http://thunder.nbajersey.us.com/ great http://www.oakley-sunglasses.cc/ man http://raptors.nbajersey.us.com/ of http://www.tommy-hilfiger.com.de/ spirit, and http://www.tiffany-jewelry.net/ "Victory http://www.nikeair-max.ca/ played http://www.coach-factoryoutlet.net.co/ Border http://www.true-religion.com.co/ Town" http://hornets.nbajersey.us.com/ is http://michaelkors.co-om.com/ not http://www.nikeairmaxins.co.uk/ only the http://jazz.nbajersey.us.com/ expression of http://uggboots.misblackfriday.com/ this campaign http://www.polo-ralph-lauren.de/ victory, http://clippers.nbajersey.us.com/ it http://www.eyeglasses-outlet.net/ is http://www.christianlouboutinoutlet.net.co/ the http://www.hollister-clothing.in.net/ victory http://redskins.nfljersey.us.com/ of http://www.tommy-hilfiger.co.nl/ the http://www.thenorth-face.ca/ revolution http://www.bottega-venetas.cc/ to http://www.ralphslaurens.co.uk/ express http://www.nike-air-max.com.de/ the http://www.nike-tnrequinpascher.fr/ establishment of http://www.ralphlaurenoutlet-online.in.net/ new http://jets.nfljersey.us.com/ China's http://saints.nfljersey.us.com/ firm http://www.kate-spadeoutlet.net/ conviction.Yin http://www.canadagoosesonline.com/ throughout http://www.nike-free-run.de/ this, http://jaguars.nfljersey.us.com/ showing http://www.maccosmetics.net.co/ the http://www.ralphslaurenoutlet.us.com/ great http://www.oakleyoutlet.ar.com/ leader http://azcardinals.nfljersey.us.com/ Chairman Mao http://www.gucci-outletsale.net/ containing http://kings.nbajersey.us.com/ macros http://www.nike-outlet.us.com/ million http://www.rayban.org.es/ the http://www.weddingdressessonline.ca/ gas http://magic.nbajersey.us.com/ swallow http://knicks.nbajersey.us.com/ Yunmeng, http://www.truereligion-outlet.com.co/ by http://lions.nfljersey.us.com/ Tianwei, http://www.designer-handbagsoutlet.us.com/ pregnant http://www.bcbg-maxazria.ca/ embrace http://www.raybans-outlet.us.com/ ancient http://www.michaelkors-uk.org.uk/ rivers http://www.ferragamo.com.co/ row http://www.nikefree-run.net/ to http://www.toms-shoesoutlet.us/ the http://www.nike-skor.com.se/ boldness http://www.wedding--dresses.co.uk/ of http://www.nike-air-max.com.au/ vision, http://www.oakleysframe.com/ courage, http://www.retro-jordans.com/ mind http://www.raybanoutlet.ca/ and http://warriors.nbajersey.us.com/ loved http://www.new-balance-schuhe.de/ ones long http://www.ralph-laurens.org.uk/ for deep and http://www.michaelkorsoutlet-online.ar.com/ sincere http://www.tommy-hilfiger.cc/ feelings.Throughout the http://www.mizuno-running.net/ life http://www.outlet-burberry.net.co/ of http://www.bcbg-dresses.com/ Chairman http://www.adidasshoescanada.ca/ Mao, http://www.tommyhilfigeroutlet.in.net/ in http://www.ray-banocchiali.it/ order http://www.nikemercurial.in.net/ to http://www.rayban-pas-cher.fr/ save the http://www.nikefree-run.org.uk/ nation, http://www.oakley-sunglassess.cc/ he http://www.pandorajewelry.top/ has http://www.longchamp.com.co/ sacrificed http://www.thenorthface.com.de/ his http://www.ghdhairstraightener.cc/ wife http://www.replica-handbags.net.co/ YangKaiHui, http://buccaneers.nfljersey.us.com/ the http://www.nike-freeruns.org.uk/ eldest http://www.thenorthfacejackets.net.co/ son http://www.uggs.co.nl/ Mao http://www.pumashoes.in.net/ Anying, brother http://www.uggs.in.net/ Mao http://www.mk-com.com/ Zemin, http://www.kate-spade.in.net/ Mao http://www.oakley.com.de/ Tan, http://www.tiffanyand-co.net.co/ Mao http://pacers.nbajersey.us.com/ Jian, http://vikings.nfljersey.us.com/ nephew http://www.christianlouboutin.org.uk/ Mao http://www.swarovskis.co.uk/ Chuxiong. http://www.ralphlaurens-polo.co.uk/ Whether http://www.pandoracharms-canada.ca/ anyone http://www.rosheruns.us/ suffering http://www.swarovski-canada.ca/ bereavement http://www.tommyhilfigerca.ca/ are http://www.juicycouture.com.co/ difficult http://www.raybans-outlet.co.uk/ to http://www.coach-purseoutlet.net/ put http://www.raybans-outlet.cc/ into http://www.moncler-outlet.us.org/ words, http://www.edhardy.us.org/ it http://coach.euro-us.net/ can http://www.pumaonline-shop.de/ not http://www.valentino-shoesoutlet.us/ afford. http://www.christianlouboutinshoesoutlet.org/ Not http://nike.shoesoutlet.cc/ to http://www.rolexwatches-canada.ca/ mention http://michaelkors.euro-us.net/ the http://www.cheapuggboots.us.com/ first http://www.burberryonlineshop.de/ wife, http://www.northfaceoutlet.com.co/ the http://www.chanel-bags.com.co/ eldest http://www.coachoutlet-online.com.co/ son of http://www.barbour-factory.com/ the http://www.nike.org.es/ pain http://www.rayban.co.nl/ of loss, http://www.nikeshoesoutlet.org.uk/ of http://www.burberry-outlet.uk/ course, http://www.newbalance.com.es/ it http://www.adidasshoes.top/ would be http://www.michael-korssale.us.com/ piercing.

