Understanding Inferential Statistics and Research Methods

Inferential Statistics

Analyzes data to generalize from samples to populations.

Sample

Subset of individuals from a larger population.

Population

Entire group of individuals being studied.

Sampling Error

Chance-related discrepancies from using small samples.

Sample Bias

Samples that misrepresent the population characteristics.

Hypothesis Testing

Process of confirming or rejecting research hypotheses.

Alternative Hypothesis

Indicates a relationship between studied variables.

Null Hypothesis

States no relationship exists between variables.

Research Hypothesis

Another term for the alternative hypothesis.

Significant Finding

Results unlikely due to chance alone.

Sample Mean

Average value calculated from a sample.

Population Mean

Average value calculated from the entire population.

Sample Standard Deviation

Measures variability within a sample.

Population Standard Deviation

Measures variability within the entire population.

Statistical Tests

Tools for analyzing different types of data.

Interval Data

Numerical data with meaningful intervals between values.

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.

Reliability of Differences

Confidence in observed differences being real.

Research Project

Study designed to answer specific research questions.

Confirming Hypotheses

Testing null hypothesis to support alternative hypothesis.

Testing Procedure

Rules for evaluating hypotheses in research.

Generalization

Applying findings from a sample to a population.

Statistical Tools

Methods used for data analysis in research.

Awkward Testing

Repeating studies can be impractical and time-consuming.

Tests of Significance

Procedure to accept or reject hypotheses.

Level of Significance

Probability threshold for rejecting the null hypothesis.

p-Value

Probability indicating evidence against the null hypothesis.

Critical Region

Area indicating rejection of the null hypothesis.

Acceptance Region

Area indicating acceptance of the null hypothesis.

One-Tailed Hypothesis Test

Test predicting direction of expected difference.

Two-Tailed Hypothesis Test

Test predicting differences without direction.

Null Hypothesis (H0)

Hypothesis stating no effect or difference exists.

Alternative Hypothesis (Ha)

Hypothesis stating an effect or difference exists.

Directional Hypothesis

Hypothesis predicting specific direction of difference.

Nondirectional Hypothesis

Hypothesis predicting difference without specific direction.

Type I Error

Rejecting H0 when it is true.

Type II Error

Accepting H0 when it is false.

Parametric Tests

Tests assuming population distribution parameters.

Nonparametric Tests

Tests not assuming population distribution parameters.

Statistical Notation

Symbols used to represent hypotheses and tests.

Research Hypothesis

Hypothesis formulated based on research questions.

Sample Space

Set of all possible outcomes in a test.

Rejection Points

Values beyond which the null hypothesis is rejected.

Significance Level

Commonly set at 5% or 1%.

Statistical Evidence

Data supporting or refuting a hypothesis.

Test Statistic

Value calculated from sample data for hypothesis testing.

Findings Significance

Importance of results in relation to hypotheses.

Research Question

Question guiding the research and hypothesis formulation.

Data Distribution

Pattern of how data values are spread.

Statistical Test Selection

Choosing appropriate test based on data and hypothesis.

Parametric Tests

Statistical tests based on specific assumptions.

Control Group

Group receiving no treatment in experiments.

Experimental Group

Group receiving treatment or intervention.

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 of two independent groups.

Paired t-Test

Compares means of matched samples.

Single-Sample t-Test

Compares sample mean to a known value.

Mean Comparison

Evaluating differences between group averages.

Random Assignment

Participants randomly assigned to conditions.

Interval Data

Data with meaningful intervals but no true zero.

Ratio Data

Data with meaningful intervals and a true zero.

t-Test for Independent Samples

Widely used to compare separate groups.

n1 and n2

Number of observations in each group.

t-Test for Correlated Samples

Compares means before and after an intervention.

Pretest

Measurement taken before treatment is applied.

Posttest

Measurement taken after treatment is applied.

Mean of Difference Scores

Average of differences between paired observations.

Summation of Differences

Total of differences between pretest and posttest.

Sum of Squares

Total of squared differences from the mean.

Sample Size (N)

Total number of observations in the study.

z-Test

Statistical test requiring normal distribution.

Effectiveness of Treatment

Determined by comparing pretest and posttest means.

Null Hypothesis

Assumes no difference between group means.

Statistical Assumptions

Conditions that must be met for valid tests.

Mean (𝜇)

Average value of a population's data.

Standard Deviation (𝜎)

Measure of data dispersion in a population.

Sample Mean (𝑋̅)

Average value of a sample's data.

Z-Test

Statistical test comparing sample and population means.

One-Sample Z-Test

Compares sample mean to population mean (𝜇).

Population Standard Deviation

Known standard deviation of the entire population.

Sample Standard Deviation

Calculated standard deviation from sample data.

Z-Score Formula

𝑧= (𝑥̅ − 𝜇)√𝑛/𝜎.

Hypothesized Population Mean

Assumed mean value for comparison in tests.

Two-Sample Z-Test

Compares means of two independent sample groups.

Independent Samples

Samples drawn from different populations.

Variance (s²)

Measure of data spread within a sample.

One-way ANOVA

Compares means with one independent variable.

Two-way ANOVA

Analyzes interaction between two independent variables.

Three-way ANOVA

Examines effects of three independent variables.

F-Test

Statistical test for comparing variances.

Type I Error

False positive; rejecting true null hypothesis.

Type II Error

False negative; failing to reject false null hypothesis.

Interval Data

Data measured on a scale with equal intervals.

Ratio Data

Data with a true zero point, allowing ratios.