Choosing the right statistical test is crucial for accurate data analysis in experimental design. This section covers hypothesis testing, parametric vs non-parametric tests, and specific tests like t-tests, ANOVA, and chi-square. It also explains their applications and considerations.

Understanding test selection helps researchers avoid errors and ensure statistical power. Factors like sample size, data type, and research questions all play a role in picking the best test. This knowledge is essential for designing effective experiments and drawing valid conclusions.

Selecting Appropriate Tests

Hypothesis Testing and Test Types

• Hypothesis testing assesses the validity of a claim or hypothesis about a population parameter based on sample data
• Parametric tests assume the data follows a specific probability distribution (normal distribution) and has certain characteristics such as equal variances between groups
  • Examples of parametric tests include t-tests and ANOVA
• Non-parametric tests do not rely on assumptions about the distribution of the data and are used when the assumptions of parametric tests are not met or the data is ordinal or nominal
  • Examples of non-parametric tests include the chi-square test and correlation analysis

Specific Statistical Tests and Their Applications

• T-test compares the means of two groups to determine if they are significantly different from each other
  • Independent samples t-test used when comparing means from two separate groups (males vs. females)
  • Paired samples t-test used when comparing means from the same group at different times or under different conditions (before vs. after treatment)
• ANOVA (Analysis of Variance) compares the means of three or more groups to determine if they are significantly different from each other
  • One-way ANOVA used when there is one independent variable (comparing test scores across multiple grade levels)
  • Two-way ANOVA used when there are two independent variables (comparing test scores by grade level and gender)
• Chi-square test assesses the relationship between two categorical variables to determine if they are independent or associated
  • Goodness of fit test compares observed frequencies to expected frequencies (survey responses compared to population proportions)
  • Test of independence examines if two variables are related (relationship between education level and voting behavior)
• Correlation analysis measures the strength and direction of the linear relationship between two continuous variables
  • Pearson correlation coefficient used for normally distributed data (relationship between height and weight)
  • Spearman rank correlation used for non-normally distributed or ordinal data (relationship between education level and income)

Considerations in Test Selection

Errors and Statistical Power

• Type I error (false positive) occurs when rejecting a true null hypothesis, concluding there is an effect when there isn't
  • Significance level (α) is the probability of making a Type I error, commonly set at 0.05
• Type II error (false negative) occurs when failing to reject a false null hypothesis, concluding there is no effect when there actually is
  • Statistical power is the probability of correctly rejecting a false null hypothesis (1 - β), commonly set at 0.80
• Effect size measures the magnitude of the difference between groups or the strength of the relationship between variables
  • Larger effect sizes require smaller sample sizes to detect significant differences or relationships

Sample Size and Test Selection

• Sample size determination is crucial to ensure the study has sufficient statistical power to detect meaningful effects
  • Larger sample sizes increase statistical power and reduce the risk of Type II errors
  • Required sample size depends on the desired power, significance level, and expected effect size
• Test selection should be based on the research question, data type, and assumptions
  • Parametric tests are more powerful but require stricter assumptions about the data
  • Non-parametric tests are more flexible but may have lower statistical power
  • Consulting with a statistician or using power analysis software can help determine the appropriate test and sample size for a given study design