Statistics Concepts Overview

Study Notes

Statistics

Mathematical technique for organizing, summarizing, and interpreting data to answer research questions.
Descriptive Statistics: Summarize data collected in a study (compute summary values or organize data into tables/figures).
Frequency Statistics: Number of scores or occurrences in a variable over time.
Bar Graphs: Use horizontal or vertical bars to display frequency distributions.
Pie Charts: Divide a circle into sectors representing proportions.
Histograms: Bar graphs depicting frequency distributions.
Central Tendency: Measures the "average" score:
- Mean: Mathematical average.
- Median: Middle score (half above, half below).
- Mode: Most frequent occurring score(s).
Variability: Describes the spread of scores:
- Range: Difference between highest and lowest scores.
- Standard Deviation: Amount of variation/dispersion (higher SD = more variability).
- 68-95-99.7 Rule: In a normal model, these percentages of values fall within specific standard deviations of the mean.
Scatterplot: Graphed cluster of dots representing two variables, helpful for identifying correlations.
Correlation Coefficient (r): Single number (-1.0 to 1.0) indicating strength and direction of association between two variables.
Hypotheses:
- Null Hypothesis (H₀): No significant difference between specified populations (observed difference due to sampling/experimental error).
- Alternative Hypothesis (H₁/H₂): Opposite of the null hypothesis, stating a significant difference exists.
- Types of Hypotheses: Between Subjects, Within Subjects.

Hypothesis Tests

Procedure: Testing claims about population properties by comparing results (chance vs. actual results).
Goal: Rule out chance as the explanation for results.
Statistical Significance: Observed effect is too large to be attributed to chance (usually p<.05).
Fail to Reject Null: p>.05.

Data Analysis

Three Stages:
- Get to know the data: Inspect for errors, outliers, and general features.
- Summarize the data: Use descriptive statistics and graphical displays (e.g., stem-and-leaf, standard deviation).
- Confirm what data reveals: Use statistical techniques to determine if the results are due to chance.
Standard Error of the Mean: Standard deviation of a sampling distribution.
Estimated Standard Error of the Mean: Estimating population parameter using sample data.
Confidence Interval: Range of values where the population parameter is likely to lie.

Inferential Statistical Tests

Dependent Samples t-test: Comparing means of two samples in the same group (e.g., effect of treatment).
Analysis of Variance (ANOVA): Compares means of three or more groups.
Post-Hoc Test: Determines which groups differ significantly if the ANOVA shows a main effect.
Repeated Measures ANOVA: Same subject measured multiple times.

Effect Size

Eta-squared (η²): Measures effect size in ANOVA.
Cohen's f: Measures effect size relative to the degree of dispersal among groups.

Other

Linear Trend: Straight line (line of best fit) through data points.
Level of Significance: Probability of making a Type I error (rejecting a true null hypothesis).
Type I Error: Rejecting a true null hypothesis.
Type II Error: Failing to reject a false null hypothesis.
Power of a Statistical Test: Probability of rejecting a false null hypothesis.
Single-Factor Independent Groups Design: Independent groups with one independent variable.
F-test: Test used to evaluate differences between group means in ANOVA (omnibus F-test).