Educational Statistics and the Central Limit Theorem

Flashcards covering levels of measurement, the Central Limit Theorem, and applications of various statistical tools in research.

Central Limit Theorem (CLT)

A foundational axiom stating that as the sample size increases (typically $n \ngeq 30$), the sampling distribution of the sample mean approaches a normal distribution, regardless of the population distribution's shape.

Nominal Level of Measurement

Variables consisting of categories without order (e.g., sex, blood type), analyzed using frequency, percentage, mode, and chi-square.

Ordinal Level of Measurement

Variables with a rank or order but unequal intervals (e.g., class rank, Likert items), analyzed using median, percentiles, Spearman rho, Mann-Whitney U, and Kruskal-Wallis tests.

Interval Level of Measurement

Numerical data with equal intervals but no true zero (e.g., test scores), analyzed using mean, SD, t-test, ANOVA, and Pearson r.

Ratio Level of Measurement

Numerical data with equal intervals and a true zero (e.g., hours of study), analyzed using mean, SD, t-test, ANOVA, Pearson r, and regression.

Sampling Distribution

A theoretical probability distribution of a statistic (such as the mean) calculated from repeated, identically sized random samples.

Independent Samples t-test

A statistical tool used to compare the mean scores of two independent groups, such as comparing teaching methods.

ANOVA

A statistical tool used to compare the means of 3 or more groups.

Pearson Correlation

A statistical tool used to determine the strength and direction of the relationship between two numerical (quantitative) variables.

Chi-square

A statistical tool used to analyze the relationship between two categorical variables.

Regression

A statistical tool used for the purpose of prediction.

Unbiased Estimator

A characteristic of the sample average where, according to the CLT, the mean of the sample averages equals the true population mean.

Parametric Tests

Statistical tests like z-tests, t-tests, and ANOVA that are justified by the CLT's assumption of normality.

Likert Item

A single survey item usually treated as ordinal, though it may be treated as interval if summed or averaged into a scale.

Positive Correlation

A relationship where both variables tend to move in the same direction; as one increases, the other increases.

Negative Correlation

A relationship where variables move in opposite directions; as one increases, the other decreases.