Statistical Methods - Eppp Knowledge

1. What notation typically represents a sample variance statistic?

   $s^2$. The lowercase s squared denotes the estimated variance based on sample data.

2. Which test is nonparametric: Kruskal–Wallis or one-way ANOVA?

   Kruskal–Wallis. The Kruskal-Wallis test compares distributions using ranks, making it a nonparametric alternative to ANOVA.

3. What is the defining feature of a nonparametric statistical test?

   Makes minimal distributional assumptions; often rank/median based. Nonparametric tests avoid strict distributional assumptions by using methods like ranking or focusing on medians.

4. What is a parameter in statistics?

   A numerical characteristic of a population (usually unknown). Parameters represent fixed, typically unobservable values that describe entire populations.

5. Which test is nonparametric: Wilcoxon signed-rank or paired-samples $t$ test?

   Wilcoxon signed-rank. The Wilcoxon signed-rank test uses ranks of differences, avoiding parametric assumptions like normality.

6. What notation typically represents a population mean parameter?

   $\mu$. The Greek letter mu denotes the true average value in the entire population.

7. Which correlation is parametric: Pearson $r$ or Spearman $\rho$?

   Pearson $r$. Pearson r assumes a linear relationship and normally distributed variables, fitting parametric criteria.

8. What is the primary purpose of inferential statistics?

   Draw population conclusions from sample data with uncertainty. Inferential statistics use sample data to make probabilistic generalizations about population parameters.

9. What is the primary purpose of descriptive statistics?

   Summarize and describe observed sample data. Descriptive statistics focus on organizing and presenting data characteristics without making inferences about broader populations.

10. Which option is descriptive (not inferential): standard deviation, $p$ value, or confidence interval?

    Standard deviation. Standard deviation measures data dispersion in the observed sample, without inferring about the population.

11. Which option best indicates a nonparametric approach: analyze ranks or analyze raw means?

    Analyze ranks. Nonparametric methods often transform data to ranks to avoid assumptions about the underlying distribution.

12. What inferential procedure provides a range estimate for a population parameter?

    Confidence interval. Confidence intervals provide a plausible range of values for the population parameter based on sample data and a specified confidence level.

13. Which test is parametric: one-way ANOVA or Kruskal–Wallis?

    One-way ANOVA. One-way ANOVA compares means across groups assuming normality and homoscedasticity, classifying it as parametric.

14. Which option is an inferential (not descriptive) activity: estimate, summarize, or display data?

    Estimate (make a population inference from a sample). Estimation involves using sample statistics to infer population parameters, distinguishing it from mere summarization or display of data.

15. Which correlation is nonparametric: Spearman $\rho$ or Pearson $r$?

    Spearman $\rho$. Spearman rho uses ranked data to assess monotonic relationships without assuming normality.

16. Which assumption is most central to many parametric tests: normality or equal medians?

    Normality (often of residuals or sampling distribution). Many parametric tests assume normality to justify the use of specific probability distributions for inference.

17. Identify the measurement scale most commonly required for parametric mean-based tests.

    Interval or ratio measurement. Parametric tests require interval or ratio scales to ensure meaningful arithmetic operations like means and variances.

18. What notation typically represents a population variance parameter?

    $\sigma^2$. Sigma squared symbolizes the true variance across the entire population.

19. Identify the measurement scale most commonly associated with nonparametric tests.

    Ordinal (and often nominal) measurement. Nonparametric tests are suitable for ordinal data where intervals are not equal, or nominal data for categorical analysis.

20. What assumption is specifically called homoscedasticity in parametric comparisons?

    Equal variances across groups. Homoscedasticity ensures that variance is constant across groups, a key assumption for valid parametric group comparisons.

21. What is a statistic in statistics?

    A numerical characteristic computed from a sample. Statistics are observable values calculated from sample data to estimate population parameters.

22. Which test is parametric: independent-samples $t$ test or Mann–Whitney $U$?

    Independent-samples $t$ test. The independent-samples t-test assumes normality and equal variances, making it a parametric method for comparing means.

23. What notation typically represents a sample mean statistic?

    $\bar{x}$. The sample mean is represented by x-bar to distinguish it from the population mean.

24. What is the defining feature of a parametric statistical test?

    Assumes a specific population distribution form (often normal). Parametric tests rely on assumptions about the underlying population distribution to derive sampling distributions.

25. What inferential procedure evaluates whether sample evidence contradicts $H_0$?

    Null hypothesis significance test. Null hypothesis significance testing assesses the probability of observing the sample data assuming the null hypothesis is true.

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