RA Statistical Analysis and Interpretation 1 — Questions and Answers
Question 1: In hypothesis testing, a p-value of 0.03 indicates which of the following?
- The probability of the null hypothesis being true is 3%
- There is a 3% chance of observing the results if the null hypothesis is true (Correct answer)
- The effect size is statistically large
- The alternative hypothesis has a 97% probability of being correct
Correct answer: There is a 3% chance of observing the results if the null hypothesis is true
The p-value represents the probability of obtaining the observed results (or more extreme) assuming the null hypothesis is true, not the probability that the null hypothesis itself is true.
Question 2: Which measure of central tendency is MOST affected by extreme outliers in a dataset?
- Median
- Mode
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean incorporates every data value in its calculation, so a single extreme outlier can substantially shift it, unlike the median or mode which are more resistant to outliers.
Question 3: What is the primary distinction between descriptive and inferential statistics?
- Descriptive statistics use graphs; inferential statistics use tables
- Descriptive statistics summarize a sample; inferential statistics draw conclusions about a population (Correct answer)
- Descriptive statistics are qualitative; inferential statistics are quantitative
- Descriptive statistics apply only to large samples; inferential to small samples
Correct answer: Descriptive statistics summarize a sample; inferential statistics draw conclusions about a population
Descriptive statistics organize and summarize data from a collected sample, while inferential statistics use that sample data to make generalizations or predictions about a broader population.
Question 4: A 95% confidence interval for a mean of 50 is (46, 54). How should this be correctly interpreted?
- There is a 95% probability the population mean is between 46 and 54
- If the study were repeated many times, 95% of such intervals would contain the true population mean (Correct answer)
- 95% of individual data points fall between 46 and 54
- The sample mean has a 95% chance of equaling 50
Correct answer: If the study were repeated many times, 95% of such intervals would contain the true population mean
A confidence interval is a frequentist concept meaning that if the procedure were repeated many times, 95% of the constructed intervals would contain the true parameter value.
Question 5: Which statistical test is most appropriate to compare the means of two independent groups when the data is normally distributed?
- Chi-square test
- Independent samples t-test (Correct answer)
- Pearson correlation
- Wilcoxon signed-rank test
Correct answer: Independent samples t-test
The independent samples t-test is designed specifically to compare the means of two separate, unrelated groups when the assumption of normality is met.
Question 6: Standard deviation is best described as a measure of:
- The central value of a dataset
- The spread or variability of data around the mean (Correct answer)
- The difference between the highest and lowest values
- The skewness of a distribution
Correct answer: The spread or variability of data around the mean
Standard deviation quantifies how much individual data points deviate from the mean on average, making it the primary measure of variability or dispersion.
Question 7: A Type I error in hypothesis testing occurs when a researcher:
- Fails to reject a false null hypothesis
- Rejects a true null hypothesis (Correct answer)
- Accepts the alternative hypothesis correctly
- Calculates an incorrect effect size
Correct answer: Rejects a true null hypothesis
A Type I error (false positive) is the incorrect rejection of a null hypothesis that is actually true, with its probability controlled by the significance level alpha.
RA Statistical Analysis and Interpretation 1
In hypothesis testing, a p-value of 0.03 indicates which of the following?