Week Ten - T-Tests

Question 1

WHEN DO WE USE A T-TEST?

Answer 1

Use when you want to compare (up to) two sample means

Question 2

3 TYPES OF T-TESTS?

Answer 2

One-sample t-test

Independent-samples t-test

Paired-samples t-test

Question 3

THE 4 GENERAL ASSUMPTIONS OF T-TESTS.

Answer 3

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

Question 4

DEFINE WHAT A ONE-SAMPLE T-TEST IS.

Answer 4

The One Sample t-test determines whether the sample mean is statistically different from a known or hypothesized population mean.

Question 5

WHAT OCCURS IN A ONE-SAMPLE T-TEST?

Answer 5

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.

Question 6

WHAT ARE THE 6 REQUIREMENTS OF A ONE-SAMPLE T-TEST?

Answer 6

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

Question 7

DEFINE AN INDEPENDENT SAMPLE T-TEST.

Answer 7

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.

Question 8

WHAT ARE THE 7 REQUIREMENTS OF AN INDEPENDENT SAMPLE T-TEST?

Answer 8

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

Question 9

FORMULA FOR ISTT

Answer 9

H0: µ1 = µ2 (“the two population means are equal”)

H1: µ1 ≠ µ2 (“the two population means are not equal”)

Question 10

IF P < .05 (in regards to variance)

Answer 10

If p < .05 then reject the null hypothesis that variances are equal. Conclude variances are NOT equal.

Question 11

HOW IS HOMOGENEITY OF VARIANCE TESTED?

Answer 11

Homogeneity of variance is tested using Levene’s test.

Question 12

If the p-value for Levene’s test is not statistically significant, WHAT DOES IT INDICATE?

Answer 12

It indicates the standard deviations for the two groups do not differ significantly. You can therefore assume the data meet the assumption of norm.

Question 13

WHEN IS HOMOGENEITY OF VARIANCE SATISFIED?

Answer 13

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.

Question 14

If the p-value for Levene’s test is statistically significant , WHAT DOES IT INDICATE?

Answer 14

It indicates the standard deviations differ for the two groups and the assumption of homogeneity of variance has been violated.

Question 15

EXPLAIN THE ROLE OF CI IN AN ISTT

Answer 15

If 95% CIs on means for independent t-test overlap no more than ~25% of their total length, the difference is statistically significant.

Question 16

WHAT IS COHEN’S D?

Answer 16

An appropriate effect size for the comparison between two means.

Measure of effect size which states the size of effect in SD units.

Question 17

COHEN’S D EFFECT SIZES

Answer 17

0. 2 considered a ‘small’ effect size
1. 5 represents a ‘medium’ effect size
2. 8 a ‘large’ effect size.

Question 18

WHAT IS A PAIRED SAMPLES T-TEST?

Answer 18

The Paired Samples t Test compares two means that are from the same individual, object, or related units.

Question 19

EXAMPLE OF PAIRED SAMPLES T-TEST

Answer 19

A measurement taken at two different times (e.g., pre-test and post-test with an intervention administered between the two time points).

Question 20

WHAT IS THE PURPOSE OF A PAIRED SAMPLES T-TEST?

Answer 20

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.

Question 21

WHAT ARE THE REQUIREMENTS OF A PAIRED SAMPLE T-TEST? (6)

Answer 21

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

Question 22

WHAT IS THE PROCESS OF A PAIRED SAMPLE T-TEST?

Answer 22

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

Question 23

95% CI FACTOR IN PAIRED SAMPLE T-TEST

Answer 23

If 95% CIs overlap in a paired samples (within-subjects design) visual inspection isn’t able to answer question of statistical significance.

Question 24

COHEN’S D FACTOR IN PAIRED SAMPLE T-TEST

Answer 24

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.

Question 25

T-TEST FORMULA IN WRITE UP

Answer 25

t(n+n - 2) t, p value, 95% CI [lower, upper], cohen’s d

Question 26

WHAT TEST DO WE USE WHEN LEVENE’S TEST IS STATISTICALLY SIGNIFICANT?

Answer 26

Welch’s stats because they alter the df to compensate for the violation of variances