Student ’ s t-test • The value of t will be compared to values in the specific table of "t distribution test" at the value of the degree of freedom. • If the value of t is less than that in the table, • If the value of t is less than that in the table, then the difference between samples is insignificant: i.e., the null hypothesis is accepted. • If the t value is larger than that in the table so the difference is significant: i.e., the null hypothesis is rejected.
Student ’ s t-test - Degrees of Freedom For the t distribution, degrees of freedom are always a simple function of the sample size, e.g., (N-1). One way of explaining df is that if we know the total or mean, and all but one score, the last (N-1) score is not free to vary. but one score, the last (N-1) score is not free to vary. It is fixed by the other scores. 4+3+2+X = 10. X=1. In case of mean comparison between two groups, one score for each group is not free to vary.
Student ’ s t-test - example Suppose we conducted a study to compare two strategies for teaching spelling. Group A had a mean score of 19. The range of scores was 16 to 22, and the standard deviation was 1.5. Group B had a mean score of 20. The range of scores was 17 to 23, and the standard deviation was 1.5. How confident can we be that the difference we found between the means of How confident can we be that the difference we found between the means of Group A and Group B occurred because of differences in our reading strategies, rather than by chance? 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
Student ’ s t-test - example A t test allows us to compare the means of two groups and determine how likely the difference between the two means occurred by chance when there was no difference in population from which the sample was drawn. The calculations for a t test requires three pieces of information: - the difference between the means (mean difference) - the standard deviation for each group - and the number of subjects in each group. - and the number of subjects in each group. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
Student ’ s t-test - example All other factors being equal, large differences between means are less likely to occur by chance than small differences. 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
Student ’ s t-test - example The size of the standard deviation also influences the outcome of a t test. Given the same difference in means, groups with smaller standard deviations are more likely to report a significant difference than groups with larger standard deviations. 10 9 8 7 6 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
Student ’ s t-test - example From a practical standpoint, we can see that smaller standard deviations produce less overlap between the groups than larger standard deviations. Less overlap would indicate that the groups are more different from each other. 10 9 8 7 6 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
Student ’ s t-test - example The size of our sample is also important. The more subjects that are involved in a study, the more confident we can be that the differences we find between our groups did not occur by chance. 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores 10 9 8 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Spelling Test Scores
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