http://www.mcmhandbags.com.co/

Vote down Vote up

7 months ago

This http://www.horloges-rolex.nl/ is http://www.toms-outlet.net/ the http://www.uggboots.net.co/ Chairman http://www.jordanretro.org/ Mao's http://www.montres-pascher.fr/ revolution http://www.adidas.com.se/ in http://www.nike-airmax.us.com/ China http://www.raybans-sunglasses.cc/ into http://www.ugg-uggboots.net/ the http://www.cheap-raybanoutlet.com/ war http://texans.nfljersey.us.com/ of http://www.prada-shoes.com.co/ liberation, the http://www.coco-chanels.us.org/ KMT http://patriots.nfljersey.us.com/ and http://www.replica-watches.com.co/ the http://www.beats-headphone.com.co/ CPC http://www.nikeair-max.es/ military http://www.jordan-shoes.com.co/ situation http://www.vans-shoes.co.uk/ in the http://www.salomon-schuhe.com.de/ transition phase, http://www.michael-kors.net.co/ in http://www.rayban-eyeglasses.com/ the http://www.newbalance-outlet.org/ war http://www.coachhandbags2016.us.com/ Kongzong http://titans.nfljersey.us.com/ occasion, http://nets.nbajersey.us.com/ the http://www.oakleysunglasses-canada.ca/ smoke http://packers.nfljersey.us.com/ of http://www.chanelhandbags.net.in/ the http://www.levisjeans.com.co/ battlefield, http://nuggets.nbajersey.us.com/ the http://www.mcm-handbags.org/ warble http://www.abercrombie-hollister.nl/ of http://www.ghdshairstraightener.org.uk/ a http://steelers.nfljersey.us.com/ seven http://www.nike-rosherun.nl/ verses. http://www.canada-goosesjackets.us.com/ Poem, http://www.tomsshoes-outlet.us.com/ with http://www.soccer-shoes.us.com/ great http://www.cheap-michaelkors.com/ courage http://www.cheap-oakleyglasses.com/ and http://www.nike-schuhe.com.de/ strategists mind, http://mcmbackpack.co-om.com/ sing a http://pelicans.nbajersey.us.com/ great http://www.abercrombie-and-fitch.us.com/ strategist, http://www.chi-flatiron.us.com/ strategist, chest http://www.the-northface.com.co/ hidden http://www.burberry-outletsale.net/ commander http://heat.nbajersey.us.com/ million http://www.air-max.com.de/ soldiers, http://www.pandorajewellery.com.au/ all-powerful, http://bulls.nbajersey.us.com/ deep http://coachoutlet.euro-us.net/ feelings http://www.christianlouboutin-shoes.ca/ male http://www.adidas-superstar.nl/ ancient http://www.abercrombiefitchs.us.com/ and http://www.kate-spade.gb.net/ modern historical http://www.yogapantscanada.ca/ figures http://cavaliers.nbajersey.us.com/ emotional http://www.omega-watches.us.com/ world.The http://pistons.nbajersey.us.com/ first http://www.giuseppe-zanotti.net/ joint http://www.salvatoreferragamo.in.net/ and http://bucks.nbajersey.us.com/ jaw http://www.toms-outlets.us.com/ joint http://www.cheaprayban.com.co/ poetry http://www.jordanrelease-dates.us.com/ mainly http://www.pandora.com.de/ scenery, http://trailblazers.nbajersey.us.com/ what http://www.burberryoutlet-sale.in.net/ scene http://www.mcmbags.us.com/ it? http://giants.nfljersey.us.com/ Neither http://northfaceoutlet.co-om.com/ lambasted http://bengals.nfljersey.us.com/ smoke, http://www.polooutlets-store.com/ nor http://www.longchamps.us.com/ is http://www.nikeair--max.fr/ it http://www.calvin-kleins.cc/ "Battlefield yellow" http://www.adidas.org.es/ and http://www.beatsbydrdrephone.com/ bridges, http://hawks.nbajersey.us.com/ but http://www.vibram-fivefingers.us.com/ in http://www.ralphlauren-au.com/ time http://www.air-max-schoenen.nl/ and http://www.supra-shoes.org/ space http://www.abercrombie-andfitch.ca/ come http://www.babyliss-pro.us.com/ together, http://www.michael-korshandbags.us.org/ the http://www.ugg-boots.ca/ grand http://www.rayban-pascher.fr/ universe, http://www.oakley-outlet.cc/ the http://www.ugg-australia.com.de/ vast http://www.oakleyoutlet.fr/ expanse of http://panthers.nfljersey.us.com/ wide-angle http://bears.nfljersey.us.com/ start, http://49ers.nfljersey.us.com/ lays http://www.omegarelojes.es/ out http://www.polos-outlet.com/ a http://www.thenorth-faces.co.uk/ school http://www.hermes-outlet.com.co/ of http://www.cheap-raybansoutlet.net/ both http://www.thejoreseproject.com/ heroic http://www.cheapmichaelkors.us.org/ desolate http://www.ralphlauren-outlet.ca/ scene, http://dolphins.nfljersey.us.com/ cheerful http://www.rolex-watches.cc/ and http://www.burberry-outlet.net.co/ lofty http://www.asicsgels.de/ sentiments http://lakers.nbajersey.us.com/ and http://www.rosherun.co.uk/ aspirations http://www.tommy-hilfiger-online-shop.de/ of http://www.mcm-bags.us.com/ the http://www.cheapjerseys.us.org/ situation, http://www.thomas-sabo.com.de/ in http://www.airjordans.us/ the http://www.cheap-jordans.net/ narrative http://www.tiffanyandco-au.com/ and http://www.chiflatiron.net.co/ lyrical, http://www.michaelkors.com.se/ and http://www.ferragamoshoes.in.net/ express http://www.gucci-taschen-outlet.de/ their http://www.burberry-handbagsoutlet.com.co/ arms. "Autumn http://coach-outlet.tumblr.com/ cross http://www.mk-outletonline.us/ the river on http://www.michael-korsoutlet.cc/ the" praise http://www.oakleyonline.us.com/ both http://supra.shoesoutlet.cc/ from http://www.oakley--sunglasses.com.au/ a http://www.cheap-baseballbats.us/ strategic extension http://www.swarovskicrystals.us.com/ into combat http://www.soccer-shoesoutlet.com/ operations http://www.michaelkorsoutletonline.net.co/ outside http://mavericks.nbajersey.us.com/ of http://www.toryburch-sandals.in.net/ me http://seahawks.nfljersey.us.com/ changes http://www.lauren-ralph.co.uk/ in http://falcons.nfljersey.us.com/ the http://www.ugg-boots-australia.com.au/ strategic http://www.pradaoutlet.com.co/ situation http://www.raybans-wayfarers.net/ of http://www.designerhandbagsoutlet.net.co/ the PLA, but http://www.beats-by-dre.com.co/ also http://www.rolex-watches.us.com/ expressed http://www.toms-shoes.net.co/ Liu http://www.katespadeoutlet.gb.net/ and http://www.michael-kors-taschen.com.de/ Deng http://www.giuseppezanotti.com.co/ forced http://www.prada-handbags.com.co/ the Yellow http://www.nike-shoescanada.ca/ River, http://www.hollisteronlineshop.com.de/ thousands http://www.nike-huarache.nl/ of http://www.ralphlaurenepolo.com/ miles into http://www.converses-outlet.com/ Dabie http://www.ralphs-laurenoutlet.co.uk/ Mountains magnificent http://timberwolves.nbajersey.us.com/ momentum http://www.airyeezy.us.com/ of http://www.swarovskijewelry.com.co/ praise. http://grizzlies.nbajersey.us.com/ "Ono http://www.beatsbydre.com.co/ into http://www.michaelkors.co.nl/ the http://colts.nfljersey.us.com/ sky," http://www.michaelkorsbags.com.co/ I http://www.montblanc-penssale.com/ heighten http://www.michael-kors-outlet-online.us.org/ the http://www.coco-chanel.com.de/ PLA http://www.burberry-handbagssale.in.net/ prosperity http://www.converse.com.de/ and http://www.michael-korsbags.co.uk/ growth http://www.christian--louboutin.in.net/ from http://www.tiffany-und-co.de/ the http://www.michaelkorsoutlet.ar.com/ majestic http://www.timberlandshoes.net.co/ momentum. http://www.pradahandbags.net.co/ All http://www.bottegaveneta-bagsoutlet.com/ of http://www.juicycoutureoutlet.net.co/ this http://www.burberry-outletcanada.ca/ is http://www.rayban.com.de/ in http://www.burberryoutletonline.cc/ "clear http://www.hollisterclothes.us.com/ river", http://www.marc-jacobsonsale.com/ "Ono", http://www.michael-kors-australia.com.au/ "Dome" http://www.toms--outlet.com.co/ among http://www.instylers.us.com/ sings. http://www.hermesbirkin-bag.net/ This http://www.gucci-outletstore.com/ magnificent http://www.toryburchsale.com.co/ heroic http://www.nikerosherun.us/ momentum, http://www.converse.net.co/ is forceful http://www.timberland-boots.in.net/ in http://www.longchamphandbagsoutlet.net/ the http://www.toryburchoutlet-sale.us.com/ vast http://celtics.nbajersey.us.com/ space http://www.insanity-workout.us.com/ of the http://www.nikefree5.net/ grand show http://www.scarpe-hoganoutlets.it/ out.Jaw-linked http://www.timberlands-paschere.fr/ "with http://www.nfljersey.us.com/ the http://www.nike-shoesoutlet.us/ people http://www.swarovski-online-shop.de/ to http://browns.nfljersey.us.com/ make http://www.converse-shoes.net/ good, http://www.ugg-bootsclearance.com/ green http://www.ugg-boots.us.org/ cloud http://www.raybans-glasses.com/ near http://www.uggsoutlet.com.co/ the http://airhuarache.shoesoutlet.cc/ moon" http://www.coachoutletstore.net.co/ is http://www.nike-roshe-run.de/ also http://www.tommyhilfiger.net.co/ optimistic http://www.zxcoachoutlet.com/ and http://rockets.nbajersey.us.com/ confident http://www.longchamp.com.de/ spirit http://www.celine-bags.org/ of http://www.tocoachoutlet.com/ the http://spurs.nbajersey.us.com/ situation and http://www.cheapjerseys.com.co/ outlook http://www.burberryhandbagsoutlet.com/ for. http://www.oakleysunglasses-outlet.net/ One http://www.airmax-90.org/ of http://www.reebok.com.de/ the http://www.cheap-nike-shoes.net/ "green http://www.the-northfacejackets.us.com/ cloud near http://www.vans-schuhe.com.de/ the http://www.michael-kors-outlet.us.org/ moon" http://wizards.nbajersey.us.com/ is http://www.cheap-omegawatches.com/ a http://www.abercrombie-fitchs.cc/ flash http://www.uggs-onsale.net/ in http://www.asics-outlet.us.com/ the http://www.toms-shoes.com.co/ pan, http://www.hermesbags.jp.net/ the http://www.abercrombie-kid.us.com/ natural http://www.rayban-sunglassesoutlet.org.uk/ landscape http://www.christian-louboutinshoes.com.co/ of