I just need help running an ANOVA in excel then running the results online at Tukey's HSD IF it is significant then I will need a simple write up of results
Statistics for Social Work (SW 8371.01, Fall 2006) Statistics for Social Work Ch. 7 T-tests 1 REVIEW: Null Hypothesis Two (or more) variables are NOT related. If there is a difference, it’s only because of sampling errors So What? Is there a relationship? Researchers are interested in relationships. Why? 2 Sampling Error Sampling error = Chance Samples may not be 100% representative of the population that they are drawn (especially with smaller sizes) Relationship between variables could just be a fluke EXAMPLE In 1990, Americans ordered pizza an average of 3 times per month. We want to know do we order more pizza in 2019? H0 :Today, Americans on average still order pizza 3 times per month. HA : Today, Americans order more pizza per month. You randomly sample 100 Arkansans. In your sample, you learn that the average number of pizza orders in a month is 5 The NULL Model 3 -3SD -2SD -1SD 0 +1SD+2SD +3SD We expect values to fall somewhere here 5, that’s pretty far away from the mean… 6 Inferential Statistics Trying to reach conclusions that extend beyond our data set. t Tests, Analysis of Variance (ANOVA), Chi Square, and Pearson’s R Often times we compare 2 different group means … Men / Women & Pizza Consumption … Older / Younger & Trauma Symptoms 7 Appropriate Use of t Tests The t Test is a significance test that compares two group means, used with: one interval-or ratio-level dependent variable one nominal-level independent variable (2 categories only) relatively small sample (or skewed sample) In social work, t Tests are often used to compare mean outcome scores of groups 8 In social work, t Tests are often used to compare mean outcome scores of groups (e.g., control and experimental or treatment groups) Independent Samples t-Test t-Tests assume normality, but with large enough sample sizes, can be used anyway. If the two sample sizes are 30 or greater, then t-test can be used Critical values of t rely upon p-value and sample size (degrees of freedom (df)) See Table 12.1 (page 124) 9 Excel t-Tests: Three Types t-Test: Paired Two Sample for Means Pretest /Post-Test; Testing the same group twice Student’s t-Test t-Test: Two-Sample Assuming Equal Variances Welch’s t-Test t-Test: Two-Sample Assuming Unequal Variances But which one to use???? 10 Welch’s t-test (assuming unequal variance) More robust Probably better at reducing a Type 1 error If our variance is equal, the statistical power is pretty much the same. When we are looking to differentiate two distributions, there are two primary characteristics we can analyze: Their Means Their Variances (i.e the spread of the distribution) Same Variance, but different MEANS Mean doesn’t change, but VARRIANCE does The “T” Distribution t-Test: Two-Sample Assuming Unequal Variances MenWomen 2012 1518 1123 1813 2510 2410 1614 166 1711 We survey 9 men and 9 women and ask them how many pizza slices they eat in a month. Have class do this in Excel. 16 Ho and HA HO Men and women on average eat the same number of pizza slices HA Men on average eat more pizza slices than women Null Model Run Descriptive Statistics THINK… Run t-Test: Two-Sample Assuming Unequal Variances Report Results 17 The NULL Model -3SD -2SD -1SD 0 +1SD+2SD +3SD We expect values to fall somewhere here Will the difference between the two means land here? 18 Run Descriptives Data Tab Data Analysis Descriptive Statistics Descriptive Statistics Input: Highlight BOTH the Men and Women columns Check Box Labels in first row Output Range: Select a cell in the same worksheet that your variables are in Check Box Summary statistics OK This table will be very useful when you are ready to report your results. t-Test: Two-Sample Assuming Unequal Variances MenWomen 2012 1518 1123 1813 2510 2410 1614 166 1711 We survey 9 men and 9 women and ask them how many pizza slices they eat in a month. Men M = 18.00 SD = 4.41 Women M = 13.00 SD = 4.97 Is there a significant difference between these two means? Is 18-13= 5, really that different or is it just a fluke? 22 t-Test: Two-Sample Assuming Unequal Variances To run a t Test, go to the ‘DATA’ tab Next, select ‘DATA ANALYSIS’ 23 Continued: t-Test: Two-Sample Assuming Unequal Variances Select ‘t Test: two-sample assuming UNEQUAL variances’ Remind them why we’re selecting “unequal variances” It’s rare that you’ll know your samples variance ahead of time. 24 Variable 1 = select all cells that have ‘Men’ data Variable 2 = select all cells that have ‘Women’ data Hypothesized Mean Difference = leave blank Checkbox Labels Alpha = defaulted to .05 (this is your significance level) 25 How do we interpret this? 26 Directional Hypothesis ; 95% confident (i.e. Men will eat more pizza than women and we want to be 95% confident this difference isn’t by chance.) 27 What’s our critical value? t = 1.74 Critical Value t = 2.25 We expect values to fall somewhere here t stat falls into the Rejection Region In this case our t value falls into the rejection region. Nonetheless, we would still Reject our Null Hypothesis, Since it’s so close, what could we do to be more confident in our decision? 