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Play to Learn. Each of the games below involves making ~30 rapid decisions with immediate feedback. The player encounters a diversity of examples, building up expertise with fundamental concepts. Game play typically lasts about two minutes.
There are 27 games in six categories (The normal distribution, Correlations, Linear regression, Z test, Inferential statistics, and Effect size).
Site: P2L.io
Alternative Menu: View list of all games, sorted by category
Goal(s): Apply proportions to the normal distribution, focusing on the center of the distribution. Connect the experience with the Empirical Rule.
How: For each set of normal distributions presented, pick the one with the shaded area matching the proportion stated (e.g., .68). Make 30 quick decisions, with immediate feedback.
Goal(s): Be better prepared to understand proportion and eventually probability when it comes to randomly selecting a member of the population with a similar or more extreme difference from the mean.
How: Each time that you are shown two normal distributions, pick the one with the correctly shaded region. Make 30 quick decisions, with immediate feedback.
Goal(s): Connect the experience with understanding percentile ranking. When inferential statistics are covered, to better assess the probability of a randomly selected sample (e.g., one-tailed hypothesis test).
How: Each time that you are shown two normal distributions, pick the one with the correctly shaded region. Make 30 quick decisions, with immediate feedback.
Goal(s): Gain experience regarding when to select the 'Area Between the Mean and Z' table to determine the area under the curve.
How: Each time you will be shown two scenarios. Pick the option where the relevant area under the curve would be greater than .500 (i.e., involves more than half the population). Make 30 quick decisions, with immediate feedback.
Goal(s): Develop an understanding that the closer the points of a scatterplot fall along a line, the stronger the correlation. In contrast, the more the points resemble a random cloud, the weaker the correlation. Be better prepared to connect the strength of a correlation, when presented as a scatterplot, with it communicated using Pearson's r. Eventually, to visualize how stronger correlations could lead to less error when using linear regression to make predictions.
How: You will be shown two scatter plots at a time and asked to select the weaker correlation. Make 30 quick decisions, with immediate feedback.
Goal(s): Develop an understanding that the closer the points of a scatterplot fall along a line, the stronger the correlation. In contrast, the more the points resemble a random cloud, the weaker the correlation. Relate the strength of a correlation, when presented as a scatterplot, with it's strength when communicated using Pearson's r. Eventually, to visualize how stronger correlations could lead to less error when using linear regression to make predictions.
How: You will be shown several examples of [1] two scatter plots or [2] a scatter plot and a Pearson's r value, and each time asked to select the weaker correlation. Make 30 quick decisions, with immediate feedback.
Goal(s): Develop the ability to classify and interpret the strength of a correlation, using the categories weak, moderate, and strong.
How: When presented with two options (Pearson's r and/or the strength of the correlation), select the weaker correlation. For example, if shown "Moderate correlation" and "r = .83", then select "Moderate correlation" as the weaker of the two correlations. Make 30 quick decisions, with immediate feedback.
Goal(s): Develop the skill to classify and interpret the strength of a correlation, using the categories weak, moderate, and strong. Be better prepared to read and interpret published articles found in general mass media (e.g., news and magazine articles, describing the strength of a correlation using the labels weak, moderate, and strong.
How: When presented with two options (Pearson's r and/or the strength of the correlation), select the weaker correlation. For example, if comparing a quote from the news using "Moderate correlation" and "r = -.23", then select r= -.23 as the weaker of the two correlations. Make 30 quick decisions, with immediate feedback.
Goal(s): For use with descriptive statistics, develop one's skill at reading Pearson's r value from a statistical software program (e.g., SPSS). Gain some familiarity with what a correlation report might look like generated by a statistical software package.
How: Compare statistical software output with values of Pearson's r. Decide which represents a correlation closer to zero. Make 30 quick decisions, with immediate feedback.
Goal(s): Gain familiarity with descriptive statistics APA style correlation write ups, and where to find the reported correlation value. Be better prepared to read and interpret APA style journal articles presenting and discussing correlations.
How: When presented with Pearson's r value or an American Psychological Association (APA) style write up of a correlation, select the weaker correlation. The APA style write ups will be descriptive reports describing a population. Make 30 quick decisions, with immediate feedback.
Linear Regression
Linear Regression
Goal(s): Gain a clearer understanding how to make predictions using a scatter plot with a best fitting line.
How: Each time you will be shown two scatter plots, pick the scatter plot that for a value of 80 miles, predicts a score of 120. The best fitting line (drawn though the data points) will help you with using scatterplots to make predictions. Make 30 quick decisions, with immediate feedback.
Z Test
Z Test
Pick either the Null Hypothesis Distribution or make the decision to Reject the Null Hypothesis.
Goal(s): Understand that the Z test indicates the number of standard errors the observed sample mean is from the center of the distribution of sample means. Notice that for sample means occurring in the tails of the sample means distribution, the Z test statistic is larger. Recall that for an alpha level of .05 the Z test cutoffs for a two-tailed hypothesis test are +/- 1.96. Develop experience regarding when to reject the null hypothesis.
How: For each scenario presented, based upon the Z test, decide whether the results are statistically significant. Make 30 quick decisions, with immediate feedback.
Goal(s): Better understand how the position of the sample mean, within the distribution of sample means, affects the p-value. Develop experience regarding when to reject the null hypothesis, based upon the p-value.
How: For each scenario presented, evaluate the p-value, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Pick either the Null Hypothesis Distribution or make the decision to Reject the Null Hypothesis.
