1 Testing for Differences between 2 sample means Flashcards
Q: How can differences between two means be assessed, and what is Cohen’s d used for?
A: Differences between two means can be assessed by calculating descriptive statistics and using inferential tests based on known probability distributions. Cohen’s d is a measure of the effect size, which quantifies the distance between the means of two conditions while taking into account the variability of the data.
Q: What does Cohen’s d measure, and how is it calculated?
A: Cohen’s d measures the difference in means between two conditions while considering the standard deviation. It is calculated using the formula:
d= (mean1-mean2)/meanSD
MeanSD is the average of the standard deviations of the two conditions.
Q: How is effect size interpreted in terms of overlap and magnitude?
A: Effect size, as measured by Cohen’s d, indicates how many standard deviations apart the means of two conditions are and how much overlap there is between the distributions. A larger effect size indicates a greater difference between the means and less overlap between the distributions. Cohen’s d values of 0.2, 0.5, and 0.8 are typically considered small, medium, and large, respectively. In terms of overlap, a d value of 0.2 corresponds to approximately 85% overlap, 0.5 to 67% overlap, and 0.8 to 53% overlap.
Q: What are the two types of t-tests used for differences in means for two conditions, and when are they appropriate?
A: The two types of t-tests for differences in means for two conditions are the related t-test and the independent t-test. The related t-test is used when participants take part in both conditions, while the independent t-test is used when participants only take part in one condition.
Q: How is the paired or related t-test conducted, and what does it measure?
A: The paired or related t-test calculates the difference in paired scores within participants, typically representing the change from pre to post measurements. It compares the means of these paired differences to determine if there is a significant difference between the conditions. The mean for the change distribution is calculated as the post-score minus the pre-score. The related t-test can be simplified to a single-sample t-test.
Q: How is the sampling distribution of the difference between two sample means generated?
A: The sampling distribution of the difference between two sample means is generated by the following steps:
Repeatedly sample from two populations.
Calculate the means of these samples.
Compute the difference between the sample means.
Repeat this process many times to generate a distribution of differences between sample means.
Q: Why is the sampling distribution of the difference between two sample means important?
A: The sampling distribution of the difference between two sample means is important because it allows researchers to assess whether the observed difference in sample means is statistically significant. This understanding helps in making inferences about the populations from which the samples were drawn.
Q: How is the distribution of differences between sample means under the null hypothesis assessed?
A: The distribution of differences between sample means under the null hypothesis is assessed by:
Repeatedly sampling from both populations.
Calculating the means of these samples.
Finding the difference between the sample means.
Using the z-score formula Z = (mA – mB) – (µA - µB) / √( sA/nA +2 sB/nB) or the t-score formula if population standard deviations are unknown.
Calculating the p-value to determine whether the null hypothesis can be rejected.
