Psychology Statistics Chapter 10

Independent-Measures Design (between-subjects)

two sets of data come from completely separate samples and we’re interested in how the data differs ‘between’ them

Repeated-Measures Design (within-subjects)

the data comes from the same sample at two different times and we’re interested in how the data differs ‘within’ each
sample from time 1 to time 2

Independent-Measures t-statistic (t)

t = (M1 - M2) - (μ1 -μ2) / SM1 - M2

problem with just adding the errors of both samples

it assumes the two sample means are equal
and therefore treats the two sample variances as equal

Pooled variance formula (S^2p)

S²p = SS1 + SS2/ df1 + df2

If the pooled variance is an average of the two sample variances, what does that mean about where the value of the pooled variance will always be located?

The pooled variance will always be located between the two sample variances.

Two sample estimated sample error formula S (M1 - M2)

S (M1 - M2) = √S2P/n1 + S2P/n2

How does the estimated standard error (for the difference between two means) account for error from two separate samples?

It adds the error for the first sample and the error for the second sample as two separate fractions under the square root.

Two sample df/total df

Df = (n1 - 1) + (n2 - 1)

Cohen’s D for independent measure

d = (M1 - M2) / √S^2p

r2 for an independent-measures t test

r2 = t2/ t2 + df total

3 assumptions must be satisfied before using an independent-measures t-statistic

1. The observations within each group are independent of one another

2. the two populations from which the samples are drawn are normal

3. the two populations from which the samples are drawn have equal variance
(homogeneity of variance)

Homogenity of variance

It means that the variances of the populations from which the samples are drawn are equal (or nearly equal). It's an assumption for many parametric statistical tests (like t-tests and ANOVA).

F-max for homogenity of variance formula

F = s2 (largest) / s2 (smallest)

What you need to know is:

• K = number of separate samples
• alpha (α)
• df (assumes equal n)

What does an obtained F-max value larger than the critical value indicate regarding homogeneity of variance and t-statistic interpretation?

It indicates that homogeneity of variance has been violated. Therefore, you cannot reliably interpret the value of your t-statistic.

Variances are unequal OR Assumptions violated

Hypothesis of two tailed test for independent t-test measure

H0: μ1 - μ2 = 0
H1: μ1 - μ2 =/= 0

Hypothesis of one tailed test for independent t test measure

H0 = μ1 ≤ μ2 (or μ1 ≥ μ2)

H1: μ1 > μ2 (or μ1 < μ2)