Week 7

Question 1

What is a between participants design and what is it sometimes called?

Answer 1

Different groups are exposed to different independent variables or treatments.
It is sometimes called an independent measures design.

Question 2

What is the independent measures t statistic formula?

Answer 2

t = (M₁ - M₂) - (μ₁ - μ₂)/s(M₁ - M₂).

Question 3

What is the formula for s(M₁ - M₂) and what is it’s major limitation?

Answer 3

s(M₁ - M₂) = the square root of s²/n₁ + s²/n₂.
(Each s² is for each sample).
CAN ONLY BE USED IF BOTH SAMPLES ARE THE SAME SIZE.

Question 4

What is the formula for s(M₁ - M₂) when samples are different sizes?

Answer 4

s(M₁ - M₂) = the square root of (pooled variance/n₁ + pooled variance/n₂).

Question 5

What does s(M₁ - M₂) represent?

Answer 5

Estimated standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂).

Question 6

What is pooled variance and what is the symbol used to represent it?

Answer 6

The average of the two sample variances.

The symbol used is s² with a subscript p.

Question 7

What is the pooled variance formula?

Answer 7

Pooled variance = SS₁ + SS₂/df₁ + df₂

Question 8

What is the alternative pooled variance formula?

Answer 8

(Alt formula) pool variance = df₁s² + df₂s²/df₁ + df₂

Each s² is for each sample

Question 9

How can you visualise the t-statistic formula is words?

Answer 9

t = data - hypothesis / error.

Question 10

What are the three assumptions that should be satisfied before you use the independent measures t formula for hypothesis testing?

Answer 10

1. The observations within each sample must be independent (random sampling fixes this).
2. The two populations from which the samples are selected must be normal (or large).
3. Homogeneity of variance.

Question 11

What are independent observations?

Answer 11

Measurements taken aren’t influenced by extraneous variables.

Question 12

What is homogeneity of variance?

Answer 12

The variances need to be the equal regarding what they are measuring, in other words if you obtain an average from two unrelated variances, it is meaningless and thus your t-statistic is meaningless.

Question 13

What can you use to test homogeneity of variance?

Answer 13

Hartley’s F-max test, or the Lavene’s test in SPSS.

Question 14

What do you preform the F-max test?

Answer 14

1. Hypothesise that two (or more) population variances are equal, therefore the samples should be similar.
2. Compute the sample variance for each sample.
3. Divide the largest variance by the smallest variance.
4. Compare that value to the F-max test table, if it’s larger, homogeneity has not been satisfied.

Question 15

How can you preform a t-test with different sample variances without the pooled variance?

Answer 15

1. Compute s(M₁ - M₂) with the different s².

2. Modify the df.

Question 16

How do you modify the df for t-tests with no pooled variance?

Answer 16

1. Calculate V₁ and V₂ with s²/n (for each).

2. df = (V₁ + V₂)² / (V₁ squared / n₁-1) + (V₂ squared / n₂-1)

Question 17

What is cohen’s d for independent measures?

Answer 17

d = M₁ - M₂/square root of pooled variance.

Question 18

What is the confidence interval formula for μ₁ - μ₂?

The mean difference between populations

Answer 18

μ₁ - μ₂ = M₁ - M₂ ± ts(M₁ - M₂).

Question 19

How does variance size affect t-statistics?

Answer 19

Larger variance produces a smaller value for the t-statistic.

Question 20

What is the Lavene’s test?

Answer 20

A test that determines homogeneity of variance in SPSS, p values less than 0.05 do not satisfy homogeneity of variance. (It will be an output when running an independent measures test in SPSS).