Sample Statistics Practice Questions

Try these questions from our free Statistics practice tests. The correct answer and an explanation follow each question.

1. When using SPSS to run an independent samples t-test, Levene's Test is automatically reported. What null hypothesis does Levene's Test evaluate?

   • A. The group means are equal
   • B. The group variances are equal
   • C. The sample sizes are equal
   • D. The distributions are normal

   Answer: B. The group variances are equal

   Levene's Test checks the assumption of homogeneity of variance (equal variances) between groups before interpreting t-test results.

2. A client requests that a statistician use a one-tailed test instead of a two-tailed test after seeing the data, solely to achieve a p-value below 0.05. This practice is best described as:

   • A. Appropriate sensitivity analysis
   • B. HARKing (Hypothesizing After Results are Known)
   • C. Legitimate exploratory analysis
   • D. P-hacking

   Answer: D. P-hacking

   Changing the test direction after observing results to achieve significance is p-hacking, a form of research misconduct.

3. A data scientist splits a dataset 80/20 into training and test sets, fits a model on training data, and evaluates on the test set. The test set accuracy is 78%. What does this metric measure?

   • A. How well the model memorized the training data
   • B. The model's ability to generalize to unseen data
   • C. The percentage of correct training predictions
   • D. The statistical significance of the model's coefficients

   Answer: B. The model's ability to generalize to unseen data

   Evaluating on a held-out test set estimates how well the model generalizes to new, unseen observations not used during training.

4. How do Statistics professionals transfer knowledge from training to practice?

   • A. Knowledge transfers automatically
   • B. Through supervised practice, mentoring, gradual independence, and ongoing feedback
   • C. By passing the certification exam only
   • D. Training and practice are unrelated

   Answer: B. Through supervised practice, mentoring, gradual independence, and ongoing feedback

   This is fundamental to Statistics practice. Through supervised practice, mentoring, gradual independence, and ongoing feedback represents the professional standard for practical in the Statistics certification framework.

Take the full Statistics practice test

What is Variability in Statistics?

• Range - The difference between the highest and lowest numbers.
• Interquartile range - The range of a distribution's middle half.
• Variance - The average of squared deviations from the mean.
• Standard deviation - The average distance from the mean.

Demean Statistics

• degrade
• despise
• disparage
• belittle
• abase
• contemn
• debase

Elements of Statistics

• A population is a collection of all the units we're interested in examining (typically people, things, transactions, or events).
• A sample is a subset of a population's units.
• A measure of reliability is a statement (typically quantitative) concerning the degree of uncertainty associated with statistical inference.
• Statistical inference is an estimate, prediction, or other generalization about a population based on information contained in a sample.
• A variable is a trait or property of an individual experimental unit in the population.
• An experimental unit is a person, thing, transaction, or event about which data is collected.

What are limitations in Statistics?

• Statistics can't be used to variable data.
• Only someone with a thorough understanding of statistics can effectively manage statistical data.
• Quantitative data is the best fit for statistical approaches.
• Ignored Qualitative Aspect
• It does not tell the whole narrative about the phenomenon.
• Laws aren't always exact.
• Individual items are beyond the scope of statistics to explain.
• Statistics have the potential to be abused.

One variable vs Two variable Statistics

• Tally charts
• Frequency tables
• Bar graphs
• Histograms
• Pictographs
• Circle graphs

• Ordered pairs
• Scatter plots
• Two-column tables of values

Statistics Questions and Answers

• Statistics laws are, on average, correct. A single observation is not a statistic, because statistics are aggregates of facts. Statistics only deal with groups and aggregates.
• Statistical methods are most useful when dealing with numerical data.
• Statistics cannot be used on data that is heterogeneous.
• If statistical results are not collected, analyzed, and interpreted with adequate care, they may be misleading.
• Only someone with a thorough understanding of statistics can effectively manage statistical data. 
• Statistical decisions may contain some inaccuracies. Inferential statistics, in particular, are prone to errors. We have no way of knowing whether or not an error has been made.