Inferential Statistics and Hypothesis Testing Guide

Inferential Statistics

Statistical methods to draw conclusions from data.

Statistical Hypothesis

A claim about a population parameter to test.

Null Hypothesis (H0)

Assumes no difference or relationship exists.

Test Statistic

Value calculated to evaluate a hypothesis.

Critical Value

Threshold for rejecting the null hypothesis.

5% Criterion

Probability level for rejecting the null hypothesis.

Sampling Error

Difference between sample statistic and population parameter.

Confidence Level

Degree of certainty in hypothesis testing.

Normal Distribution

Data clustered symmetrically around a mean.

T-Test

Statistical test comparing means between groups.

Degrees of Freedom

Number of independent values in a calculation.

T-Statistic

Calculated value from sample data for t-tests.

One Sample t-Test

Compares sample mean to a known value.

Paired t-Test

Compares means from dependent samples.

Two Sample t-Test

Compares means from independent samples.

F-Test

Tests for equality of variances between samples.

Statistically Significant

Results unlikely due to chance, typically p < 0.05.

Insufficient Evidence

Not enough data to reject the null hypothesis.

Mean

Average value of a data set.

Standard Error

Estimate of the variability of sample means.

Symmetrical Data

Data values evenly distributed around the mean.

Statistical Test

Procedure to evaluate hypotheses using data.

Criminal Court Analogy

Assumes innocence until proven guilty beyond doubt.

Relationship

Connection or correlation between two variables.

Mean Height Example

Comparison of IMSA students' height to national average.

Dependent Samples

Data sets linked by common subjects or conditions.

Independent Samples

Data sets with no connection between subjects.

Descriptive Statistics

Summarizes basic features of data in studies.

Measures of Central Tendency

Estimates the 'middleness' of a data set.

Arithmetic Mean

Average calculated by dividing sum by sample size.

Median

Middle value in ordered data set.

Mode

Most frequently occurring value in data set.

Measures of Variability

Describes dispersion or spread of data.

Range

Difference between maximum and minimum values.

Standard Deviation (SD)

Indicates how much measurements vary around the mean.

Sample Size (n)

Number of data points collected in a data set.

F-test

Tests for significant differences in variance.

P-value

Probability measure to determine statistical significance.

Two Sample T-test

Used when variances of two samples are unequal.

Frequency Distribution

Representation of raw scores in data set.

Histogram

Graphical representation of frequency distribution.

Statistical Population

Complete set of individuals or objects under study.

Statistical Sample

Subset of population used for data collection.

Random Sample

Sample where each individual has equal selection chance.

Relative Frequency

Percentage of scores within a specific range.

Gaussian Curve

Graphical representation of normal distribution.

Degree of Freedom

Number of independent values in a statistical calculation.

Variance

Average of squared differences from the mean.

Mean Deviation

Average of absolute differences from the mean.

Statistical Analysis

Process of collecting and interpreting data.

Hypothesis Testing

Method to determine if a hypothesis is supported.