L6 - Two Group Designs of Independent and Dependent Samples

Question 1

3 types of groups?

Answer 1

Naturally occuring groups - INDEPENDENT

Groups defined by researchers - INDEPENDENT

Matched sets of measurements - DEPENDANT

Question 2

What are independent groups also referred to as?

Answer 2

Between-subjects groups/designs

Independent samples

Question 3

What are dependant groups also referred to as?

Answer 3

Within-subjects groups/designs
Dependant samples
Repeated measures
Paired groups

Question 4

What is the aim of the independent samples t test?

Answer 4

to determine whether two groups either come from the same population or represent different populations on the focal construct in the research question.

Question 5

What are the 3 different ways the groups might differ from each other?

Answer 5

• diff pop means, same variance
• diff pop means, diff variance
• same pop mean, diff variance - this one is of little interest

Question 6

What are the two possible explanations for different sample means found between groups?

Answer 6

• sampling variability
• groups represent different populations

we can distinguish between these two options..
any sample mean more than 2 standard errors from a null hypothesised population mean was inferred to from an alternative population.

Question 7

What is a sampling distribution of mean differences?

Answer 7

This is a distribution of the difference between sample means.

If they come from the same population, mean 1 - mean 2 should = 0

Question 8

What is pooled variance?

Answer 8

This is the weighed average variances of two groups, and is used for the sampling distribution of mean differences.

this is found by:

((n1 - 1)xsd1 + (n2-1)sd2))/ n1+n2-2

Question 9

What is the standard error of the mean difference?

Answer 9

= square root ( pooled variance x ((n1+n2)/n1xn2)

This is the expected variability in the sample mean differences for two groups drawn from the same population, having the same population variance.

Question 10

How do we calculate the test statistic for independent samples t test?

Answer 10

Tobs = t = ((M1-M2) - (diff between null hypotehesised means, zero))/ standard error of means diff

Question 11

What is the degrees of freedom for the test statistic for indepdendent samples t test?

Answer 11

df = n1 + n2 - 2

Question 12

What distribution does the test statistic for independent samples follow?

Answer 12

students t dist

bell shaped, symmetric, but critical points are further out in the tails.

Question 13

What are the assumptions of independent samples t test?

Answer 13

• independence of observations
• population scores are normally dist
• pop variances are same for each group - HOMOGENEITY OF VARIANCE

Question 14

What is defined as a robust hypothesis test?

Answer 14

A robust hypothesis test is when the ACTUAL proportion of false rejections of a TRUE NULL HYPOTHESIS using a simulation when statistical assumptions are not being met remains the same as the nominal value as the defined alpha value.

Question 15

When is a hypothesis test too liberal?

Answer 15

when the number of false rejections is too high.

• actual number of false rejections greater than alpha
• obtained p value is smaller than its expected value
• will be more likely to reject a true null hypothesis, than defined by alpha

Question 16

When is a hypothesis test too conservative?

Answer 16

• when the actual proportion of false rejections is less than alpha
• obtained p value is larger than its expected value.
• will be less likely to reject a true null hypothesis than the proportion defined by alpha

Question 17

What are conditions that affect robustness of hypothesis tests?

Answer 17

• sample size - equal across groups is best
• standard deviation - equal across groups is best
• distribution - normal is best

Question 18

WHEN is the independent samples t test robust to violation of homogeneity of variances ???

Answer 18

when..
SAMPLE SIZE of the two groups is the same
DISTRIBUTIONS are either NORMAL or MODERATELY NON-NORMAL

Question 19

under what conditions will the independent samples t test be too liberal when homogeneity of variances is violated?

Answer 19

• when smaller group has LARGER variance

and larger group as SMALLER variance

Question 20

under what conditions will the independent samples t test be too conservative when homogeneity of variances is violated?

Answer 20

• when larger group has larger variance, and smaller group has smaller variance.

Question 21

How do we correct for homogeneity of variance?

Answer 21

• standard error is calculated using separate variances for each group, rather than pooled variance
• df are adjusted to make the actual false rejection rate closer to nominal value of alpha.

(“equal variances not assumed”), using Levene’s test for the equality of variances.

Question 22

What is Levene’s test?

Answer 22

This is a statistical test for assessing whether or not group variances are equal.

If value is significant (p

Question 23

Why would we use standardised mean differences, and list 2 examples of them.

Answer 23

We use them to make more meaningful inferences at the population level, because they may have been based on an arbitrary metric.

Examples of this are:
Cohen’s d
Hedges’ g

–> they are estimators of the unknown population standardised mean difference parameter.

Question 24

What are cohens’ d and hedges’ g?

Answer 24

They are two measures of the difference in standard deviation units between means of two groups, under the assumption of homogeneity of variances.

Question 25

How do cohen’s d and hedges’ g differ in calculation?

Answer 25

They differ in the amount of cases used in the denominator calculation for the standardiser of their formula.

Question 26

Is Hedges’ g biased?

Answer 26

Yes it has an upward bias, but it is consistent

Question 27

What is unbiased hedges g?

Answer 27

It is the unbiased version of hedges’ g.

It’s calculated by multiplying hedges’ g to a correction factor.

Question 28

When homogeneity of variances is violated, which standardised mean difference estimator should be used?

Answer 28

Bonnet’s delta.

Question 29

What are two ways you can have dependant groups?

Answer 29

1. when the same people are measured at 2 time points

2. when the two groups are formed by pairs of individuals being linked by a common characteristic.

Question 30

How do we calculate the Test statistic for a dependent samples t test?

Answer 30

Tobs = (sample mean diff between scores on DV - null hypothesised mean diff)/standard error of difference scores

Question 31

Why is it important to use a dependent t test for dependent samples, and not an independent test?

Answer 31

Because, usually when an independent test is run, the p value will be larger, smaller t value and double the degrees of freedom.

This can be explained as, in the calculation of the standard error of mean difference scores, the correlation between the groups is subtracted.

THUS…
greater correlation =
smaller standard error.. larger t value.. smaller p value…. MORE EFFICIENT!

Question 32

What are the assumptions made in a dependent samples t test?

Answer 32

• independence of observations within each group
• differences scores are normally distributed

NO assumption of homogeneity of variances!!! because the focus is on the difference scores.

Question 33

What is the difference between cohen’s d and hedges’ g in dependent samples?

Answer 33

cohens’d uses a standardiser based on n

hedges g uses a standardised based on n-1

Question 34

What estimator for standardised should be used for mean different for individual change?

Answer 34

Either cohen’s d or hedges’ g.

Question 35

What standardised mean difference estimator should be used for matched groups?

Answer 35

Dunlap’s d.
this uses pooled standard deviation of both groups for the standardiser.

bonnet’s delta can also be used

Question 36

What is the key difference between standardisers for individual change and matched groups?

Answer 36

The standardiser for matched groups includes the correlation between scores for the two dependent groups.

The standardiser for individual change does not.