Week 3 - Lecture 3 Flashcards
what are the 2 types single sample tests?
-** Goal**: compare the *sample mean *to a *known population mean *
**Test types: **
- z-test: population variance is known *
- t-test: *population variance is *unknown *
what are the 2 types of two-sample tests?
Comparison between two means: **
- repeated measures (within-subjects): *same participants in both conditions* (e.g. comparing test scores before and after treatment)
- independent groups (between-subjects): **different participants in each condition (e.g. comparing stress levels between two groups reading different articles)
How do you do a repeated measures t-test (within-subjects)?
Example: investigating the effect of a treatment on social anxiety
- hypothesis: social anxiety before treatment vs. after treatment
- null hypothesis (H0): no difference between before and after treatment
- alternative hypothesis (H1): difference exists between before and after treatment
what are the steps for calculating a repeated measures t-test (within-subjects)?
- state hypotheses in words and symbols
- **calculate the difference (D) scores **for each participant (X1-X2)
- calculate the standard deviation (SD) of the difference scores
- calculate the **standard error (SE) **of the difference scores
- calculate the t-value using the formula t = D/SE
- compare the obtained t-value with the critical t-value from the t-tables
- make a** decision **(reject or fail to reject the H0)
- Interpret results
-** critical t-value: Based on degrees of freedom (df = N-1)
- Interpretation: **If t-obtained > t-critical, reject H0 (treatment had an effect)
How do you do an independent groups t-test (between-subjects)?
Example: testing whether reading an article about COVID-19 leads to more panic purchasing than reading about the fly
hypothesis:
- Null (H0): no difference in the number of items purchased between the two conditions
- Alternative (H1): a difference exists between the conditions
what are the steps for calculating an independent groups t-test (between subjects)?
- state hypotheses in words and symbols
- calculate the sum of squares (SS) for each group
- calculate the pooled variance
- calculate the **standard error (SE) **of the difference between means
- calculate the** t-value **
- use the** t-tables **to find the critical t-value
- compare the obtained t-value to the critical t-value
-
interpret results
- critical t-value: based on the degrees of freedom (df = N1 + N2 - 2)
- interpretation: If t-obtained > t-critical, reject H0 (a significant difference exists)
What are key assumptions for the validity of the statistical tests, particularly t-tests?
1. Normality **
- *sampling distribution *should be normal *
- if the sample size is large enough (n > or = 30), the test is robust to violations
**2. Random sampling **
- data should be randomly sampled* to ensure generalizability *
**3. Independence of Observations **
- observations* in different groups must be *independent *
4. For Independent Groups t-test:
- Homogeneity of Variance: Assumes that the *variance in both groups are equal *
why type of t-test is the following scenario?
Investigating the impact of a treatment on reducing social anxiety in children
repeated measures t-test
- procedure: measure anxiety before and after treatment
- key result: significant reduction in social anxiety post-treatment
what type of t-test is the following scenario?
Comparing panic purchasing between participants reading about COVID-19 vs the flu
Independent Groups t-test
- procedure: participants read one of two articles and then purchased items
- key result: significant difference in items purchased
what are the critical differences between Repeated Measures and Independent Groups t-tests?
Repeated Measures t-test:
- same participants in both conditions
- focus on the difference between two measurements for the same participants
Independent Groups t-test:
- different participants in each condition
- focus on comparing the means between two independent groups
