Inferential testing

Question 1

Definition of Inferential Statistics

Answer 1

• Definition: Inferential statistics allows researchers to make generalizations or predictions about a population based on a sample of data.
• Purpose: To test hypotheses and make inferences about a population.

Question 2

Types of Inferential Tests

Answer 2

1. Parametric Tests
   o Assumptions: Normal distribution, equal variances, interval/ratio data.
   o Examples:
    t-test: Compares means between two groups.
    ANOVA (Analysis of Variance): Compares means across three or more groups.
2. Non-Parametric Tests
   o Assumptions: No requirement for normal distribution or equal variances; can be used with ordinal or nominal data.
   o Examples:
    Mann-Whitney U: Compares differences between two independent groups.
    Wilcoxon Signed-Rank Test: Compares differences between two related groups.
    Chi-Square Test: Assesses relationships between categorical variables.

Question 3

Null and Alternative Hypotheses

Answer 3

• Null Hypothesis (H0): Assumes no effect or difference; any observed difference is due to sampling error.
• Alternative Hypothesis (H1): Assumes there is an effect or difference. The aim is to provide evidence against the null hypothesis.

Question 4

Significance Levels (p-value)

Answer 4

• Definition: The probability of observing the data if the null hypothesis is true.
• Common Levels:
  o p < 0.05: Statistical significance; reject the null hypothesis.
  o p < 0.01: Stronger evidence against the null hypothesis.
• Interpreting p-values: A low p-value indicates that the observed data is unlikely under the null hypothesis.

Question 5

Types of Errors

Answer 5

1. Type I Error (α)
   o Definition: Rejecting the null hypothesis when it is true (false positive).
   o Control: Set a lower significance level (e.g., p < 0.01) to reduce risk.
2. Type II Error (β)
   o Definition: Failing to reject the null hypothesis when it is false (false negative).
   o Control: Increase sample size to improve power.

Question 6

Statistical Power

Answer 6

• Definition: The probability of correctly rejecting the null hypothesis when it is false (1 - β).
• Factors Affecting Power:
  o Sample size: Larger samples increase power.
  o Effect size: Larger effects are easier to detect.
  o Significance level: A higher alpha increases power but also Type I error risk.

Question 7

Effect Size

Answer 7

• Definition: A measure of the strength or magnitude of a relationship or difference found in a study.
• Common Measures:
  o Cohen’s d: For t-tests, calculated as the difference between means divided by the pooled standard deviation.
  o Eta squared (η²): For ANOVA, indicates the proportion of variance explained by the independent variable.

Question 8

Assumptions of Statistical Tests

Answer 8

1. Normality: Data should be approximately normally distributed (for parametric tests).
2. Homogeneity of Variance: Variances across groups should be roughly equal (for ANOVA).
3. Independence: Observations should be independent of one another.

Question 9

Choosing the Right Test

Answer 9

• When to use Parametric Tests: When data meets the assumptions of normality and equal variance.
• When to use Non-Parametric Tests: When data violates parametric assumptions or is ordinal/nomial.

Question 10

Reporting Results

Answer 10

• APA Format: Always report:
  o Test statistic (e.g., t, F, χ²)
  o Degrees of freedom (df)
  o p-value (exact value, e.g., p = 0.032)
  o Effect size (e.g., Cohen’s d)
  o Confidence intervals if applicable.