Goal(s): Understand that the Z test provides the exact location of the observed sample mean (relative to the center of the sample means distribution). Notice that for sample means occurring in the tails of the sample means distribution, the Z test statistic is larger and the p-value is smaller. Observe how the Standard Error of the Mean and the Z test are calculated. Recall that for an alpha level of .05 the Z test cutoffs for a two-tailed hypothesis test are +/- 1.96. Understand that even when the null hypothesis is true, 5% of the time the Z test statistic will still be +/- 1.96 or more standard errors away from the center of the sample means distribution. Notice how the width (i.e., standard error) of the distribution of sample means narrows as sample size increases, leading to a more sensitive hypothesis test. Finally, develop experience regarding when to reject the null hypothesis.
How: For each scenario presented, decide based upon the Z test, whether the results are statistically significant (such that the null hypothesis should be rejected and the research hypothesis supported). Make 30 quick decisions, with immediate feedback.
Pick either the Null Hypothesis Distribution or make the decision to Reject the Null Hypothesis.
Goal(s): Understand that the Z test provides the exact location of the observed sample mean (relative to the center of the sample means distribution). Notice that for sample means occurring in the tails of the sample means distribution, the Z test statistic is larger and the p-value is smaller. Observe how the Standard Error of the Mean and the Z test are calculated. Recall that for an alpha level of .05 the Z test cutoffs for a two-tailed hypothesis test are +/- 1.96. Understand that even when the null hypothesis is true, 5% of the time the Z test statistic will still be +/- 1.96 or more standard errors away from the center of the sample means distribution. Notice how the width (i.e., standard error) of the distribution of sample means narrows as sample size increases, leading to a more sensitive hypothesis test. Finally, whether given the Z test or the p-value, develop experience regarding when to reject the null hypothesis.
How: For each scenario presented, decide based upon the Z Test or p-value, whether the results are statistically significant (such that the null hypothesis should be rejected and the research hypothesis supported). Make 30 quick decisions, with immediate feedback.
Goal(s): Gain greater familiarity with the formulas, and the information going into them, for the standard error of the mean and the Z test. Increase accuracy at evaluating whether the setup of the formulas will lead to a correct result.
How: For each scenario presented, evaluate whether the two formulas (for standard error and the Z test) are using the correct values. Involves referring to both the null hypothesis and the sample information. Make 12 decisions, with immediate feedback.
Inferential Statistics
Inferential Statistics
Goal(s): Increased experience with the single sample Z test. Gain expertise with hypothesis testing (comparing the p-value with the alpha level). Notice that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, compare the p-value with the alpha level of .05, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Goal(s): Increased experience with the single sample Z test. Gain expertise with interpreting the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Notice that if the result is considered "statistically significant," then the null hypothesis is rejected. Become familiar with interpreting statistical results as they might be produced by a software program (e.g., SPSS).
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "Sig. (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Goal(s): Increased experience with the single sample t test. Gain expertise with hypothesis testing (comparing the p-value with the alpha level). Notice the possibility of taking sample size into consideration, such that for a sample size of 30 or more, a Z test might be used even when the population standard deviation and distribution shape are unknown; consult with your instructor regarding best practices. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, compare the p-value with the alpha level, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Single Sample t Test, Sig. (2-tailed)
Goal(s): Increased experience with the single sample t test. Gain expertise with how to interpret the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Notice the possibility of taking sample size into consideration, such that for a sample size of 30 or more, a Z test might be used even when the population standard deviation and distribution shape are unknown; consult with your instructor regarding best practices. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected. Become familiar with interpreting statistical results as they might be produced by a software program (e.g., SPSS).
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "Sig. (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Goal(s): Increased experience with the paired sample t test. Gain expertise with how to handle interpreting the "p-value (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "p-value (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Paired Sample t Test, Sig. (2-tailed)
Goal(s): Increased experience with the paired sample t test. Gain expertise with how to handle interpreting the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected. Become familiar with interpreting statistical results as they might be produced by a software program (e.g., SPSS).
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "Sig. (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Independent Samples t Test, p-value
Goal(s): Increased experience with the independent sample t test (e.g., used when comparing the treatment group to the control group). Gain expertise with how to handle interpreting the "p-value (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "p-value (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 decisions, with immediate feedback.
Independent Samples t Test, Sig. (2-tailed)
Goal(s): Increased experience with the independent sample t test (e.g., used when comparing the treatment group to the control group). Gain expertise with how to handle interpreting the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test, and whether the assumption of homogeneity of variance is violated. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected. Become familiar with interpreting statistical results as they might be produced by a software program (e.g., SPSS).
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test, and whether the homogeneity of variance is violated. Evaluate the "Sig. (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 decisions, with immediate feedback.
Effect Size
Effect Size
Goal(s): Greater familiarity with Cohen's d categories (small, medium, and large). Increased experience at judging effect size, based upon a histogram and a visual representation of the null hypothesis.
How: For each scenario, decide which scenario presents the smaller Cohen's d. Make 30 quick decisions, with immediate feedback.
Effect Size & Hypothesis Testing
Goal(s): Notice how, for statistically significant results based on large sample sizes, the effect size can range from small to large.
How: For each scenario, decide which scenario presents the smaller Cohen's d. Make 30 quick decisions, with immediate feedback.
Robert & John Kelley
Games developed by Robert G. Kelley, Ph.D.
This application was initially developed during a Spring 2018 sabbatical at MiraCosta College. Development of the games is based upon perceptual learning theory. Special thanks to Mr. John Kelley for assistance with Unity.
Assumptions, Goals & Purpose
Learning can be fun and occur through game-like testing (e.g., frequent, rapid, low stakes)
The time needed to develop expertise can be shortened by using numerous non-repeating examples, in multiple formats, providing the opportunity for people to test their understanding frequently with immediate performance feedback.
Canvas Course Integration
These games can be embedded into Canvas quizzes, where successful completion of the activity provides an 'answer' (unique for each student/attempt) that can be entered into the Canvas quiz, so that the student receives credit in the Canvas gradebook.
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