Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 10: The t Test for Two Independent Samples - Coggle Diagram
Chapter 10: The t Test for Two Independent Samples
Pooled Variance
Pooled variance accounts for differences in sample size by giving more weight to samples with more data points.
Two ways to interpret the estimated standard error
1) it measures the standard distance between the sample mean diff and the pop mean diff
2) When the null hyp is true, it measures the average size of the sample mean diff or how much difference is reasonable to expect between the two sample means
Confidence Intervals
The confidence interval estimates the size of the pop mean diff between the 2 pop or treatment conditions.
The width of the interval depends on the percentage of confidence used so that a larger percentage produces a wider interval.
The width of the interval depends on the sample size so a larger sample produces a narrower interval.
The confidence interval is not a pure measure of effect size.
A mean difference of 0 is exactly what would be predicted by the null hypothesis if we were doing a hypothesis test. If a mean diff of 0 was included in the confidence interval, then we would conclude it is an acceptable value, which is the same as failing to reject the null hypothesis.
Homogeneity of Variance
Most important when there is a large discrepancy between the sample sizes.
If you violate the HoV assumption there are two questionable values: the hypothesized population value & the meaningless average of the variances.
Hartley's F-Max test is used to determine whether the HoV assumption has been satisfied
Small value near 1.00 = similar sample variances so HoV assumption is reasonable
Large value = large difference between sample variances so the HoV assumption has been violated
The preferred outcome when testing for HoV is to fail to reject the null hypothesis showing there is no significant difference between the two population variances.
Independent-measures research design: The two sets of data comes from two completely separate groups of participants.
also referred to as a between-subjects design
Null hypothesis
Alternative hypothesis
degrees of freedom = df for first sample + df for second sample
Sample Variance & Sample Size
Larger variance leads to larger error
Larger variance produces a smaller value for the t statistic & reduces likelihood of finding significant result
Larger sample size leads to smaller error
Larger sample leads to larger t value and increases the likelihood of rejecting null hypothesis
Larger variance produces smaller measures of effect size (Cohen's d & r^2)
Sample size has no effect on Cohen's d and small influence on r^2
