Statistics: T-tests and Research Designs

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Questions and Answers

What is the main advantage of using a within-subject design?

It allows testing of fewer participants.

It eliminates individual differences. (correct)

It prevents any form of drop out.

It is always more cost-effective.

Which of the following describes matched pairs design?

It is less powerful than within-subject design.

Each pair is matched on important characteristics. (correct)

All participants take part in every condition.

Participants are randomly assigned to conditions.

What is a potential drawback of a within-subject design?

It always requires more participants.

It does not account for individual differences.

It can suffer from order effects. (correct)

It is less powerful than between-subject designs.

What should be the minimum number of participants for reliable results in a paired samples t-test?

12 Signup and view all the answers

Which test is used to compare means in a within-subject or matched pairs design?

Paired samples t-test Signup and view all the answers

Which of the following is NOT an assumption of parametric tests like the t-test?

Sample sizes larger than 30 Signup and view all the answers

What should you do if your data violate the assumptions of a paired samples t-test?

Run a non-parametric test. Signup and view all the answers

If the assumptions for a t-test are not met, what is the nature of the test?

It becomes a non-parametric test. Signup and view all the answers

Which of the following is a condition for using the binomial test?

Scores should be from a random sample. Signup and view all the answers

In a chi-square test of independence, what is the minimum sample size requirement?

<ol start="40"> <li></li> </ol> Signup and view all the answers

What does a significant result in a t-test indicate regarding the null hypothesis?

There is little chance of obtaining the observed difference if the null hypothesis is true. Signup and view all the answers

What is a key feature of the order effects in within-subjects designs?

They can bias the results due to the sequence of conditions. Signup and view all the answers

What type of hypothesis is being tested when you predict a specific direction of an effect?

One-tailed hypothesis. Signup and view all the answers

In a paired samples t-test, what does it assess?

The differences between the scores of paired observations. Signup and view all the answers

What is a key assumption of the chi-square goodness-of-fit test?

Each category must have an expected N of 5 or above. Signup and view all the answers

What is one characteristic of parametric tests compared to non-parametric tests?

Parametric tests are sensitive to assumption violations. Signup and view all the answers

What does the binomial test compare?

Observed proportions with expected proportions. Signup and view all the answers

What would you do if the expected frequency in a category is less than 5 during a chi-square test?

Use Fisher's exact test instead. Signup and view all the answers

Which of the following scenarios would require the use of the Wilcoxon signed ranks test?

Assessing differences between related samples with non-normal data. Signup and view all the answers

Study Notes

T-tests

Determine the likelihood of an observed difference between conditions if the null hypothesis is true.
Assess whether the variance between conditions is larger than the variance within conditions.
Calculate t-value by dividing the variance explained by the independent variable (IV) by the unexplained variance.

Within-subjects Design

All participants participate in all conditions.
Example: Comparing scores in a real-world situation versus a simulated environment; comparing essay grades before and after a workshop.
Advantages: Accounts for individual differences, more powerful, fewer participants needed, often preferred for longitudinal studies.
Disadvantages: Potential order effects (practice or fatigue), participant dropout.

Matched-Pairs Design

Participants are matched on relevant characteristics (e.g., IQ, gender, age).
One participant from each pair is assigned to each condition.
Advantages: Combines benefits of within and between-subjects designs, eliminates order effects, accounts for individual differences.
Disadvantages: Time-consuming and difficult to match participants perfectly.

Paired Samples T-test

Compares means of two conditions in within-subjects or matched-pairs designs.
Calculates the probability of obtaining a mean difference as large or larger by chance.
Assumes interval or ratio data, a sample size of at least 12, normally distributed differences.

Assumptions and Testing

Interval or ratio data for the dependent variable.
Sample size of at least 12 participants.
Differences between conditions are normally distributed.
Verify normality of differences using the Shapiro-Wilk test (non-significant p-value > 0.05 indicates normality).

Non-parametric Alternatives

If assumptions are not met, use non-parametric tests.
Wilcoxon signed-ranks test for related samples: Alternative to the paired samples t-test if data violates assumptions.

Expected Frequencies (Chance Levels)

Probabilities vary depending on the context (e.g., coin flip = 50%, dice roll = 16.67%).

Binomial Test

Determines if an observed proportion differs significantly from an expected proportion by chance.
Assumes nominal data, a single dichotomy, random sampling, independent scores, known expected distribution, and normality.

Chi-square Test of Independence

Compares proportions between two groups with nominal data.
Assumes nominal data, random sampling, independent scores, and expected frequencies of 5 or more in each category.
Calculates expected frequency using marginal totals and sample size.

Fisher's Exact Test

Non-parametric alternative to the chi-square test of independence, useful when assumptions of chi-square aren't met.

One-tailed vs. Two-tailed Hypotheses

One-tailed: Predicts a difference in a specific direction.
Two-tailed: Predicts a difference without specifying direction.

Chi-square Goodness-of-Fit Test

Compares observed proportions to expected proportions with nominal data and multiple levels.
Assumes nominal data, random sampling, independent scores, and expected frequencies of 5 or more in each category.

Reporting p-values

Report p-values to three decimal places, use lower case italicized p and the exact value, e.g p=0.041, not p < 0.05.

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Description

This quiz covers T-tests, including their application in determining variance and assessing differences under the null hypothesis. It also explores within-subjects and matched-pairs designs, highlighting their advantages and disadvantages in research. Perfect for those studying statistics and research methodologies.