28 Directional Hypothesis ; 95% confident (i.e. Men will eat more pizza than women and we want to be 95% confident this difference isn’t by chance.) 29 What’s our p value? p = .05 p = .01 We expect values to fall somewhere here p value falls into the Rejection Region In this case our t value falls into the rejection region. Nonetheless, we would still Reject our Null Hypothesis, Since it’s so close, what could we do to be more confident in our decision? 30 t(16)=2.25, p<.05 t-test:="" two-sample="" assuming="" unequal="" variances="" ="" men="" women="" mean="" 18="" 13="" variance="" 19.5="" 24.75="" observations="" 9="" 9="" hypothesized="" mean="" difference="" 0="" df="" 16="" t="" stat="" 2.254938=""><=t) one-tail="" 0.01925="" t="" critical="" one-tail="" 1.745884=""><=t) two-tail="" 0.0385="" t="" critical="" two-tail="" 2.119905="" ="" reporting="" the="" results="" (one="" example)="" social="" workers="" at="" the="" university="" of="" arkansas="" at="" little="" rock="" conducted="" an="" independent-samples="" t-test="" (assuming="" unequal="" variance)="" to="" see="" if="" men,="" on="" average,="" consumed="" more="" pizza="" than="" women.="" there="" was="" a="" significant="" difference="" in="" the="" pizza="" consumption="" for="" men="" (m="18.00," sd="4.41)" compared="" to="" women="" (m="13.00," sd="4.97);" t(16)="2.25,"><.05. these results suggest… statistics for social work ch 7: anova (f-tests) 33 why anova the world is more complicated than this. what if we wish to compare the means of more than two populations? what if we wish to compare populations each containing several subgroups? analysis of variance sampling distribution of f contains all the possible f values along with the probability of each f value, assuming sampling is random from the null hypothesis population. the sampling distribution of f gives all the possible f values along with the probability of each f value, assuming sampling is random from the null hypothesis population. like the t distribution, the f distribution also varies with the degrees of freedom the process of arriving at the sampling distribution is similar to the other distributions such as t. the only difference being that we are now interested in the different sample variances. the variance becomes important in calculation of the f value. the f distribution is never negative (variance can never be negative) the f distribution is always positively skewed, and uses a one-tailed assessment for hypothesis-testing the median f value = 1 (approximately) 35 the f distribution if we accept our null, the difference will fall somewhere here rejection region – proceed to post hoc p value & f critical p gets smaller / f gets bigger the f distribution uses variance as the test statistic fobt is a ratio of two independent variance estimates of the same population variance fobt = between-groups mean square within-groups mean square has two df’s: one for the numerator and the other for the denominator 37 f ratio reflects the variations among the means of several groups in relation to the variation within the groups. . between groups: variability between groups as described. within groups variance looks at the amount of variability of the dv within each individual group if you have a large between groups variance, f will be large and this will mean that iv has an effect on dv at different levels between groups mean square = the variation between the means of each group divided by between groups df (number of groups – 1) within groups mean square = the variation in the dv among the individual cases within each group divided by the within groups df (sum of the df for each group) total df = n-1 to calculate the variance & standard deviation: subtract the mean from the individual case values, and square the difference compute the sum of the squared differences (sum of squares), divide the sum of squares by n or (n-1) to get the variance. why not do a bunch of t tests? x.05.05 xx.05 xxx type i error: the error componds with each t-test: (.95)(.95)(.95)=.857 our new p value is actually .143 not .05! do these means come from the same population? (i.e. null hypothesis) suppose we want to compare three populations means to see if a difference exists somewhere among them. 39 do these means come from the same population? (i.e. null hypothesis) 40 do these means come from the same population? (i.e. null hypothesis) variability between the means 41 hypotheses in anova one of these is not like the other. 42 do these means come from the same population? (i.e. null hypothesis) variability within the distribution remember that each sample has its own speard / varaiblitiy. 43 anova is a variability ratio variability between the means variability within the distribution overall mean distance from overall mean internal spread anova is a variability ratio overall mean distance from overall mean internal spread = variance between variance within f ratio this is what gives us the f ratio 45 when to use anova when an experiment has these="" results="" suggest…="" statistics="" for="" social="" work="" ch="" 7:="" anova="" (f-tests)="" 33="" why="" anova="" the="" world="" is="" more="" complicated="" than="" this.