 # Independent Sample T-test Formula

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Independent Sample T-test Formula

Independent-samples t-tests
But what if you have more than two groups? One suggestion: pairwise comparisons (t-tests)

Multiple independent-samples t-tests
That’s a lot of tests! # groups # tests 2 groups = 1 t-test 3 groups = 3 t-tests 4 groups = 6 t-tests 5 groups = 10 t-tests ... 10 groups = 45 t-tests

Inflation of familywise error rate
Familywise error rate – the probability of making at least one Type I error (rejecting the Null Hypothesis when the null is true) Every hypothesis test has a probability of making a Type I error (a). For example, if two t-tests are each conducted using a = .05, there is a probability of committing at least one Type I error.

Inflation of familywise error rate
The formula for familywise error rate: # groups # tests nominal alpha familywise alpha 2 groups t-test 3 groups t-tests 4 groups t-tests 5 groups t-tests ... 10 groups 45 t-tests

Analysis of Variance: Purpose
Are there differences in the central tendency (mean) of groups? Inferential: Could the observed differences be due to chance?

Assumptions of ANOVA Normality – scores should be normally distributed within each group. Homogeneity of variance – scores should have the same variance within each group. Independence of observations – observations are randomly selected.

Logic of Analysis of Variance
Null hypothesis (Ho): Population means from different conditions are equal m1 = m2 = m3 = m4 Alternative hypothesis: H1 Not all population means equal.

Lets visualize total amount of variance in an experiment
Total Variance = Mean Square Total Between Group Differences (Mean Square Group) Error Variance (Individual Differences + Random Variance) Mean Square Error F ratio is a proportion of the MS group/MS Error. The larger the group differences, the bigger the F The larger the error variance, the smaller the F

Logic--cont. Create a measure of variability among group means
MSgroup Create a measure of variability within groups MSerror

Example: Test Scores and Attitudes on Statistics
Loves Statistics Hates Statistics Indifferent 9 4 8 7 6 5 11 12 3

Find the sum of squares between groups
Find the sum of squares within groups Total sum of squares = sum of between group and within group sums of squares.

To find the mean squares: divide each sum of squares by the degrees of freedom (2 different dfs)
Degrees of freedom between groups = k-1, where k = # of groups Degrees of freedom within groups = n-k MSbetween= SSbetween/dfbetween MSwithin= SSwithin/dfwithin F = MSbetween / MSwithin Compare your F with the F in Table D