Last updated February 4, 2008
Oakley Gordon, Ph.D.
To use these tools your browser needs to be able to run Java applets (Version 1.4.2 or later). For assistance please refer to the technical help page.
Normal Distribution Tool: provides 'z' to 'p' as well as 'p' to 'z' functions.
t Distribution Tool: provides 't' to 'p' as well as 'p' to 't' functions.
F Distribution Tool: provides 'F' to 'p' as well as 'p' to 'F' functions.
Chi Square Distribution Tool: provides 'Chi Square' to 'p' as well as 'p' to 'Chi Square' functions.
PRE Tool: provides 'PRE' to: 'p', 'F', and 'est. eta squared' functions. Based upon the 'Model Comparison Approach' by Charles Judd and Gary McClelland.
These simulations ('sims') are designed to develop through hands on learning a deeper understanding of the process of acquiring knowledge through statistical analyses. Many of the concepts covered are not explicitly stated within the sim but serve as part of the underlying logic of what is occurring, which should help nourish an intuitive understanding of the concepts. Feel free to explore. Sim 1 introduces the basic scenario of the sims and so should be completed first.
Important Notes:
- If you wish to obtain credit for completing these simulations you need to access them through the Oak Homework software (rather than through this web page).
- On the Mac these sims will only run on the Safari and Camino browser.
Sim 1: This sim introduces the basic scenario of all the sims ( investigating a species known as 'Haflas'). It provides the experience of exploring a population based upon samples drawn from the population. It also provides a foundation for eventually understanding the statistical concept of the 'sampling distribution of the mean' as well as the effect of N and variance on the reliability of estimates of the population mean. This sim assumes that the students know that the sample mean is an unbiased estimate of the population mean and that they also have been introduced to confidence intervals.
Sim 2: This sim further develops the idea of the 'sampling distribution of the mean' and shows how the Central Limit Theorem works to create a sampling distribution that is more normally distributed than the original population. The sim assumes that the students have already been introduced to probability and the sampling distribution of the mean.
Sim 3: This sim uses the t test for independent group means to analyze the data from a true experimental design, the study is then viewed within the context of other studies from other researchers investigating the same topic. This approach both broadens an understanding of statistical analysis and lays the foundation for understanding the concept of power. The sim assumes that the students have been introduced to null hypothesis testing and to the t test for 2 independent group means.
Sim 4: This sim involves using correlation to examine the relationship between two variables. The sim also introduces the concept of there being two possible goals of analysis, to see if a correlation exists (i.e. is different than zero, using null hypothesis statistical testing), or to focus on the determining the strength of the correlation in the population (using confidence intervals). It assumes that the students have been introduced to correlation and null hypothesis testing.
Sim 5: This sim provides practice at selecting the appropriate analysis, carrying it out, and interpreting the results for a variety of different experimental designs. It assumes that the students have been exposed to a variety of statistical procedures for carrying out null hypothesis significant testing.
These applets provide the students with a chance to practice computing various aspects of statistics as many times as they would like. Each time through the data are randomly generated (with small N's so that the computations are not too laborious) so the student may practice each procedure as many times as desired without repeating the same data. The applets simply display the data, ask for certain values to be computed, and then show the correct answers. If you want to use these you have to put up with my preference of symbols and formulas.
Practice 1: This provides practice at computing descriptive and inferential statistics from a small sample. The student is to compute the N, sum, mean, median, mode, SS, S squared (variance of sample as SS/N), S (square root of S squared) of the sample; and estimate the mean (est. mu), variance (est. sigma squared = SS/(N-1)), and standard deviation (est. sigma = square root of variance estimate) of the population from which the sample was drawn. In my class lectures I explain about the bias in the estimate of the standard deviation and why the students need to compute it anyway.
Practice 2: This provides practice at performing the t test for two independent groups. The examples are generated in sets of three, consisting of a random ordering of a two-tail test, and both one-tail tests. H0 is rejected in approximately half the samples.
Practice 3: This provides practice at performing the t test for two dependent groups (a.k.a. 'paired-samples' or 'correlated groups'). The examples are generated in sets of three, consisting of a random ordering of a two-tail test, and both one-tail tests. H0 is rejected in approximately half the samples
Practice 4: This provides practice at computing correlation (Pearson's r), testing the r for statistical significance, and computing the regression equation. H0 is rejected in approximately half the samples
Practice 5: This provides practice at completing an ANOVA one-factor summary table when two of the SS are provided and enough information to determine the degrees of freedom. H0 is rejected in approximately half the samples
Practice 6: (under construction). This provides practice at interpreting p values (tieing together the concepts of p values, statistical significance, whether or not H0 is rejected, and what can or cannot be implied about population parameters).