Review of Statistics Group Results

Which type of statistics? When comparing two group scores-Use the t-test. When comparing more than two scores: Use the Analysis of Variance (ANOVA), which is an F-test Both the t and the F tests are ratios.

T-Test t = group difference within group variability within group variability Therefore the numerator is the difference between the means of the two groups, and the denominator is the variability between each individual score and the group mean.

Examples Group One Mean of Group One is 25 Mean of Group Two ( not shown) is 65

Variability within group. Compare each score to the group mean in absolute value: = = = = = = = 15 Add together and the variability of group one is 30 Add together and the variability of group one is 30 Group Two ( not shown) variability is 10 Group Two ( not shown) variability is 10 Total within group variability is 40 Total within group variability is 40

T-test example t = 65 ( mean of group Two) -25( mean of group one) Divided by the within group variability -40 t = t ratio = 1.00

T-Ratio The value of t increases as the difference between your group means increases Within group variability- want this number to be small as it indicates your groups were relatively equal on the measure. A large amount of variability would increase the denominator and decrease the size of the t- statistic, thus decreasing the chance your study worked.

Critical Value The critical value is a number which has been calculated to represent the smallest number you must obtain with the t-ratio to obtain significance. This number depends on your number of participants and number of conditions. Each critical value represents a normal distribution for that number of participants and groups and the critical value is the mean. To find your critical value, you must calculate your degrees of freedom.

Degrees of Freedom The degrees of freedom are the number of scores free to “vary” given the stated mean. The t-statistic has only one number for degrees of freedom. Where N= total number of participants and n= total number of groups: df = ( N-n) N=60 participants, n= 2 groups, df=58

T-test critical value t(58)=1.0 Critical Value = p-value: this is the probability that your actual findings are incorrect. Science recognizes nothing above a p<.05 Did this experiment work? At what probability level?

One-tailed vs. Two Tailed test When comparing scores to critical values, one must look at the hypothesis. Did the hypothesis predict one group would perform better than another? One tailed test. Or…did the hypothesis predict one group would differ from the other. This makes a difference in the critical value as it is an area under the normal curve. A one tailed test is less conservative than a two: One tail t(58)=1.67 critical value Two tail t(58) =2.00 critical value

Analysis of Variance (ANOVA) Used when there is more than one group. Is an extension of the t-test F=t squared. Tells us there is an over-all difference between the three or more groups.

Analysis of Variance F = Systematic variance Error Variance Error Variance Systematic Variance is the deviation of the group means from the Grand means. The grand mean is the mean of the means.

Systematic Variance Group 1 M= 35, Group 2 M= 25, Group 3 M=30. Grand Mean: = 90/3 =30 Systematic Variance = = = = = 0 Systematic variance is 10

Error Variance Is the same as Within group variability. Compare the mean of group one to the individual scores of the group as well as group two, and group 3. Add together to obtain the within group variability (error variance) Error variance among this group = 2 ( very Low! What does this mean)