Module 7

Uniform Distribution

A distribution where all values occur approximately equally often, resembling a rectangular shape in a histogram.

Poisson Distribution

A discrete probability distribution applicable when counting occurrences during a given time interval, distance, or area.

Normal Distribution

A distribution characterized by a bell-shaped curve, where the mean, median, and mode are equal.

Skewness

The measure of asymmetry in a distribution, indicating whether scores are more clustered to one side of the mean.

Empirical Rule

A statistical rule stating that almost all values lie within three standard deviations of the mean in a normal distribution.

Sampling Distribution

A theoretical probability distribution of sample estimates based on many possible samples of a certain size.

Central Limit Theorem

A theorem stating that the sampling distribution of the mean approaches a normal distribution as the sample size becomes large.

Parametric Tests

Statistical tests that assume data follows a certain distribution, typically the normal distribution.

Nonparametric Tests

Statistical tests that do not assume a specific distribution; used when parametric test conditions are not satisfied.

Chi-Squared Test

A statistical test used to determine whether there is a significant association between two nominal variables.

Hypothesis Testing

A process used to determine the validity of a hypothesis by comparing data against a null hypothesis.

Null Hypothesis

The hypothesis that there is no effect or difference; it is what we seek to test against.

Alternative Hypothesis

The hypothesis that indicates the presence of an effect or difference; it is what we aim to support.

Significance Level (α)

The threshold for determining whether a p-value indicates statistical significance, commonly set at 0.05.

P-Value

The probability of obtaining test results at least as extreme as the observed results under the null hypothesis.

Levene’s Test

A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Independent Samples T-Test

A parametric test used to compare the means of two independent groups.

Mann-Whitney U Test

A nonparametric test used to compare differences between two independent groups.

Wilcoxon Signed-Rank Test

A nonparametric test used to compare two related samples or repeated measurements.

Kruskal-Wallis Test

A nonparametric test used to compare three or more independent groups.

Spearman’s Rank Correlation

A nonparametric measure of rank correlation, assessing how well the relationship between two variables can be described.

Kendall’s Tau

A nonparametric measure of rank correlation, assessing how well the relationship between two variables can be described. It’s like Spearman rank but for smaller samples and can handle tied ranks more effectively.

Chi-Squared Test of Independence

A chi-squared test used to determine if there is a significant relationship between two categorical variables.

Effect Size

A quantitative measure of the magnitude of a phenomenon, often used to indicate the strength of an observed effect.

Categorical Variables

Variables that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group.

Ordinal Variables

Variables that represent ordered categories; intervals between values are not necessarily equal.

Nominal Variables

Variables that represent categories without a specific order; they are also called categorical variables.

Histogram

A graphical representation of the distribution of a dataset, showing the frequency of data points within specified intervals.

Test Statistic

A standardized value that is calculated from sample data during a hypothesis test.

Mutually Exclusive Events

Events that cannot occur at the same time; if one event occurs, the other cannot.

Expected Frequencies

The theoretical frequency of outcomes expected if the null hypothesis is true.

Observed Frequencies

The actual frequencies observed in the data for each category.

Type I Error

The error made when a true null hypothesis is incorrectly rejected.

Type II Error

The error made when a false null hypothesis is not rejected.

Asymptotic P-Value

The p-value that is estimated under certain conditions of large sample sizes, simplifying calculations.

Assumptions of Parametric Tests

Conditions that need to be met for parametric tests to be valid, such as normality, homogeneity of variances, and interval data.

Power of a Test

The probability that it correctly rejects a false null hypothesis; ability to detect an effect when there is one.

Normality Assumption

The assumption that data follows a normal distribution; crucial for many parametric tests.

Random Sampling

A sampling method in which each member of the population has an equal chance of being selected.

Confidence Interval

A range of values derived from a sample, likely to contain the value of an unknown population parameter.

Response Variable

The dependent variable that is being tested and measured in an experiment.

Explanatory Variable

The independent variable that is used to explain variations in the response variable.

Box Plot

A standardized way of displaying the distribution of data based on a five-number summary.

Crosstabulation

A method used to summarize the relationship between two categorical variables.

Post Hoc Tests

Statistical tests conducted after an analysis of variance (ANOVA) to determine which specific group means are different.

Effect Size Measures

Quantitative measures that are used to estimate the size of an effect or the strength of a phenomenon.