http://www.oakley-sunglasses.mex.com/ the http://www.oakley-glasses2016.com/ moon http://www.poloralphlaurenoutlet.net.co/ out http://www.nikestore.com.de/ of http://www.ralphlaurenonlineshop.de/ sight http://www.timberlandbootsoutlet.us.com/ of http://www.ray-bans.cc/ the http://www.burberry-outletstore.net/ thick http://www.cheap-rolexwatches.co.uk/ clouds, http://www.hollisterclothingstore.org/ is http://www.michaeljordan.com.de/ extremely http://www.co-aol.com/ brilliant, http://www.fashion-clothes.us.com/ brilliant, wonderful, http://www.cheapthomassabos.co.uk/ of http://www.nfl-jersey.us.com/ course, http://www.oakleysoutletonline.cc/ is http://www.gucci-shoesoutlet.net/ the http://raiders.nfljersey.us.com/ vision of http://www.hollister-abercrombie.com.se/ the http://www.coach-factory.in.net/ revolutionary http://www.barbour-jacketsoutlet.com/ war http://www.oakleyoutlet.it/ optimistic http://www.handbagsoutlet.net.co/ outlook.Neck http://www.newoutletonlinemall.com/ joint, http://www.tomsoutlet-online.net/ went http://www.christianlouboutinshoes.jp.net/ on http://www.nikestore.us/ to http://www.uggboots.com.de/ reach http://www.basketballshoes.com.co/ the emotional depths of hearts, "the http://www.tiffanyandco-ca.ca/ hometown http://www.nike-factorys.us/ of http://www.soft-ballbats.com/ Hong http://broncos.nfljersey.us.com/ tone" http://www.rolexwatchesforsale.us.com/ - http://www.hogan.com.de/ absolutely; http://www.oakley.org.es/ "the letter http://rams.nfljersey.us.com/ his wife http://www.thenorthfacejackets.fr/ and http://www.michaelkorsbags.us.org/ children" http://www.adidas-schuhe-online.de/ - http://www.coachblackfriday.com/ does http://www.prada.com.de/ not http://www.nike-air-force.de/ pass, http://www.vans-shoes.net/ apparently http://www.ralphlauren-polos.com.co/ nervous, intense, day http://www.mmoncler-outlet.com/ and http://www.guccishoes-outlet.net/ night http://www.ralphlaurenpolos.in.net/ Kongzong http://www.airhuarache.co.uk/ war, http://www.newbalance-shoes.org/ to http://www.truereligion-outlet.us.org/ attend http://www.weddingdresses-sale.com/ to http://www.eyeglass-outlet.net/ his http://www.coach-factoryyoutletonline.net/ wife http://www.longchamp-bags.us.com/ and http://chiefs.nfljersey.us.com/ children, http://www.nike-schoenen.co.nl/ but http://76ers.nbajersey.us.com/ on http://cowboys.nfljersey.us.com/ the http://www.michaelkors.so/ "hometown http://www.michaelkorsoutletonline-sale.us.com/ Hong tone http://www.gucci-handbags.in.net/ - http://www.swarovski-australia.com.au/ his http://www.hollisters-canada.ca/ wife http://www.pulseras-pandora.com.es/ and http://www.coach-outletonline.net.co/ children http://www.nikeskoes.dk/ believe" http://www.cheapshoes.com.co/ or unlimited http://www.nike-roshe-run.com.es/ expect. http://www.burberrybagsoutlet.net/ In http://www.michaelkors-canadaoutlet.ca/ the http://www.tory-burchshoesoutlet.net/ TV http://www.nike-air-max.com.se/ series http://www.michael-kors.com.es/ "liberation", http://www.uhren-shop.com.de/ in http://www.coach-outletonline.ca/ the http://www.nbajersey.us.com/ side http://www.marc-jacobs.us.com/ of http://airmax.shoesoutlet.cc/ Chairman http://eagles.nfljersey.us.com/ Mao, http://www.ok-em.com/ Zhou http://www.jimmy-chooshoes.com/ Enlai http://www.longchampoutlet.com.co/ was http://www.the-northface.net.co/ the http://chargers.nfljersey.us.com/ first http://www.ralphlaurenoutlet-online.us.com/ Lu http://www.weddingdressesuk.org.uk/ Xun's http://www.guccishoes.com.co/ "not http://www.air-huarache.co.uk/ really http://ravens.nfljersey.us.com/ ruthless http://www.ralphlaurenoutlet.us.com/ hero" http://www.airmax-2015.org/ to http://www.guccishoes-uk.org.uk/ give http://www.coachoutletstore-online.com.co/ a http://www.polos-ralphlauren.us.com/ comment, http://www.oakley-glassesoutlet.net/ it http://www.p90xworkout.us.com/ is http://www.uggsaustralia.com.co/ very http://www.nike-maxfr.com/ appropriate.Tail-linked http://www.mcm-backpacks.com/ "Man http://monsterbeats.co-om.com/ Yu http://www.tnf-jackets.us.com/ frequency Alice http://bills.nfljersey.us.com/ Wang, http://www.tiffanyand-co.us/ Veuve http://www.burberry-2016.uk/ playing http://www.newbalancecanada.ca/ Border http://airmax.misblackfriday.com/ Town." http://www.jimmy-choos.com/ The http://www.longchamp-handbagsoutlet.us.com/ "Alice http://www.truereligionjeans.net.co/ Wang," http://www.pandora-charms.org.uk/ the http://www.maccosmetics.gr.com/ term, http://suns.nbajersey.us.com/ the http://www.iphone-cases.net.co/ performance of http://www.adidas-superstar.de/ this http://thunder.nbajersey.us.com/ great http://www.oakley-sunglasses.cc/ man http://raptors.nbajersey.us.com/ of