Statistics Analysis Techniques

Describing Results

• Comparing group percentages: Analyzing the proportion of subjects in different groups exhibiting a characteristic. This allows easy comparisons.
• Correlating scores: Assesses the relationship between two variables, quantifying how one predicts the other. This is often done using correlation coefficients.
• Comparing group means: Calculates average scores of different groups to identify significant differences. This typically uses t-tests or ANOVA.

Frequency Distributions

• A frequency distribution summarizes the occurrences of each score in a dataset. This reveals data shape and spread.
• Graphical representations, like pie charts, bar graphs, frequency polygons, and histograms, display frequency distributions.
  • Pie charts show proportions in categories.
  • Bar graphs use rectangular bars to represent categorical data.
  • Frequency polygons connect points representing frequency of each score.
  • Histograms show score frequencies within specified ranges (like bar graphs but for continuous data).

Measures of Central Tendency and Variability

• Central tendency: Summarizes a dataset using a single value representing the data's center.
  • Mean (M): Average score, calculated by summing all scores and dividing by the total count.
  • Median (Mdn): Middle score, dividing the dataset into two equal halves. Useful for ordinal data.
  • Mode: Most frequently occurring score, applicable for nominal data.
• Variability: Describes the spread of scores in a dataset.
  • Standard Deviation (SD): Average distance of scores from the mean, indicating data spread.
  • Variance (s²): Square of the standard deviation, representing the degree of spread.

Correlation Coefficient

• Quantifies the strength and direction of a relationship between two variables.
• Ranges from -1.0 (perfect negative correlation) to +1.0 (perfect positive correlation).
• Values close to 0 indicate weak relationships.

Effect Size

• Quantifies the strength of a relationship between variables beyond statistical significance.
• Helps assess the practical significance of findings.

Regression Equations and Multiple Correlation

• Used to predict one variable based on another (or others).
• Y represents the variable you want to predict, while X represents independent variables.

Partial Correlation

• Addresses the third-variable problem by holding a third variable constant to determine the relationship between two key variables.

Structural Equation Models

• Describes the expected relationships among quantitative non-experimental variables.
• Uses path diagrams (visual representations) to represent causal relationships.

Inferential Statistics

• Used to make conclusions about a population based on sample data.
• Helps evaluate hypotheses.

Null and Research Hypotheses

• Null hypothesis (H₀): Posits no effect or difference in the population.
• Research hypothesis (H₁): Suggests a significant effect or difference.

t-test

• Determines if there's a significant difference between the means of two groups.
• One-tailed test: When the research hypothesis specifies a direction of difference.
• Two-tailed test: When no direction of difference is specified.

F-test

• Compares systematic variance (between-group differences) against error variance (within-group differences), in samples with more than two groups.
• A large F-ratio indicates a higher likelihood of significant results.

Confidence Intervals (CI)

• Provides a range of values where the true population parameter is likely to fall.
• Common level is 95%.

Type I and II Errors

• Type I error: Rejecting a true null hypothesis (false positive).
• Type II error: Failing to reject a false null hypothesis (missed opportunity).

Power of a Statistical Test

• Probability of correctly rejecting the null hypothesis when it's false.
• Influenced by sample size, effect size, and significance level.

Selecting an Appropriate Statistical Test

• Criteria depend on the variables (e.g., groups, types), such as t-tests for 2 groups with interval/ratio data, ANOVA for 3 or more groups, and correlations or regression for relationships between multiple interval/ratio variables.

Effect Size Measures (Cohen's d, Pearson r)

• Cohen's d: Effect size for comparing two means.
• Pearson r: Effect size for correlation. r² represents shared variance.