Lecture 11 - Independent groups t-tests, assumptions of t-tests, & confidence intervals Flashcards
What is Cohen’s d and how is it used in comparing two means?
Cohen’s d is a measure of effect size that expresses the difference between two means in terms of standard deviations. It is calculated using the formula:
- see photo
- where M1 and M2 are the means of the two groups, and s pooled is the pooled standard deviation. Cohen’s d is used alongside independent groups t-tests to determine the strength of the difference between two groups
Explain the difference between d and t in the context of effect size
d is a measure of effect size that expresses the difference in standard deviations and is not affected by sample size. t is a test statistic that expresses the difference in standard errors and will be larger in larger samples. This means d can be extreme even in small samples, while t might still be non-significant.
What is the logic behind the independent groups t-tests?
the independent groups t-test is used to determine if the means from two separate groups of participants are significantly different from each other. It tests how likely a given difference between two sample means would be if both samples were drawn from the same population.
outline the steps involved in conducting an independent groups t-test
- state the statistical hypotheses:
- H0 : μ1= μ2 and H1: μ ≠ μ2 - calculate the estimated variance based on both samples:
- see photo - calculate the pooled variance from both estimates:
- see photo - Calculate the variance of both sampling distributions
- see photo - calculate the standard error of the difference
- see photo - Calculate t-obtained:
- see photo - find t-critical given α and df total:
- see photo - Compare t-obtained to t-critical and interpret results:
- see photo
provide an example of an independent groups t-test scenario and the steps to solve it
Scenario:
When learning to ride the half-pipe on a skateboard, is it better to practice in a few long sessions (massed practice) or in many shorter sessions (spaced practice)? An independent groups experiment was conducted was massed practice (20 participants) and spaced practice (15 participants). the dependent variable was the number of successful repetitions on the half-pipe immediately after learning.
Steps:
- see photo
what are the statistical assumptions of the independent groups t-test?
the assumptions of the independent groups t-test are:
- normality of sampling distributions
- homogeneity of variance between conditions
(𝑠1≈ 𝑠2)
- independence of observations (separate people in each group)
How do the assumptions differ between independent groups t-test and repeated measures t-test?
- independent groups t-test: normality of sampling distributions, homogeneity of variance, and independence of observations
- repeated measures t-test: Normality of sampling distributions, homogeneity of variance between conditions, and justified pairing of raw scores (two scores per participant)
what is the concept of confidence intervals in hypothesis testing?
confidence intervals provide a range of values within which the true mean (or mean difference) is likely to lie with a certain level of confidence (e.g. 95%). It offers an alternative to traditional significance testing by showing the range within which we can be confident the true mean lies
How are confidence intervals calculated?
confidence intervals are calculated using the formula:
- see photo
- where M is the sample mean, t critical is the critical t value, and Sm is the standard error of the mean
Provide an example of calculating a 95% confidence interval
In 2000, the average level of CO2 from 25 air tests was 360 pp, with a standard error of 11. To calculate the 95% confidence interval:
- see photo
- therefore, the 95% confidence interval is (337.30, 382.70)
