Week 8: Inferential statistics and tests of difference (t tests)

Name factors involved with descriptive statistics?

• To describe the sample, such as arousal levels.

• Uses means, median, mode, variance, frequencies (depending on data type)

• Describing data in specific sample

• Can be presented in a table or diagram etc

Name some factors involved with inferential statistics

• Tells us something about the population based on the sample

• Aims at drawing conclusions based on the data from the sample

• Uses various statistical tests- make assumptions about the characteristics of data

• Trying to make generalisations from the data to the wider population

What does the p-value represent in inferential statistics?

The probability of observing the effect as large as observed, or larger, if the null hypothesis is true.

What is the typical threshold for rejecting the null hypothesis?

p < 0.05.

What are parametric tests based on?

• Population parameters

• Assumptions about the underlying population data.

• Assumption that our samples are similar to underlying probability distributions, e.g. normal distribution

• → Larger the sample, more likely the data will achieve a normal distribution

What is a key feature of non-parametric tests?

They do not make strict assumptions about the data distribution.

→ Don’t need to have a normal distribution to perform a non-parametric test

What are advantages of parametric tests?

• More assumptions

• Less universal

• Larger power (can detect effects with small samples)

What are disadvantages of non-parametric tests?

• Fewer assumptions

• More universal - can always be applied

• Lower power (larger samples required to detect effects)

Name some assumptions for parametric tests

1. The scale which we measure the dependent variable on should be interval or ratio level data

2. The populations the sample are drawn from should be normally distributed - influenced by sample size

3. The variances of the populations should be approximately equal (homogeneity of variances- today) if comparing more than one group (around the mean)

4. No outliers or extreme scores: can be screened

-> Violation of any of these would require the use of non-parametric tests

Who developed the t-test?

William Gosset in 1908.

→ He developed the idea of how to make inferences about differences in populations based on differences between small samples

When are t tests used?

We want to compare differences in means:

• 2 separate groups (independent/repeated measures)

• 1 group measured on 2 occasions

• Whether 1 group differs from a specific mean

What is the null hypothesis for t-tests?

The population means from the two groups are equal.

What is the research hypothesis for t-tests?

The population means from the two groups are not equal.

What does degrees of freedom refer to in t-tests?

The number of individual scores that can vary without changing the sample mean.

What is a one-tailed t-test?

A test that predicts the direction of the difference between groups.

What is a two-tailed t-test?

A test that does not predict the direction of the difference between groups.

What is the purpose of the repeated measures t-test?

To compare the same participants under two different conditions.

What is Cohen's d used for?

To measure the effect size in t-tests.

What should be reported when formally reporting statistical results?

Type of test performed, test statistic, statistical significance, mean difference, and effect size.

What does Levene's test check for?

Homogeneity of variances between groups.

What is the output of the paired samples t-test in SPSS?

Descriptive statistics, paired samples correlation, and paired samples test results.

What is the difference between independent and repeated measures t-tests?

Independent t-tests compare different groups, while repeated measures t-tests compare the same group under different conditions.

What does a significant p-value (p < 0.05) indicate?

That there is a statistically significant difference between the groups being compared.

What is the effect size in the context of t-tests?

A standardized measure of the magnitude of an effect, indicating how many standard deviations the means differ by.