http://www.tommy-hilfiger.com.de/ spirit, and http://www.tiffany-jewelry.net/ "Victory http://www.nikeair-max.ca/ played http://www.coach-factoryoutlet.net.co/ Border http://www.true-religion.com.co/ Town" http://hornets.nbajersey.us.com/ is http://michaelkors.co-om.com/ not http://www.nikeairmaxins.co.uk/ only the http://jazz.nbajersey.us.com/ expression of http://uggboots.misblackfriday.com/ this campaign http://www.polo-ralph-lauren.de/ victory, http://clippers.nbajersey.us.com/ it http://www.eyeglasses-outlet.net/ is http://www.christianlouboutinoutlet.net.co/ the http://www.hollister-clothing.in.net/ victory http://redskins.nfljersey.us.com/ of http://www.tommy-hilfiger.co.nl/ the http://www.thenorth-face.ca/ revolution http://www.bottega-venetas.cc/ to http://www.ralphslaurens.co.uk/ express http://www.nike-air-max.com.de/ the http://www.nike-tnrequinpascher.fr/ establishment of http://www.ralphlaurenoutlet-online.in.net/ new http://jets.nfljersey.us.com/ China's http://saints.nfljersey.us.com/ firm http://www.kate-spadeoutlet.net/ conviction.Yin http://www.canadagoosesonline.com/ throughout http://www.nike-free-run.de/ this, http://jaguars.nfljersey.us.com/ showing http://www.maccosmetics.net.co/ the http://www.ralphslaurenoutlet.us.com/ great http://www.oakleyoutlet.ar.com/ leader http://azcardinals.nfljersey.us.com/ Chairman Mao http://www.gucci-outletsale.net/ containing http://kings.nbajersey.us.com/ macros http://www.nike-outlet.us.com/ million http://www.rayban.org.es/ the http://www.weddingdressessonline.ca/ gas http://magic.nbajersey.us.com/ swallow http://knicks.nbajersey.us.com/ Yunmeng, http://www.truereligion-outlet.com.co/ by http://lions.nfljersey.us.com/ Tianwei, http://www.designer-handbagsoutlet.us.com/ pregnant http://www.bcbg-maxazria.ca/ embrace http://www.raybans-outlet.us.com/ ancient http://www.michaelkors-uk.org.uk/ rivers http://www.ferragamo.com.co/ row http://www.nikefree-run.net/ to http://www.toms-shoesoutlet.us/ the http://www.nike-skor.com.se/ boldness http://www.wedding--dresses.co.uk/ of http://www.nike-air-max.com.au/ vision, http://www.oakleysframe.com/ courage, http://www.retro-jordans.com/ mind http://www.raybanoutlet.ca/ and http://warriors.nbajersey.us.com/ loved http://www.new-balance-schuhe.de/ ones long http://www.ralph-laurens.org.uk/ for deep and http://www.michaelkorsoutlet-online.ar.com/ sincere http://www.tommy-hilfiger.cc/ feelings.Throughout the http://www.mizuno-running.net/ life http://www.outlet-burberry.net.co/ of http://www.bcbg-dresses.com/ Chairman http://www.adidasshoescanada.ca/ Mao, http://www.tommyhilfigeroutlet.in.net/ in http://www.ray-banocchiali.it/ order http://www.nikemercurial.in.net/ to http://www.rayban-pas-cher.fr/ save the http://www.nikefree-run.org.uk/ nation, http://www.oakley-sunglassess.cc/ he http://www.pandorajewelry.top/ has http://www.longchamp.com.co/ sacrificed http://www.thenorthface.com.de/ his http://www.ghdhairstraightener.cc/ wife http://www.replica-handbags.net.co/ YangKaiHui, http://buccaneers.nfljersey.us.com/ the http://www.nike-freeruns.org.uk/ eldest http://www.thenorthfacejackets.net.co/ son http://www.uggs.co.nl/ Mao http://www.pumashoes.in.net/ Anying, brother http://www.uggs.in.net/ Mao http://www.mk-com.com/ Zemin, http://www.kate-spade.in.net/ Mao http://www.oakley.com.de/ Tan, http://www.tiffanyand-co.net.co/ Mao http://pacers.nbajersey.us.com/ Jian, http://vikings.nfljersey.us.com/ nephew http://www.christianlouboutin.org.uk/ Mao http://www.swarovskis.co.uk/ Chuxiong. http://www.ralphlaurens-polo.co.uk/ Whether http://www.pandoracharms-canada.ca/ anyone http://www.rosheruns.us/ suffering http://www.swarovski-canada.ca/ bereavement http://www.tommyhilfigerca.ca/ are http://www.juicycouture.com.co/ difficult http://www.raybans-outlet.co.uk/ to http://www.coach-purseoutlet.net/ put http://www.raybans-outlet.cc/ into http://www.moncler-outlet.us.org/ words, http://www.edhardy.us.org/ it http://coach.euro-us.net/ can http://www.pumaonline-shop.de/ not http://www.valentino-shoesoutlet.us/ afford. http://www.christianlouboutinshoesoutlet.org/ Not http://nike.shoesoutlet.cc/ to http://www.rolexwatches-canada.ca/ mention http://michaelkors.euro-us.net/ the http://www.cheapuggboots.us.com/ first http://www.burberryonlineshop.de/ wife, http://www.northfaceoutlet.com.co/ the http://www.chanel-bags.com.co/ eldest http://www.coachoutlet-online.com.co/ son of http://www.barbour-factory.com/ the http://www.nike.org.es/ pain http://www.rayban.co.nl/ of loss, http://www.nikeshoesoutlet.org.uk/ of http://www.burberry-outlet.uk/ course, http://www.newbalance.com.es/ it http://www.adidasshoes.top/ would be http://www.michael-korssale.us.com/ piercing.

