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Chapters 10, 12, & 14: Inferential Statistics and Hypothesis Testing -…
Chapters 10, 12, & 14: Inferential Statistics and Hypothesis Testing
Chapter 10 – Introduction to Hypothesis Testing
The research hypothesis predicts that a treatment or variable will have an effect.
The research hypothesis reflects what the researcher hopes to support.
Research hypotheses can be directional or non-directional.
The null hypothesis states that there is no treatment effect.
Hypothesis testing begins by assuming the null hypothesis is true.
The null hypothesis is rejected only when evidence is strong enough.
7Researchers compare sample data to what would be expected by chance.
Sampling error creates natural differences between sample means and population means.
Hypothesis testing determines whether observed differences are larger than expected by chance.
The critical region contains extreme sample outcomes.
Scores in the critical region are unlikely if the null hypothesis is true.
Obtaining a score in the critical region leads to rejection of H₀.
Alpha (α) represents the probability of making a Type I error.
Common alpha levels are .05 and .01.
Smaller alpha levels require stronger evidence before rejecting H₀.
A Type I error occurs when a true null hypothesis is rejected.
A Type II error occurs when a false null hypothesis is not rejected.
Lowering alpha decreases the chance of a Type I error.
Reducing Type I error risk can increase Type II error risk.
Researchers either reject or fail to reject H₀.
Failing to reject H₀ does not prove it is true.
Statistical significance does not guarantee practical significance.
Sample size influences the likelihood of finding significance.
Larger effects are easier to detect statistically.
Hypothesis testing provides a structured framework for decision making.
Chapter 12 – Hypothesis Tests with Two Independent Samples
Independent samples consist of different participants in each group.
No participant can belong to both groups.
Independent samples are commonly used in experimental research.
The independent-measures t test compares two population means.
It determines whether differences between means are statistically significant.
The test evaluates treatment effects across separate groups.
Variability exists within each sample.
Variability influences the size of the standard error.
Greater variability makes it harder to detect significant differences.
The independent t test combines sample variances into a pooled estimate.
Pooled variance provides a more stable estimate of population variance.
Both sample variances contribute to the pooled value.
Standard error measures expected mean differences due to chance.
Larger sample sizes reduce standard error.
Smaller standard errors increase sensitivity.
Degrees of freedom equal n₁ + n₂ − 2.
Degrees of freedom affect critical t values.
Larger degrees of freedom generally reduce critical values.
Observations must be independent.
The dependent variable should be measured on an interval or ratio scale.
Populations should be approximately normal.
Population variances should be relatively equal.
A significant t value suggests a real difference between populations.
Researchers compare obtained t values to critical values.
Effect size should be reported alongside significance tests.
Chapter 14 – Analysis of Variance (ANOVA)
ANOVA compares three or more group means simultaneously.
ANOVA prevents the inflation of Type I error caused by multiple t tests.
ANOVA evaluates whether treatment effects exist among groups.
ANOVA separates variability into different components.
Between-treatments variability reflects treatment effects plus chance.
Within-treatments variability reflects chance differences only.
The F ratio compares between-group variability to within-group variability.
Large F values suggest treatment effects may exist.
F values near 1.00 suggest little treatment effect.
Mean squares are estimates of variance.
Mean Square Between measures treatment-related variation.
Mean Square Within measures random variation.
Each variance estimate has associated degrees of freedom.
Between-groups df equals k − 1.
Within-groups df equals N − k.
Obtained F values are compared to critical F values.
Significant F values lead to rejection of the null hypothesis.
ANOVA identifies whether differences exist somewhere among groups.
Post hoc tests determine which groups differ.
Post hoc procedures are used after a significant ANOVA result.
Tukey's HSD is a common post hoc test.
Samples must be independent.
Populations should be normally distributed.
Variances should be approximately equal across groups.
ANOVA can compare multiple groups efficiently.
ANOVA reduces Type I error rates.
ANOVA is widely used in behavioral science research.
ANOVA provides the foundation for more advanced statistical analyses.