PS296 Lecture Notes - Lecture 15: Squared Deviations From The Mean, 2Degrees
INDEPENDENT SAMPLES T TEST
Assumption of homogeneity of variance:
Rule of thumb: when calculating t statistic by hand:
Assume homogeneity of variance when:
1) variance of one sample is no more than 4x the variance of the other sample
2) sample sizes are equal or approximately equal
Levene's Test for Equality of Variances
-when the p value for Levene's test is significant (p > .05) it means that the variances are not equal
-when the p value is non-significant (p < .05) it means the variances are equal
-for Levene's test, we want the p value to be non-significant because this means the variances are equal
-if variances are not equal, we then have heterogeneity of variance
-if SPSS says equal variances are not assumed, we have heterogeneity of variance and we need to
correct our answers, specifically by changing our degrees of freedom
-when homogeneity is not met, it affects our degrees of freedom (usually from a whole number to
decimals) and significance is a little lower (but written as a little higher) + t would be a little less
significant
Degrees of Freedom for Independent Samples:
-two sample variances are used to calculate the t statistic: s²1 and s²2
-each sample variance has n-1 degrees of freedom
-across the two samples we have (n1 – 1) + n2 – 1) or n1 + n2 – 2 degrees of freedom
-we are using an independent samples t test when we are testing means from two different groups
-we are using related samples t test when we are testing two different means from the same group
Example: Outdoor learning vs indoor learning
H0: mu1 = mu2. Memory is the same in both groups
HA: mu1 ≠ mu2. Member is different in each group
Outdoor: xbar1 = 7.8
indoor: xbar2 = 6.6
dbar = 1.3
n1 = 10 n2 = 10 thus N = 20
df = N – 2 = 18
-columns x1 – xbar 1 and x2 – xbar2 should total about 0
-then we need to get the sum of the squared deviations for both groups
sigma xbar1 = 7.60
sigma xbar2 = 8.40
-we now need to calculate the variance (sigma squared) not the SD for each group
s²1 = .844
s²2 = .933
7.60 – 8.40
.844 + .933
10 10 SE is square rooted
= 1.20
square root of .177