http://www.mcmhandbags.com.co/

Vote down Vote up

11 months ago

spring. http://www.insanity-workout.us.com/ I http://www.mcm-bags.us.com/ love April, http://www.nike-free-run.de/ just warm, http://www.vans-schuhe.com.de/ there http://www.rayban.co.nl/ is http://www.michael--kors.us.com/ an infinite http://www.nikefactory.org/ poetic http://www.nikestore.us/ heart. http://www.ralphlaurenoutlet.us.com/ Nothing http://www.michaelkors-uk.org.uk/ else and enjoy http://www.tnf-jackets.us.com/ a few http://www.longchamp.com.de/ bundles http://www.lauren-ralph.co.uk/ safflower, see a http://www.cheap-michaelkors.com/ few http://www.oakley-sunglasses.mex.com/ green http://www.newbalance-shoes.org/ leaves. http://www.hollister-abercrombie.com.se/ Marching http://www.omega-watches.us.com/ cloud footprint, http://www.soccer-shoes.us.com/ holding http://raptors.nbajersey.us.com/ wind http://www.nike-schuhe.com.de/ elegant, romantic look http://www.rayban.org.es/ for http://www.zxcoachoutlet.com/ earth, pleasant http://www.timberlandshoes.net.co/ taste and http://www.tommyhilfiger.net.co/ meticulous http://www.nike-air-max.com.de/ scene, http://www.converse.net.co/ pavilions http://www.cheapjerseys.us.org/ seek http://www.jordanretro.org/ rhyme http://www.uggboots.net.co/ style, hazy http://www.omegarelojes.es/ look for warm http://www.nike-roshe-run.com.es/ memories. http://www.polos-ralphlauren.us.com/ In April, http://www.michael-korshandbags.org.uk/ stretch http://www.uhren-shop.com.de/ the fragrance, http://www.montres-pascher.fr/ bathed http://www.ugg-australia.com.de/ in http://rockets.nbajersey.us.com/ a beautiful http://www.swarovski-canada.ca/ spring. http://www.oakleysunglasses-canada.ca/ Life encounter http://www.air-huarache.co.uk/ warmest, than the flowering http://www.ralphlaurenpolos.in.net/ season http://www.toryburch-sandals.in.net/ for http://supra.shoesoutlet.us.com/ Love http://www.tiffany-jewelry.net/ romantic youth. http://www.moncler-outlet.us.org/ Xu http://www.cheap-jordans.net/ had http://www.coach-outletonline.net.co/ a http://www.yogapantscanada.ca/ dream, http://www.guccioutlet-sale.in.net/ a dream of http://www.lululemonoutlet.gb.net/ you http://www.uggsaustralia.com.co/ as I hold an http://www.polooutlets-store.com/ umbrella, if not http://www.swarovskijewelry.com.co/ with http://www.pradahandbags.net.co/ an http://www.uggsoutlet.com.co/ umbrella, http://monsterbeats.co-om.com/ and http://cavaliers.nbajersey.us.com/ I http://mavericks.nbajersey.us.com/ wish http://www.mcm-backpacks.com/ you rain together, in http://www.new-balance-schuhe.de/ the http://www.designer-handbagsoutlet.us.com/ cold world planted http://www.tiffanyandco-canada.ca/ a http://www.uggs.co.nl/ touch http://www.designerhandbagsoutlet.net.co/ of http://www.swarovski-australia.com.au/ sadness. In http://www.burberry2016.co.uk/ fact, http://www.swarovski-online-shop.de/ similar to http://www.the-northface.com.co/ the Red, so http://www.marc-jacobs.us.com/ there will http://www.nfl-jersey.us.com/ always be http://www.outlet-burberry.net.co/ a man, http://www.coach-factory.in.net/ sooner http://www.prada-handbags.com.co/ or http://www.northfaceoutlet.com.co/ later http://www.ralphlaurenepolo.com/ will http://www.uggs.in.net/ be admitted to each http://www.michaelkors.com.se/ other's heart, http://timberwolves.nbajersey.us.com/ the heart http://www.oakleyoutlet.ar.com/ can be deposited http://www.hollisteronlineshop.com.de/ romantic http://www.pandoracharms-canada.ca/ sea http://www.bottega-veneta.us.com/ waves. http://www.ferragamo.com.co/ In April, http://uggboots.misblackfriday.com/ more http://www.nike-shoesoutlet.us.com/ than the arrival of spring, there are flowers. After some time, the http://www.instylers.us.com/ roses bloom. http://www.ugg-boots.ca/ I do http://www.converse.com.de/ not http://airmax.misblackfriday.com/ think http://www.swarovski-crystal.us.com/ the http://www.asicsgels.de/ arrival of another passionately http://www.hollisters-canada.ca/ blooming, and so http://www.calvin-kleins.us.com/ long http://www.soft-ballbats.com/ as the http://www.nikeair-max.ca/ rose. http://www.jordanrelease-dates.us.com/ Rose Bloom http://www.adidas-superstar.nl/ is http://www.true-religion.com.co/ an http://www.cheapuggboots.us.com/ indulgence, http://www.toms-shoes.net.co/ but http://www.nike-huarache.nl/ also http://www.oakleyoutlet-online.us.com/ a http://www.tory-burchshoesoutlet.net/ loose, open is http://www.polo-ralph-lauren.de/ a http://www.chi-flatiron.us.com/ an event. April is http://lakers.nbajersey.us.com/ good, do not bother http://www.tiffany-und-co.de/ to http://www.pumashoes.in.net/ feel, http://www.fashionclothes.us.com/ and http://www.mcmhandbags.com.co/ need to catch up http://www.woolrich-clearance.com/ in http://www.christianlouboutinshoesoutlet.org/ full swing, as long http://www.cheapshoes.com.co/ as http://www.longchamp-handbagsoutlet.us.com/ in http://www.canadagooses-2016.com/ normal http://www.bcbg-dresses.com/ days, mild http://www.hollisterclothes.us.com/ air filled, http://www.levisjeans.com.co/ occasionally http://www.christianlouboutinoutlet.net.co/ calling http://www.coachblackfriday.com/ for http://www.chiflatiron.net.co/ rain, http://www.tomsoutletonline.net/ water was http://www.iphone-cases.net.co/ full http://www.tiffany-andco.us.com/ of http://www.cheapoakley-sunglasses.in.net/ poetic, http://www.barbour-jacketsoutlet.com/ it makes http://www.thomas-sabo.com.de/ me a http://www.michaelkorsoutlet.ar.com/ light, http://www.tommyhilfigerca.ca/ which is http://www.thenorthface.com.de/ quiet no http://airhuarache.shoesoutlet.us.com/ April sound beautiful. http://www.burberry-outletcanada.ca/ In April, http://trailblazers.nbajersey.us.com/ the http://www.rosheruns.us/ beautiful landscape, Tian http://www.truereligion-outlet.com.co/ Mei http://www.michael-kors-handbags.us.com/ love. http://www.beatsbydrdre.co.com/ Carrying http://www.nike-air-max.us/ fragrant http://www.adidas-schuhe-online.de/ April, http://www.nike.org.es/ quietly http://www.swarovski--uk.me.uk/ savor a http://www.ghdhair-straighteners.co.uk/ tree flowers, listening to http://www.lululemoncanada.ca/ the http://www.ugg-uggboots.net/ whisper http://www.nikeair-max.es/ whisper http://www.kate-spade.gb.net/ swallow, http://www.tommy-hilfiger.com.de/ taste http://www.ugg-boots.us.org/ the http://www.harrods-london.co.uk/ breath of http://www.coachoutletstore-online.com.co/ spring, there is http://hornets.nbajersey.us.com/ hope, there http://www.nikestore.com.de/ is http://www.hogan.com.de/ vision, cut http://www.ray-ban-outlet.us.com/ a http://www.michaelkors-outlet-online.com.co/ river flows, http://www.ralph-lauren.com.au/ a http://www.mk-outlet.us.com/ pulse http://www.longchampoutlet.com.co/ v feelings, http://www.converse-shoes.net/ cemented http://www.ralphlaurenoutlet-online.us.com/ timeless http://www.toms-shoes.com.co/ landscape, http://www.mizuno-running.net/ also there http://www.handbagsoutlet.net.co/ is http://www.ferragamoshoes.in.net/ love in http://nike.shoesoutlet.us.com/ the http://heat.nbajersey.us.com/ world http://www.juicycouture.com.co/ gazing http://www.ralphlaurenoutlet-online.in.net/ fragrant. http://www.airhuarache.co.uk/ In April http://www.nike--freerun.co.uk/ door, http://www.newbalancecanada.ca/ the http://clippers.nbajersey.us.com/ chimes http://www.ray-bansunglasses.net/ rang http://76ers.nbajersey.us.com/ miss, the memory http://www.replica-watches.com.co/ still http://www.celine-bags.org/ playing http://www.horloges-rolex.nl/ the happy note. http://www.hollister-clothing.in.net/ A http://www.coach-factoryyoutletonline.net/ cup of http://www.adidas.com.se/ tea, a book, http://www.michaelkorsoutlet-online.ar.com/ flowers, http://www.ralph-laurens.org.uk/ Yang http://www.christianlouboutin-shoes.ca/ Liu http://www.chanel-bags.com.co/ Hanyan, http://www.pandorajewellery.com.au/ quiet http://www.asics-outlet.us.com/ and http://www.nikefree5.net/ elegant, bearing http://www.burberry-bagsoutlet.com/ extraordinary. http://www.michael-kors.net.co/ Do http://www.nike-air-max.com.se/ not http://www.adidas-superstar.de/ seek http://www.tommy-hilfiger.co.nl/ fame http://www.thenorthfacejackets.net.co/ and http://magic.nbajersey.us.com/ wealth stay, unperturbed owned http://www.ralphlaurenonlineshop.de/ Zen. http://suns.nbajersey.us.com/ Window http://www.supra-shoes.org/ beautiful http://www.abercrombiefitchs.us.com/ spring http://www.oakleys-glasses.us.com/ flowers field; gurgling http://www.timberlandbootsoutlet.us.com/ brook, singing http://www.michaelkors-canadaoutlet.ca/ with running http://www.yoga-pants.net.co/ away. http://kings.nbajersey.us.com/ Occasionally http://www.cheap-nike-shoes.net/ swim to http://www.abercrombie-andfitch.ca/ a http://www.rayban-wayfarer.in.net/ group http://www.montblanc--pens.in.net/ of http://www.giuseppe-zanotti.net/ ducks, rattle http://www.michaelkorsbags.us.org/ Huan calls, http://www.nike-roshe-run.de/ frolic with green http://www.cheap-baseballbats.net/ waters. Farming http://www.adidasshoes.top/ April http://www.salvatoreferragamo.in.net/ day, http://www.newoutletonlinemall.com/ everywhere http://www.longchamphandbagsoutlet.net/ is http://www.tocoachoutlet.com/ a http://www.prada-shoes.com.co/ busy scene, http://www.uggboots.com.de/ Guyu http://www.raybans.us.org/ before, http://www.pandora-charms.org.uk/ melons http://www.christianlouboutinshoes.jp.net/ points beans, there are flat line spacing, fertilization, http://www.poloralphlaurenoutlet.net.co/ hunched lost http://airmax.shoesoutlet.us.com/ species, the joy of his http://www.replica-handbags.net.co/ face that http://www.ralphlauren-polos.co.uk/ says harvest http://www.burberryonlineshop.de/ expectations! The http://celtics.nbajersey.us.com/ more http://www.abercrombie-kid.us.com/ time older people http://www.oakley.org.es/ more light. After http://www.hollisterclothingstore.org/ years http://www.ghd-hairstraightener.net/ of http://www.thomas-sabos.org.uk/ temper, things http://www.thenorth-faces.co.uk/ subjected http://www.replicarolex-watches.us.com/ to tie http://www.bebeclothing.in.net/ him http://www.burberry-outletstore.net/ down, http://www.cheaprayban.com.co/ perhaps http://www.airmax-90.org/ a heart http://www.burberrys-outlet2016.com/ is http://www.oakley-outletstore.in.net/ no http://www.retro-jordans.com/ longer http://www.toms-outlets.us.com/ young, http://www.nike-skor.com.se/ once http://www.beats-by-dre.com.co/ surging, already http://www.nike-rosherun.nl/ become http://www.thejoreseproject.com/ Delicate http://www.coach-purseoutlet.net/ thin clouds. http://www.nike-air-max.com.au/ Habit of http://www.adidasshoescanada.ca/ swaying lights http://www.nike-maxfr.com/ at http://www.cheap-raybans.com/ night, the old window to perform http://warriors.nbajersey.us.com/ a http://www.pandora.com.de/ so http://www.tomsoutlet-online.com/ small http://www.abercrombie-hollister.nl/ print, ze wish http://www.longchamp.com.co/ to http://www.katespadeoutlet.gb.net/ write to http://www.coachhandbags2016.us.com/ their http://www.salomon-schuhe.com.de/ emotions http://www.ugg-bootsclearance.com/ quietly http://nets.nbajersey.us.com/ placed words. The more traveled road, you http://www.gucci-shoes.net/ just do http://www.oakleysunglass-outlet.net/ not http://pacers.nbajersey.us.com/ think http://www.burberryoutlet2016.us.com/ long; more tours over http://www.nbajersey.us.com/ the landscape, http://www.pandorajewelry.top/ you just http://www.nikefree-run.org.uk/ do http://www.ralphslauren-outlet.co.uk/ not feel sad. http://www.michaelkorsoutletonline-sale.us.com/ Time flies http://www.pradaoutlet.com.co/ when, once http://www.cheapmichaelkors.us.org/ again the heart http://www.longchamps.us.com/ of http://www.eyeglassesonline.us.com/ the sea http://www.pumaonline-shop.de/ waves, a http://www.coco-chanels.us.com/ heart http://www.oakley.com.de/ can http://www.ralphlauren-polos.com.co/ calm down, http://www.toryburchsale.com.co/ will http://thunder.nbajersey.us.com/ still http://www.burberry-outlet.net.co/ light http://www.cheap-oakleyglasses.us.com/ pull Yuet Wah, on http://www.nikeskos.dk/ the film http://www.christian--louboutin.in.net/ pairs. http://www.coach-factoryoutlet.net.co/ Idle words, http://bucks.nbajersey.us.com/ with http://www.oakley--sunglasses.com.au/ the http://www.thenorth-face.ca/ most sincere feelings for http://www.abercrombie-fitchsale.com/ you http://knicks.nbajersey.us.com/ to http://www.weddingdressesuk.org.uk/ write http://www.maccosmetics.net.co/ the http://www.tiffany-andco.com.au/ most beautiful http://www.rolexwatchesforsale.us.com/ verse. http://www.tommy-hilfigeroutlet.com/ Dreaming