Study Notes on T-Test for Independent Means

T-Test for Independent Means

  • Introduction to T-Test for Independent Means

    • This statistical test is part of inferential statistics, used to make inferences about the differences between two different groups or samples.

  • Purpose of the T-Test

    • It compares the means of two independent groups to determine if there is a statistically significant difference.
    • Example Groups:
    • Experimental Group: Super vitamin babies.
    • Control Group: Non-super vitamin babies.

  • Research Context Example

    • Study Objective: Investigate differences in the mean age of first steps between the two groups (super vitamin and no vitamin).

  • Terminology

    • The 't' in t-test refers to the t score, which will indicate whether the results are statistically significant.
    • The test is called for independent means because the scores from both groups are obtained from different participants, with no overlap in subjects.
    • Often referred to as independent samples t-test in software like SPSS.

Examples of T-Test Applications

  • Example 1

    • Title: Journaling Study
    • Experimental Group: Participants journaling about traumatic experiences.
    • Control Group: Participants journaling about daily plans.
    • Independent Variable: Type of journal (trauma or daily plans).
    • Dependent Variable: Physical health ratings.
    • Purpose: Compare physical health ratings between the two groups using the independent samples t-test.

  • Example 2

    • Title: Information Processing Experiment
    • Independent Variable: Type of information processing.
    • Group 1: Shallow processors (scanning a word for letter 'e').
    • Group 2: Deep processors (semantically processing the word for pleasantness).
    • Dependent Variable: Memory recall (number of words recalled).
    • Goal: Compare means between shallow processors and deep processors based on the memory recall variable.

Hypothesis Testing in T-Tests

  • Null and Research Hypotheses

    • Null Hypothesis (H0): The populations have equal means.
    • Research Hypothesis (H1): The population means are not equal.
    • Importance: Researchers aim to reject the null hypothesis, indicating a statistically significant difference between group means.

  • Statistical Significance

    • Alpha Level (): Typically set at 0.05 or 0.01.
    • A significance score below the alpha level indicates a statistically significant result:
    • Example: A p-value of 0.032 indicates a 97% confidence that the observed difference is not due to random error.
    • The t-test seeks to establish that observed differences arise from actual effects of the independent variable, rather than chance.

Assumptions of the T-Test

  • Before running an independent samples t-test, certain assumptions must be met:
    • Distribution of data must adhere to specific criteria, which will be reviewed in class.
    • Preliminary analysis of variance is necessary to calculate the t-test.

Calculation Steps for the T-Test

  1. Compute Variance

    • Essential for calculating the t-test; involves basic arithmetic (addition, subtraction, division).

  2. Determine Variance for Each Group's Distribution

    • Calculate variance for Group 1 and Group 2.
    • Example scores: 6.82 (Group 1) and 2.42 (Group 2).

  3. Prepare Combined Variance

    • Add the variances of both groups.
    • Calculate the standard deviation using square root of this combined variance.

  4. Determine Degrees of Freedom

    • Use a table to find the t-score cutoff based on degrees of freedom.

  5. Calculate T-Score

    • Use the means of both groups divided by the standard deviation:
      t = rac{( ext{Mean}1 - ext{Mean}2)}{SD}

  6. Hypothesis Testing

    • Compare the calculated t-score against the critical value to determine whether to reject the null hypothesis.

Effect Size and Statistical Power

  • Effect Size

    • An estimate that quantifies the strength of a phenomenon or difference observed.
    • For t-tests, effect size will help determine the practical significance of findings.

  • Power Analysis

    • Statistical power refers to the probability of correctly rejecting the null hypothesis (detecting an effect if one exists).
    • Can be calculated using power tables or statistical software.

Controversies and Limitations

  • Multiple T-Tests: Conducting numerous t-tests increases the risk of Type I errors (false positives).
    • Known as p-hacking: unprincipled approach seeking significant results.
    • Researchers should exercise caution and consider adjusting their variables or employing multiple dependent variables.

Assignment and Homework

  • Homework Tasks

    • Three problems based on independent samples t-tests.
    • Complete an assumptions worksheet necessary before calculating t-tests.

  • Lab Reports

    • Combine lab reports numbers 7 and 8.
    • Execute a t-test and a paired sample t-test.
    • Clearly identify and restate research hypotheses during calculations.