Week Ten - T-Tests Flashcards
WHEN DO WE USE A T-TEST?
Use when you want to compare (up to) two sample means
3 TYPES OF T-TESTS?
One-sample t-test
Independent-samples t-test
Paired-samples t-test
THE 4 GENERAL ASSUMPTIONS OF T-TESTS.
Data are interval or ratio
Population of scores is normally distributed
t-tests are reasonably robust to violations
Scores for independent-samples t-test are independent
i.e., knowing one score provides no information about any other score.
Equal variances (for independent-samples t-test) Homogeneity of variance (assume SDs are equal) Levene’s test
DEFINE WHAT A ONE-SAMPLE T-TEST IS.
The One Sample t-test determines whether the sample mean is statistically different from a known or hypothesized population mean.
WHAT OCCURS IN A ONE-SAMPLE T-TEST?
In a One Sample t-test, the test variable is compared against a “test value”, which is a known or hypothesized value of the mean in the population.
WHAT ARE THE 6 REQUIREMENTS OF A ONE-SAMPLE T-TEST?
Continuous (i.e., interval or ratio level)
Scores on the test variable are independent (i.e., independence of observations)
Random sample of data from the population
Normal distribution (approximately) of the sample and population on the test variable
Homogeneity of variances (i.e., variances approximately equal in both the sample and population)
No outliers
DEFINE AN INDEPENDENT SAMPLE T-TEST.
The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.
WHAT ARE THE 7 REQUIREMENTS OF AN INDEPENDENT SAMPLE T-TEST?
Dependent variable that is continuous (i.e., interval or ratio level)
Independent variable that is categorical (i.e., two or more groups)
Cases that have values on both the dependent and independent variables
Independent samples/groups (i.e., independence of observations)
Random sample of data from the population
Homogeneity of variances (i.e., variances approximately equal across groups)
Normal distribution (approximately) of the dependent variable for each group
No outliers
FORMULA FOR ISTT
H0: µ1 = µ2 (“the two population means are equal”)
H1: µ1 ≠ µ2 (“the two population means are not equal”)
IF P < .05 (in regards to variance)
If p < .05 then reject the null hypothesis that variances are equal. Conclude variances are NOT equal.
HOW IS HOMOGENEITY OF VARIANCE TESTED?
Homogeneity of variance is tested using Levene’s test.
If the p-value for Levene’s test is not statistically significant, WHAT DOES IT INDICATE?
It indicates the standard deviations for the two groups do not differ significantly. You can therefore assume the data meet the assumption of norm.
WHEN IS HOMOGENEITY OF VARIANCE SATISFIED?
The homogeneity of variance is satisfied when the variances of the DV at the two levels of the IV (Silence and Static) are equal or nearly equal.
If the p-value for Levene’s test is statistically significant , WHAT DOES IT INDICATE?
It indicates the standard deviations differ for the two groups and the assumption of homogeneity of variance has been violated.
EXPLAIN THE ROLE OF CI IN AN ISTT
If 95% CIs on means for independent t-test overlap no more than ~25% of their total length, the difference is statistically significant.
WHAT IS COHEN’S D?
An appropriate effect size for the comparison between two means.
Measure of effect size which states the size of effect in SD units.
COHEN’S D EFFECT SIZES
- 2 considered a ‘small’ effect size
- 5 represents a ‘medium’ effect size
- 8 a ‘large’ effect size.
WHAT IS A PAIRED SAMPLES T-TEST?
The Paired Samples t Test compares two means that are from the same individual, object, or related units.
EXAMPLE OF PAIRED SAMPLES T-TEST
A measurement taken at two different times (e.g., pre-test and post-test with an intervention administered between the two time points).
WHAT IS THE PURPOSE OF A PAIRED SAMPLES T-TEST?
The purpose of the test is to determine whether there is statistical evidence that the mean difference between paired observations on a particular outcome is significantly different from zero.
WHAT ARE THE REQUIREMENTS OF A PAIRED SAMPLE T-TEST? (6)
Dependent variable that is continuous (i.e., interval or ratio level)
Related samples/groups (i.e., dependent observations)
Population of scores is normally distributed
Random sample of data from the population
No outliers in the difference between the two related groups
Scores for individuals are independent
WHAT IS THE PROCESS OF A PAIRED SAMPLE T-TEST?
Is the difference between means different from zero?
- Two scores for each participant, one from each
condition
- Calculate difference scores for all participants
- Calculate the mean difference score
95% CI FACTOR IN PAIRED SAMPLE T-TEST
If 95% CIs overlap in a paired samples (within-subjects design) visual inspection isn’t able to answer question of statistical significance.
COHEN’S D FACTOR IN PAIRED SAMPLE T-TEST
For Paired-sample t-test, the value for Cohen’s d does not take into account the correlation of the two conditions.
This effect size is not directly comparable with d from independent samples t-test.
T-TEST FORMULA IN WRITE UP
t(n+n - 2) t, p value, 95% CI [lower, upper], cohen’s d
WHAT TEST DO WE USE WHEN LEVENE’S TEST IS STATISTICALLY SIGNIFICANT?
Welch’s stats because they alter the df to compensate for the violation of variances
