Independent Sample t-test and Dependant Samples Flashcards
Two-sample hypotheses
-Statements about means of 2 different groups - different or not?
-We want to learn if the mean of the two groups are different from one another
What impacts the statistic tests we use
-Design of experiment impacts which statistics we can use - both within and between are valid and appropriate for different scenarios
Distinction must be clear
When to use a t test
-Comparisons of 2 group means or a single mean to a reference value
- data must have an interpretable mean and SD to run a t-test
Data must be interval or ratio
- nominal does not have interpretable mean or SD
- ordinal has mean but SD hard to interpret
Assumptions must be met:
- appropriate data type
- normality
- Independence
- Equality of variance (Welch’s test removes this assumption)
Computing a independent sample t-test
-Test between two means of two groups of data all divided by the standard error of that difference
-Assess whether distance is significant - t-test accounts for extra noise by finding ratio between size of difference and precision of which it is estimated
Independent t test equation
t(df) = mean of group 1 - mean of group 2/ Pooled standard error of difference
Pooled SD =a single SD to represent variability in BOTH groups - assuming same variability
Results of independent samples t test
Larger +positive t-value = mean of group 1 is above mean of group 2
Near 0 t-value = mean of group 1 is indistinguishable from mean of group 2
Large -negative t-value = mean of group 1 is below mean of group 2
How to test assumption of normality
Shapiro-Wilk
if violated:
One sample test = Wilcoxon Rank
Independent sample = Mann-Whitney U
Homogeneity of variance
distributions of groups have the same SD
-Levene’s test - assesses the null hypothesis that different groups of samples are from populations of equal variance
-Significant value = difference variances, pooled estimate is not appropriate
What do we do when we get a significant value
Welch’s t-test - uses unpooled measure of SD, this is valid whether groups have equal variances or not
Equation for Welchs t test
mean of group 1 - mean of group 2/ unpooled standard error of difference
Paired samples t-test
sample principle as independent samples
Comparing means of 2 dependent distributions (pts contributed to both conditions)
-Assumptions of independent samples is violated in standard t-test meaning paired t test must be run
-This is due to two dependent distributions having a priority structure
Paired t test equation
(Mean of paired differences - 0) divide by
(standard error of mean paired difference)
