Term 2 Lecture 3: independent and dependent samples t-tests

Question 1

Matched samples (paired related dependent/ repeated measures designs)

Answer 1

where the

same subjects respond on two occasions

Question 2

Independent samples

Answer 2

The comparison of two independent groups is one of the most
common uses of the t-test. Independent groups may arise for
example in experiments, when comparing two groups that
were subject to different experimental conditions (or to
comparing an experimental group with a control group).
This test is also often used to compare two mutually exclusive
groups, such as males and females.

Question 3

Degrees of freedom

Answer 3

This t-statistic has df = n1 + n2 – 2

Question 4

Assumptions for t-test for independent samples

4 - and what is the 4th aka

Answer 4

Random assignment to groups
• Independence of observations
• Normality: The sampling distribution of the difference of
the means is normal (which is the case if the sampling
distributions of the means of each group are both normal).
• Homogeneity of variances: The variances of the two
populations are equal.
The last assumption, homogeneity of variances, is often called
“homoscedasticity”. It can be tested using the “Levene’s test
for equality of variances”. If the variances are not equal
(“heteroscedasticity”), a modification of the t-test can be
used

Question 5

modification of the t-test can be

used

Answer 5

Levene’s Test for Equality of Variances

second line on SPSS output for equal variances not assumed

Question 6

Effect Size For independent samples we can compute an estimate of

where 𝑠𝑝 = is the pooled standard deviation - the weighted average of the two sample standard deviations

Answer 6

Cohen’s d

Question 7

write up of a t test

Answer 7

This experiment investigated whether the “XY”-training programme
for mothers of low birthweight (LBW) babies may help to improve
mental development of their children. LBW infants were randomly
assigned to two groups: an experimental group (n=25), whose
mothers undertook the training; and a control group (n=31), whose
mothers received no training. After the training, when the infants
were 24 months old, they were assessed using the Bayley’s Mental
Development Index.
The mean of the experimental group was 117.20, whereas the mean
of the control group was considerably lower at 106.71. The standard
deviations were 12.68 and 12.95, respectively. A two-tailed Student’s
t-test for independent samples was performed to compare the
groups. This test showed that the difference between group means
was statistically significant at the 5% significance level (t(54) =
3.041, p = 0.004, two-tailed test). The 95% confidence interval of
the mean difference was [3.57; 17.41]. So the results suggest that
the “XY”-training had a positive effect on the mental development of
LBW infants. The observed effect size, estimated by Cohen’s d, was
𝑑 = 0.82.

Question 8

what increases power? (3)

Answer 8

1. How big is the difference between μ0 and μ1:
   • the larger the effect size, the more powerful the test
   —–As the difference |μ0- μ1| gets larger,β gets smaller,
   and Power increases
2. The standard error:
   • the smaller the standard error, the more powerful the test
   ——–As the standard error gets smaller, β gets smaller
   too, and Power increases
3. The significance level (α):
   • the larger α, the more powerful the test (but the greater the risk of alpha-error!)

Since the standard error gets smaller as the sample size rises, we can make a test more powerful by increasing the sample size of a
planned study.

Question 9

Calculating power

when? why then?

what do we need to specify? (2)

Answer 9

before data collection,
in order to determine the sample size necessary to detect an effect of a given size.

To calculate power, we need to specify:
• the minimum effect size that we would like to detect
if an effect exists, and
• the desired power (usually 80%)

From these numbers, we can determine the sample size we need