Student's t-Test Vocabulary

Flashcards on Student's t-Test

Student's t-Test

A statistical test used to determine if there is a significant difference between the means of two groups when the population standard deviation is unknown.

Estimated SEM

Sample standard deviation divided by the square root of the sample size. Represented as: 𝑠𝑥ҧ= 𝑠 / √𝑛

t-statistic

A statistic calculated when the population standard deviation is unknown, using the sample standard deviation to estimate the standard error of the mean. Represented as: 𝑡𝑥ҧ= (𝑥ҧ − 𝜇𝑥ҧ) / 𝑠𝑥ҧ = (𝑥ҧ − 𝜇𝑥ҧ) / (𝑠 / √𝑛)

William S. Gosset

Statistician who worked for Guinness Brewery and published under the pseudonym 'Student'; developed the t-distribution.

Degrees of Freedom (df)

A parameter that affects the shape of the t-distribution, related to the sample size. Calculated as: 𝑑𝑓 = total n - number of samples. For a one-sample study: df = n – 1.

t-Distribution

A family of distributions that are bell-shaped and symmetrical, but flatter and have higher probabilities in the tails compared to the z-distribution. The shape depends on the degrees of freedom.

Critical t

The value from the t-distribution table used to determine statistical significance, based on the alpha level and degrees of freedom.

One-Sample t-Test

A statistical test used to compare the mean of a sample to a known population mean.

Independent-Measures Design

Also known as between-subject design or unpaired test. Separate sample is used for each population.

Repeated-Measures Design

Also known as within-subject design or paired test. The same sample is tested for all treatments.

Assumptions of Independent-Samples t-Test

Normality, Homogeneity/ equality of variance (the populations from which samples are selected have equal variances in the DV), and Independence (samples were randomly selected from the population).