Dependent-Samples t-Test Overview
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Questions and Answers

What defines dependent samples in hypothesis testing?

  • Samples must consist of more than 100 observations.
  • The samples are assumed to have the same variance.
  • Samples are collected independently from different populations.
  • Each participant's data in one sample is paired with a specific participant's data in another sample. (correct)

    • How is the mean difference calculated in dependent samples?

  • By averaging the differences between each pair of observations. (correct)
  • By multiplying the means of both samples together.
  • By using only the largest and smallest differences.
  • By subtracting the mean of sample A from the mean of sample B.

    • Which of the following is correct regarding hypothesis testing in t-tests for dependent samples?

  • Dependent t-tests cannot have a two-tailed hypothesis.
  • The null hypothesis states that the two sample means are equal. (correct)
  • The alternative hypothesis proposes no effect or difference.
  • Significance levels for one-tailed tests must be set at 0.01.

    • Which formula is used to calculate the t-statistic in dependent-samples t-tests?

    <p>$t = \frac{M_D - 0}{s_D / \sqrt{n}}$</p> Signup and view all the answers

    What is the degrees of freedom (df) for a dependent-samples t-test with 8 pairs of observations?

    <p>7</p> Signup and view all the answers

    What does the null hypothesis (H0) state in a dependent-samples t-test?

    <p>The mean difference is equal to 0.</p> Signup and view all the answers

    Which formula is used to calculate the t-obtained for a dependent-samples t-test?

    <p>$D - ar{D}$</p> Signup and view all the answers

    What does a t-obtained value indicate in hypothesis testing?

    <p>The standardized difference between the sample mean difference and the population mean difference.</p> Signup and view all the answers

    Which step is NOT included in calculating the estimated standard error of the mean difference in a dependent-samples t-test?

    <p>Calculate the population mean difference.</p> Signup and view all the answers

    What is measured by the symbol $s_D^2$ in the context of a dependent-samples t-test?

    <p>The population variance of the difference scores.</p> Signup and view all the answers

    In hypothesis testing, when do you reject the null hypothesis in a dependent-samples t-test?

    <p>When the t-obtained is greater than t-critical.</p> Signup and view all the answers

    Which calculation is necessary to obtain the sample mean difference in a dependent-samples t-test?

    <p>Add together all difference scores and divide by n.</p> Signup and view all the answers

    What characterizes a dependent-samples t-test?

    <p>It requires dependent samples.</p> Signup and view all the answers

    What is the first step when calculating the mean difference in a dependent-samples t-test?

    <p>Find the difference for each pair of scores.</p> Signup and view all the answers

    In hypothesis testing using a dependent-samples t-test, what is the null hypothesis (H0)?

    <p>The means of the two populations are equal.</p> Signup and view all the answers

    What does the formula D = X1 - X2 represent in the context of a dependent-samples t-test?

    <p>The difference between each pair of scores.</p> Signup and view all the answers

    What is required for the application of a dependent-samples t-test concerning sample size?

    <p>Equal sample size is necessary.</p> Signup and view all the answers

    For both dependent and independent-samples t-tests, what is one common requirement for the dependent variable?

    <p>It must be normally distributed.</p> Signup and view all the answers

    When conducting a dependent-samples t-test, what is the requirement regarding the variance?

    <p>Homogeneity of variance is necessary.</p> Signup and view all the answers

    Which of the following tests would show the best fit if comparing the means of two related groups?

    <p>Dependent-samples t-test</p> Signup and view all the answers

    Study Notes

    Dependent-Samples t-Test Overview

    • A statistical test used to compare means of two related groups
    • Used for matched-groups designs and within-subjects designs
    • Assesses if there is a significant difference between means of related groups

    Comparison of Between-Subjects and Within-Subjects Designs

    • Between-Subjects Design:
      • Different participants are exposed to different levels of the independent variable (IV)
      • Each person serves in only one condition
      • Independent or matched samples are used in each condition
    • Within-Subjects Design:
      • One group of participants experiences all levels of the IV
      • Each participant serves in all conditions of the IV
      • The same sample is used in all conditions

    Appropriate Statistics

    • Independent-Samples Design: independent-samples t-test
    • Matched-Groups Design: dependent-samples t-test
    • Within-Subjects Design: dependent-samples t-test

    Dependent-Samples t-Test Requirements

    • Randomly selected samples
    • Dependent variable (DV) measured using ratio or interval scale
    • DV is normally distributed
    • Homogeneity of variance
    • Requires dependent samples (and equal sample sizes)

    General Model for Z-Test and Single-Sample t-Test

    • Compares a sample to a population
    • Hypotheses are tested against an original population and a treated population

    General Model for Independent-Samples t-Test

    • Compares two independent samples to see if they significantly differ
    • Two populations are compared
    • Null hypothesis (HO): μ₁ - μ₂ = 0
    • Alternative hypothesis (HA): μ₁ ≠ μ₂

    General Model for Dependent-Samples t-Test

    • Compares two related samples to see if there is a significant difference
    • Compares pairs of scores from the same individuals
    • Null hypothesis (HO): μD = 0
    • Alternative hypothesis (HA): μD ≠ 0

    Definitional Formulas

    • Single-Sample t-Test: tobt = (X - μ) / sX
    • Dependent-Samples t-Test: tobt = (D - μD) / sD

    t-Tests Formulas

    • Single-Sample t-Test: tobt = (sample mean - population mean) / estimated standard error
    • Dependent-Samples t-Test: tobt = (sample mean difference - population mean difference) / estimated standard error of the mean difference

    Steps for a Dependent-Samples t-Test

    • Step 1: Calculate the estimated variance (sD2) of the population using ∑(D - D̄)2 / (n - 1)
    • Step 2: Calculate the estimated standard error (sD) of the mean difference using √sD2 / n
    • Step 3: Calculate the t-obtained (tobt) using (D̄ - μD) / sD

    Hypothesis Testing

    • Step 1: State the hypotheses (research and statistical)
    • Step 2: Set the significance level (α = .05) and determine the critical t-value (tcrit)
    • Step 3: Select and compute the appropriate statistic (dependent-samples t-test)
    • Step 4: Make a decision (reject or fail to reject null hypothesis based on comparing tobt and tcrit)
    • Step 5: Report statistical results (t(df) = tobt, p < .05)
    • Step 6: Write a conclusion (IV and DV relationship in words)
    • Step 7: Compute estimated effect size (d)
    • Step 8: Compute r2: Measures the proportion of variance in the DV explained by the IV

    Degrees of Freedom

    • Single-Sample t-Test: df = n - 1, where n is the number of scores
    • Dependent-Samples t-Test: df = n - 1, where n is the number of pairs of scores

    Effect Size (d) Interpretation

    • 0.2: Small effect
    • 0.5: Medium effect
    • 0.8: Large effect

    Percentage of Variance Explained (r2) Interpretation

    • 0.01: Small effect
    • 0.09: Medium effect
    • 0.25: Large effect

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    Description

    This quiz provides an overview of the dependent-samples t-test, a statistical test used to compare the means of two related groups. It covers the differences between between-subjects and within-subjects designs and discusses the appropriate statistical tests for each design. Test your understanding of these concepts and their applications in research.

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