="" what="" if="" we="" wish="" to="" compare="" the="" means="" of="" more="" than="" two="" populations?="" what="" if="" we="" wish="" to="" compare="" populations="" each="" containing="" several="" subgroups?="" analysis="" of="" variance="" sampling="" distribution="" of="" f="" contains="" all="" the="" possible="" f="" values="" along="" with="" the="" probability="" of="" each="" f="" value,="" assuming="" sampling="" is="" random="" from="" the="" null="" hypothesis="" population.="" the="" sampling="" distribution="" of="" f="" gives="" all="" the="" possible="" f="" values="" along="" with="" the="" probability="" of="" each="" f="" value,="" assuming="" sampling="" is="" random="" from="" the="" null="" hypothesis="" population.="" like="" the="" t="" distribution,="" the="" f="" distribution="" also="" varies="" with="" the="" degrees="" of="" freedom="" the="" process="" of="" arriving="" at="" the="" sampling="" distribution="" is="" similar="" to="" the="" other="" distributions="" such="" as="" t.="" the="" only="" difference="" being="" that="" we="" are="" now="" interested="" in="" the="" different="" sample="" variances.="" the="" variance="" becomes="" important="" in="" calculation="" of="" the="" f="" value.="" the="" f="" distribution="" is="" never="" negative="" (variance="" can="" never="" be="" negative)="" the="" f="" distribution="" is="" always="" positively="" skewed,="" and="" uses="" a="" one-tailed="" assessment="" for="" hypothesis-testing="" the="" median="" f="" value="1" (approximately)="" 35="" the="" f="" distribution="" if="" we="" accept="" our="" null,="" the="" difference="" will="" fall="" somewhere="" here="" rejection="" region="" –="" proceed="" to="" post="" hoc="" p="" value="" &="" f="" critical="" p="" gets="" smaller="" f="" gets="" bigger="" the="" f="" distribution="" uses="" variance="" as="" the="" test="" statistic="" fobt="" is="" a="" ratio="" of="" two="" independent="" variance="" estimates="" of="" the="" same="" population="" variance="" fobt="Between-groups" mean="" square="" within-groups="" mean="" square="" has="" two="" df’s:="" one="" for="" the="" numerator="" and="" the="" other="" for="" the="" denominator="" 37="" f="" ratio="" reflects="" the="" variations="" among="" the="" means="" of="" several="" groups="" in="" relation="" to="" the="" variation="" within="" the="" groups.="" .="" between="" groups:="" variability="" between="" groups="" as="" described.="" within="" groups="" variance="" looks="" at="" the="" amount="" of="" variability="" of="" the="" dv="" within="" each="" individual="" group="" if="" you="" have="" a="" large="" between="" groups="" variance,="" f="" will="" be="" large="" and="" this="" will="" mean="" that="" iv="" has="" an="" effect="" on="" dv="" at="" different="" levels="" between="" groups="" mean="" square="the" variation="" between="" the="" means="" of="" each="" group="" divided="" by="" between="" groups="" df="" (number="" of="" groups="" –="" 1)="" within="" groups="" mean="" square="the" variation="" in="" the="" dv="" among="" the="" individual="" cases="" within="" each="" group="" divided="" by="" the="" within="" groups="" df="" (sum="" of="" the="" df="" for="" each="" group)="" total="" df="N-1" to="" calculate="" the="" variance="" &="" standard="" deviation:="" subtract="" the="" mean="" from="" the="" individual="" case="" values,="" and="" square="" the="" difference="" compute="" the="" sum="" of="" the="" squared="" differences="" (sum="" of="" squares),="" divide="" the="" sum="" of="" squares="" by="" n="" or="" (n-1)="" to="" get="" the="" variance.="" why="" not="" do="" a="" bunch="" of="" t="" tests?="" x="" .05="" .05="" x="" x="" .05="" x="" x="" x="" type="" i="" error:="" the="" error="" componds="" with="" each="" t-test:="" (.95)(.95)(.95)=".857" our="" new="" p="" value="" is="" actually="" .143="" not="" .05!="" do="" these="" means="" come="" from="" the="" same="" population?="" (i.e.="" null="" hypothesis)="" suppose="" we="" want="" to="" compare="" three="" populations="" means="" to="" see="" if="" a="" difference="" exists="" somewhere="" among="" them.="" 39="" do="" these="" means="" come="" from="" the="" same="" population?="" (i.e.="" null="" hypothesis)="" 40="" do="" these="" means="" come="" from="" the="" same="" population?="" (i.e.="" null="" hypothesis)="" variability="" between="" the="" means="" 41="" hypotheses="" in="" anova="" one="" of="" these="" is="" not="" like="" the="" other.="" 42="" do="" these="" means="" come="" from="" the="" same="" population?="" (i.e.="" null="" hypothesis)="" variability="" within="" the="" distribution="" remember="" that="" each="" sample="" has="" its="" own="" speard="" varaiblitiy.="" 43="" anova="" is="" a="" variability="" ratio="" variability="" between="" the="" means="" variability="" within="" the="" distribution="" overall="" mean="" distance="" from="" overall="" mean="" internal="" spread="" anova="" is="" a="" variability="" ratio="" overall="" mean="" distance="" from="" overall="" mean="" internal="" spread="Variance" between="" variance="" within="" f="" ratio="" this="" is="" what="" gives="" us="" the="" f="" ratio="" 45="" when="" to="" use="" anova="" when="" an="" experiment="">