http://www.oakleys-sunglasses.us.com/ Seamless, life http://www.rayban-sunglassesoutlet.co.uk/ is http://www.toryburchoutlet-sale.us.com/ a http://www.reebok.com.de/ dream. http://www.burberrys-outlet.co.uk/ Edge to http://www.tommy-hilfiger-online-shop.de/ edge http://nuggets.nbajersey.us.com/ to http://mcmbackpack.co-om.com/ edge of http://www.abercrombie-and-fitch.us.com/ the http://www.nikeair--max.fr/ water, http://www.nikefree-run.net/ quiet http://www.nikeshoesoutlet.org.uk/ message to http://www.longchamp-bags.us.com/ dream landscapes http://www.the-northface.net.co/ rhyme, http://www.chanelhandbags.net.in/ taste http://www.coachoutlet-online.com.co/ Shochiku http://www.burberry-outletonlinesale.in.net/ often http://www.michael-kors.com.co/ think of quiet, http://www.truereligionjeans.net.co/ the http://www.polo-outlets.com.co/ wind http://www.vans-shoes.co.uk/ Yi companion mundane. And http://www.burberryoutlet-sale.in.net/ rest http://www.barbour-factory.com/ in http://pistons.nbajersey.us.com/ April, fragrant, http://www.coco-chanel.com.de/ quiet http://www.maccosmetics.gr.com/ calm http://www.weddingdressessonline.ca/ from http://www.guccishoes.com.co/ leisurely. Cantabile http://michaelkors.euro-us.net/ April, http://www.prada.com.de/ loaded http://www.the-northfacejackets.us.com/ with poetic http://www.hermesbags.jp.net/ Love, http://www.p90xworkout.us.com/ may http://www.cheapjerseys.com.co/ the http://www.burberry-handbagsoutlet.com.co/ years of http://www.nikerosherun.us/ quiet http://www.toms--outlet.com.co/ good, heart http://www.michaelkors.so/ from http://www.lululemon-australia.com.au/ Midsummer night, http://www.beatsbydre.com.co/ I http://www.scarpe-hoganoutlets.it/ stood http://www.mcm-handbags.org/ in http://www.guccishoes-uk.co.uk/ the http://coach.euro-us.net/ garden http://michaelkors.co-om.com/ of http://www.rayban.com.de/ flowerbeds http://www.airmax-2015.org/ being. http://www.vans-shoes.net/ Front Blossoms scene, http://www.uggs-onsale.net/ a hundred thousand http://grizzlies.nbajersey.us.com/ Jiao Mei. http://www.nike-tnrequinpascher.fr/ In http://www.toms-shoesoutlet.net/ that http://www.soccer-shoesoutlet.com/ Hidee http://www.airjordans.us/ Painting http://www.michael-kors-outlet-online.us.org/ graceful http://www.canada-goosesjackets.us.com/ vine http://www.jimmy-chooshoes.com/ on soft, http://www.juicycoutureoutlet.net.co/ shy Turui http://www.ray-banocchiali.it/ aromatic flowers bursts Descent of Wanxiang, http://www.ralphlaurenoutletonline.us.org/ intoxicating http://www.michael-kors.com.es/ air http://www.rolexwatches-canada.ca/ of Zinfandel seduce http://www.newbalance-outlet.org/ the http://www.bcbg-maxazria.ca/ human soul, http://www.raybanoutlet.ca/ I http://www.kate-spade.in.net/ do not http://www.bottegaveneta-bagsoutlet.com/ know http://www.tiffanyand-co.net.co/ how http://www.coachoutletstore.net.co/ many http://www.rolex-watch.me.uk/ deeply moved at http://www.babyliss-pro.us.com/ the child's http://www.oakleysunglasses-cheap.in.net/ feelings. http://www.guccihandbags.net.co/ But http://www.newbalance.com.es/ this http://www.beats-headphone.com.co/ time, http://www.nikemercurial.in.net/ it's never http://www.nike-airmaxinc.co.uk/ hard http://www.tomsshoes-outlet.us.com/ to see http://www.michaeljordan.com.de/ Plum http://www.ralphs-lauren.co.uk/ Fang-shadows. http://spurs.nbajersey.us.com/ I http://www.ugg-boots-australia.com.au/ know http://www.air-max.com.de/ that http://www.christian-louboutinshoes.com.co/ in http://www.mmoncler-outlet.com/ this http://www.hermesbirkin-bag.net/ midsummer find http://www.nike-air-force.de/ plum, http://www.hermes-outlet.com.co/ good http://www.raybans-sunglassesoutlet.in.net/ Yisi mortal http://www.cheapoakley-sunglasses.com/ pretenders http://www.giuseppezanotti.com.co/ Yaotai http://www.converses-outlet.com/ Regard. Nevertheless, plum glamorous, sentiments and http://www.rayban-sunglasses.us.org/ style are http://www.adidas.org.es/ forever http://www.guccishoes.in.net/ embedded http://www.michaelkors.co.nl/ in http://www.michael-kors-taschen.com.de/ my http://www.christianlouboutin.org.uk/ mind, http://www.jimmy-choos.com/ any mountain thunder, http://www.truereligion-outlet.us.org/ fire and waves, http://www.jordan-shoes.com.co/ not withered and http://www.michael-kors-australia.com.au/ dying in http://www.timberlands-paschere.fr/ my heart, my heart God http://www.nike-schoenen.co.nl/ forever http://www.tommyhilfigeroutlet.in.net/ cast http://coachoutlet.euro-us.net/ bottom blossoming http://wizards.nbajersey.us.com/ plum http://www.mkoutletonline.us.com/ Fanghun shadows. Therefore, http://www.edhardy.us.org/ in http://www.nike-shoescanada.ca/ this http://www.rolex-watches.us.com/ June, http://www.burberry-handbags2016.in.net/ she http://www.michael-kors-outlet.us.org/ explains, http://www.marcjacobs.us.com/ in http://pelicans.nbajersey.us.com/ this http://northfaceoutlet.co-om.com/ group http://www.mcmbags.us.com/ of brilliant http://www.gucci-taschen-outlet.de/ pink http://www.gucci-outletstore.com/ team being, I http://bulls.nbajersey.us.com/ want to pull http://hawks.nbajersey.us.com/ offering http://www.rosherun.org.uk/ plum, http://www.basketballshoes.com.co/ plum pondering http://www.ralphlauren-outlet.ca/ soul. http://jazz.nbajersey.us.com/ "Marie http://www.pulseras-pandora.com.es/ has beauty, http://www.eyeglassframes.in.net/

http://www.valentino-shoesoutlet.us.com/

Vote down Vote up

over 5 years ago

Ignore my comment below as it is just a fragment of what I wanted to submit. None of my stats books gives a null hypothesis as "there is no significant difference between expected and observed data." The reason is that the expected values are what you expect if Ho is correct. So obviously one must formulate Ho first. On p. 463 of the 4th ed of Zar, Ho is given as "The sample data come from a population having a 3:1 ratio of..." That ratio is then applied to the sample of 100 to give expected values of 75 and 25.

Vote down Vote up

over 5 years ago

the null hypothesis (H0), which is the hypothesis that states there is no significant difference between expected and observed data.

Vote down Vote up

about 9 years ago

How do I determine the level of significance if I have 3 null observed results from a sample population of 20? Where does the level of significance come from?