Understanding Inferential Statistics and Research Methods

Inferential Statistics

Analyzes sample data to generalize about populations.

Sample

Subset of individuals from a larger population.

Population

Entire group from which samples are drawn.

Hypothesis Testing

Process of confirming or rejecting a hypothesis.

Null Hypothesis

Indicates no relationship between variables.

Alternative Hypothesis

Indicates a relationship between variables exists.

Sampling Error

Chance variation in sample results.

Sample Bias

Samples that misrepresent the population.

Sample Mean

Average value of a sample's data points.

Population Mean

Average value of a population's data points.

Sample Standard Deviation

Measure of sample data variability.

Population Standard Deviation

Measure of population data variability.

Statistical Tests

Tools for analyzing different types of data.

Interval Data

Numerical data with meaningful intervals.

Ratio Data

Numerical data with a true zero point.

Nominal Data

Categorical data without a specific order.

Ordinal Data

Categorical data with a defined order.

Research Hypothesis

Statement predicting a relationship between variables.

Testing Procedure

Method to evaluate hypothesis validity.

Significant Finding

Result unlikely due to chance alone.

Reliability of Differences

Consistency of observed differences across studies.

Generalization

Applying findings from a sample to a population.

Research Project

Systematic investigation to answer a specific question.

Confirming Hypothesis

Supporting research hypothesis through statistical tests.

Variable

Any factor that can change or vary.

Independent Variable

Factor manipulated to observe effects.

Dependent Variable

Factor measured to assess impact of independent variable.

Tests of Significance

Procedures to accept or reject hypotheses.

Level of Significance

Probability threshold for rejecting a hypothesis.

p-Value

Probability indicating evidence against null hypothesis.

Critical Region

Area where null hypothesis is rejected.

Acceptance Region

Area where null hypothesis is not rejected.

One-Tailed Hypothesis

Predicts direction of expected difference.

Two-Tailed Hypothesis

Tests for differences without directional prediction.

Directional Hypothesis

Alternative hypothesis predicting specific direction.

Nondirectional Hypothesis

Alternative hypothesis predicting any difference.

Type I Error

Rejecting null hypothesis when it is true.

Type II Error

Accepting null hypothesis when it is false.

Parametric Tests

Assume population parameters for statistical testing.

Nonparametric Tests

Do not assume population parameters for testing.

Acceptance Region Decision

Correctly accepting null hypothesis when true.

Rejection Region Decision

Correctly rejecting null hypothesis when false.

Sample Space

All possible outcomes in a statistical test.

Research Hypothesis

Prediction made by the researcher about outcomes.

Null Hypothesis (H0)

Hypothesis stating no effect or difference exists.

Alternative Hypothesis (Ha)

Hypothesis stating an effect or difference exists.

Statistical Notation

Symbols used to represent hypotheses in testing.

Significance Level

Commonly set at 5% or 1% for tests.

Evidence Against Null

Stronger evidence indicated by smaller p-values.

Test Statistic

Value calculated from sample data for hypothesis testing.

Research Question

Question guiding the hypothesis and statistical test.

Distribution of Data

Pattern of data points in a dataset.

Nature of Research

Type of inquiry guiding hypothesis formulation.

Statistical Test Selection

Choosing appropriate test based on data characteristics.

Parametric Tests

Statistical tests based on specific assumptions.

Control Group

Group receiving no treatment in experiments.

Experimental Group

Group receiving treatment in experiments.

Normality

Data follows a normal distribution pattern.

Homogeneity of Variances

Equal variances across multiple groups.

Linearity

Data shows a linear relationship.

Independence

Data points are independent of each other.

t-Test

Statistical test comparing means of two groups.

Independent t-Test

Compares means from separate groups.

Paired t-Test

Compares means from matched samples.

Single-Sample t-Test

Compares sample mean to known population mean.

Independent Samples t-Test

Widely used to compare separate groups.

n1 and n2

Number of observations in two groups.

t-Test for Correlated Samples

Compares means before and after treatment.

Mean Before

Average score before treatment or intervention.

Mean After

Average score after treatment or intervention.

Effectiveness of Treatment

Determined by comparing pretest and posttest means.

t-Statistic Formula

t = D̅ / (√(ΣD² - (ΣD)² / n(n-1)))

D̅

Mean of the difference scores.

ΣD

Summation of difference scores.

ΣD²

Sum of squares of difference scores.

N

Sample size in statistical tests.

z-Test

Parametric test requiring normal distribution.

Random Assignment

Participants randomly assigned to conditions.

Null Hypothesis

Assumes no difference between group means.

Interval Data

Data measured on a scale with equal intervals.

Ratio Data

Data with a true zero point.

Statistical Assumptions

Conditions that must be met for valid tests.

Mean (𝜇)

Average value of a population.

Standard Deviation (𝜎)

Measure of data dispersion in a population.

Sample Mean (𝑋̅)

Average value of a sample.

Z-test

Statistical test comparing sample and population means.

One-sample Z-test

Compares sample mean to population mean (𝜇).

Sample Size (𝑛)

Number of observations in a sample.

Hypothesized Population Mean

Assumed average value for population in testing.

Z-test Formula

𝑧= (𝑥̅ − 𝜇) / (𝜎/√𝑛).

Two-sample Z-test

Compares means of two independent samples.

Independent Groups

Samples drawn from different populations.

Variance (𝑠²)

Measure of data spread in a sample.

ANOVA

Analysis of Variance; compares means of multiple groups.

F-test

Statistical test for comparing variances.

One-way ANOVA

Compares means with one independent variable.

Two-way ANOVA

Examines interaction between two independent variables.

Three-way ANOVA

Analyzes effects of three independent variables.

Type I Error

False positive; rejecting true null hypothesis.

Type II Error

False negative; failing to reject false null hypothesis.