Difference Between Means of Two Independent Samples: Z-test vs T-test
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Questions and Answers

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.

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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?

<p>There should be no relationship between the observations in each group or between the groups.</p> Signup and view all the answers

Why is it important to avoid significant outliers when conducting a z-test or t-test?

<p>Outliers can negatively affect the statistical test, reducing the validity of the result.</p> Signup and view all the answers

What is the sixth assumption for conducting a z-test or t-test on two independent samples?

<p>There must be homogeneity of variances.</p> Signup and view all the answers

What is the assumption related to variances that must be met in ANOVA?

<p>Homogeneity of variances</p> Signup and view all the answers

What test can be used when the assumption of homogeneity of variances has been violated?

<p>Welch test or Brown and Forsythe test</p> Signup and view all the answers

What is the null hypothesis (Ho) in the context of the ANOVA test for the life satisfaction of Male and Female University Students?

<p>There is no significant difference between the life satisfaction of Male and Female University Students.</p> Signup and view all the answers

What is the significance of having a smaller standard deviation (SD) compared to a higher SD?

<p>The smaller the SD, the better.</p> Signup and view all the answers

What statistical test is suitable for situations where homogeneity of variances assumption is violated?

<p>Welch test</p> Signup and view all the answers

What is the sample size threshold that determines a small sample in statistical analysis?

<p>Below 29</p> Signup and view all the answers

What is Cohen's d used for?

<p>Measuring the difference between two group means.</p> Signup and view all the answers

How is Cohen's d interpreted for a very small effect?

<p>0.00 &lt; 0.20</p> Signup and view all the answers

What does One-Way ANOVA test for?

<p>Statistically significant differences between the means of three or more independent groups.</p> Signup and view all the answers

Why is One-Way ANOVA considered an omnibus test?

<p>It tests whether the explained variance in data is significantly greater than the unexplained variance, overall.</p> Signup and view all the answers

What assumptions must be met for One-Way ANOVA?

<ol> <li>The dependent variable must be normally distributed in each group being compared. 2. Independence of observations.</li> </ol> Signup and view all the answers

Why is a post hoc test needed after One-Way ANOVA?

<p>To determine which specific groups differed from each other.</p> Signup and view all the answers

What are some recommended tests of homogeneity of variances?

<p>Cochran’s Test, Hartley’s Test, Levene’s Test</p> Signup and view all the answers

What are the hypotheses for testing the difference between two means?

<p>Ho: 𝜇1 = 𝜇2, Ha: 𝜇1 ≠ 𝜇2</p> Signup and view all the answers

How is the null hypothesis stated for the difference between two means?

<p>Ho: 𝜇1 - 𝜇2 = 0</p> Signup and view all the answers

What do you conclude if p-value is less than 0.05 in hypothesis testing?

<p>Significant</p> Signup and view all the answers

What test is used when the distribution of the scores is not normal?

<p>Mann-Whitney U test</p> Signup and view all the answers

What does a p-value greater than 0.05 indicate in testing for homogeneity of variances?

<p>There is homogeneity of variances</p> Signup and view all the answers

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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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.

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