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Questions and Answers
What is the first assumption for conducting a z-test or t-test on two independent samples?
What is the first assumption for conducting a z-test or t-test on two independent samples?
The dependent variable must be measured on a continuous scale.
Give an example of a variable that meets the first assumption for a z-test or t-test.
Give an example of a variable that meets the first assumption for a z-test or t-test.
IQ score
What is the second assumption for conducting a z-test or t-test on two independent samples?
What is the second assumption for conducting a z-test or t-test on two independent samples?
The independent variable must consist of two categorical, independent groups.
What does it mean for observations to be independent in the context of z-test or t-test?
What does it mean for observations to be independent in the context of z-test or t-test?
Why is it important to avoid significant outliers when conducting a z-test or t-test?
Why is it important to avoid significant outliers when conducting a z-test or t-test?
What is the sixth assumption for conducting a z-test or t-test on two independent samples?
What is the sixth assumption for conducting a z-test or t-test on two independent samples?
What is the assumption related to variances that must be met in ANOVA?
What is the assumption related to variances that must be met in ANOVA?
What test can be used when the assumption of homogeneity of variances has been violated?
What test can be used when the assumption of homogeneity of variances has been violated?
What is the null hypothesis (Ho) in the context of the ANOVA test for the life satisfaction of Male and Female University Students?
What is the null hypothesis (Ho) in the context of the ANOVA test for the life satisfaction of Male and Female University Students?
What is the significance of having a smaller standard deviation (SD) compared to a higher SD?
What is the significance of having a smaller standard deviation (SD) compared to a higher SD?
What statistical test is suitable for situations where homogeneity of variances assumption is violated?
What statistical test is suitable for situations where homogeneity of variances assumption is violated?
What is the sample size threshold that determines a small sample in statistical analysis?
What is the sample size threshold that determines a small sample in statistical analysis?
What is Cohen's d used for?
What is Cohen's d used for?
How is Cohen's d interpreted for a very small effect?
How is Cohen's d interpreted for a very small effect?
What does One-Way ANOVA test for?
What does One-Way ANOVA test for?
Why is One-Way ANOVA considered an omnibus test?
Why is One-Way ANOVA considered an omnibus test?
What assumptions must be met for One-Way ANOVA?
What assumptions must be met for One-Way ANOVA?
Why is a post hoc test needed after One-Way ANOVA?
Why is a post hoc test needed after One-Way ANOVA?
What are some recommended tests of homogeneity of variances?
What are some recommended tests of homogeneity of variances?
What are the hypotheses for testing the difference between two means?
What are the hypotheses for testing the difference between two means?
How is the null hypothesis stated for the difference between two means?
How is the null hypothesis stated for the difference between two means?
What do you conclude if p-value is less than 0.05 in hypothesis testing?
What do you conclude if p-value is less than 0.05 in hypothesis testing?
What test is used when the distribution of the scores is not normal?
What test is used when the distribution of the scores is not normal?
What does a p-value greater than 0.05 indicate in testing for homogeneity of variances?
What does a p-value greater than 0.05 indicate in testing for homogeneity of variances?
Study Notes
Assumptions for z-test and t-test
- The dependent variable must be measured on a continuous scale (interval or ratio level)
- The independent variable must consist of two categorical, independent groups
- The observations must be independent
- There should be no significant outliers
- The dependent variable should be approximately normally distributed for each group of the independent variable
- There must be homogeneity of variances
Testing for Homogeneity of Variances
- If homogeneity of variances fails, use Welch or Brown and Forsythe test
- Alternatively, use Kruskal-Wallis H Test
- Welch test is best in most situations
Types of Tests
- Parametric tests: z-test, t-test (1 - 33.33%, 2 - 66.66%)
- Non-Parametric test: Mann Whitney U-test
ANOVA
- One-way ANOVA: used to determine whether there are any statistically significant differences between the means of three or more independent groups
- One-way ANOVA compares the means between the groups and determines whether any of those means are statistically significantly different from each other
- Assumptions: dependent variable must be normally distributed in each group, homogeneity of variances
Interpreting Cohen's d
- 0.00 < 0.20: very small effect
- 0.21 < 0.50: small effect
- 0.51 < 0.80: medium effect
- 0.81 or higher: large effect
Hypotheses
- H₀: µ1 = µ2
- Hₐ: µ1 ≠ µ2
Testing the Difference Between Two Means
- Use z-test or t-test
- Remember: if p > 0.05, Not Significant; if p < 0.05, Significant
Testing for Normality of Data
- Shapiro Wilk Test (n < 50)
- Kolmogorov-Smirnov (n ≥ 50)
- Remember: if p > 0.05, Normally Distributed; if p < 0.05, Not Normally Distributed
Testing for Homogeneity of Variances
- Levene's Test
- Remember: if p > 0.05, There is homogeneity of variances; if p < 0.05, There is no homogeneity of variances
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Description
Learn about the differences between Z-test and T-test when comparing means of two independent samples. Explore the assumptions required for each test and understand when to use them.
