T Tests Notes

Independent Samples t-tests Notes

Instructor Information

  • Presenter: Nick Carcioppolo, PhD

  • Course Code: COS 355

Presentation Outline

  • What is an independent samples t-test?

  • Conducting and interpreting t-test output on JASP

  • Exercise on computing and interpreting t-tests.

  • Open CorrDat dataset in JASP

Origins of the t-test

  • Core concept discussed:

    • The Guinness Brewery’s role in the invention of significant statistical methods, referenced from Scientific American.

Definition of a t-test

  • Independent Sample t-test:

    • An inferential statistic used to determine whether the means for two groups of scores differ statistically.

    • Key question: Can differences between two mean scores be generalized to the larger population?

Requirements for Applying t-test

  • Independent Variable (IV): Categorical variable with 2 levels

  • Dependent Variable (DV): Quantitative variable

Analysis Preparation

  • Dataset Description:

    • CorrDat Dataset: Analyzed using a boxplot of conflict-dominating style split by gender.

    • Discussion Questions:

    • What do you observe?

    • What hypothesis can be proposed?

Hypothesis Formulation

  • Hypothesis 1 (H1): Men will be more likely to use a dominating conflict style than women.

Steps for Conducting t-tests in JASP

  1. Access t-tests Menu:

    • Select “Independent Samples t Test” in the classical test menu.

  2. Select Dependent Variable (DV):

    • Variable: “CSDomin”

    • Transfer to the dependent variable(s) box.

  3. Select Grouping Variable (IV):

    • Variable: “gender” (demo2)

    • Transfer to the Grouping Variable box.

  4. Outputs to obtain:

    • a. Effect size (Cohen’s d)

    • b. Descriptives

    • c. Boxplot (optional; beneficial for interpreting output and ensuring correct results interpretation)

Running Your Analysis

  • Issues:

    • Address any data-related issues encountered.

    • Review the codebook for accurate data labeling.

    • Clean data in Excel if necessary after closing JASP.

Summary of Findings

  • Descriptive Statistics:

    • Group Descriptives:

    • Male:

      • N = 242

      • Mean (M) = 3.211

      • Standard Deviation (SD) = 0.703

      • Standard Error (SE) = 0.045

    • Female:

      • N = 663

      • Mean (M) = 3.093

      • Standard Deviation (SD) = 0.758

      • Standard Error (SE) = 0.029

  • Independent Samples T-Test Output:

    • Test Variable: csdomin

    • t = 2.106

    • df = 903

    • p = 0.035

    • Cohen's d = 0.158

    • Note: Conducted using Student's t-test.

Write-up of Results

  • Hypothesis: Males are more likely to exhibit a dominating conflict style than females.

  • Method:

    • An independent sample t-test was performed with gender as the IV and conflict dominating style as the DV.

  • Results:

    • Males (M = 3.21; SD = 0.70; n = 242) showed a greater likelihood of using a dominating conflict style compared to females (M = 3.09; SD = 0.76; n = 663).

    • Statistically significant difference was observed: t(903) = 2.11, p = 0.04, with a small effect size (Cohen’s d = 0.16).

Conclusion

  • The results indicate that males tend to employ dominating conflict styles more than females, pointing to a small effect size in this difference.

  • For t-tests, the report should include:

    • Restated hypothesis

    • Identification of IV and DV

    • Limitations on the sample, if applicable

    • Full details of analyzed statistics: M, SD, N for each group; test statistic, df, value, p-value, effect size, etc.

Understanding Effect Size

  • Importance:

    • The statistical significance (p-value) indicates the probability that a difference or association exists but does not convey the difference's magnitude.

  • Calculation of Effect Size:

    • Necessary to estimate the size of the effect in addition to the significance of the results.

Cohen's d

  • Definition:

    • Cohen’s d indicates the difference between two mean scores expressed in standardized units (standard deviations).

  • Utility:

    • Used particularly when comparing categorical IVs in relation to scores on an outcome DV.

  • Magnitude Relation:

    • Addresses the magnitude of the t-test statistic while adjusting for sample size.

Formula for Cohen's d

d=X<em>mean,experimental−X</em>mean,controlSpooledd = \frac{X<em>{mean, experimental} - X</em>{mean, control}}{S_{pooled}}

  • Where:

    • (X_{mean}): Mean of each group

    • (S_{pooled}): Pooled standard deviation

Interpretation Conventions for Cohen's d

  • In social/behavioral sciences:

    • Small Effect: around 0.20 (range 0.15-0.39)

    • Medium Effect: around 0.50 (range 0.40-0.74)

    • Large Effect: around 0.80 (range 0.75-1.09)

Additional Exercises

  • Next Exercise:

    • Utilize the CorrDat dataset to create and test a hypothesis regarding the relationship between gender and verbal aggressiveness.

    • Analyze and interpret results for statistical significance and effect size; confirm whether it supports your hypothesis.

Homework Assignment

  • Task:

    • Develop a hypothesis connecting gender to conflict with a mother.

    • Run the necessary analysis and compile results in a paragraph format.

  • Variables in JASP to be used: Sex, momconfl

  • Submission: Due on Blackboard by the next class, including:

    1. Formulated hypothesis

    2. Write-up of results

    3. Analysis output from JASP