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Use this calculator from VassarStats--a supremely useful website for statistical computation created by Professor Emeritus of Psychology at Vassar College Richard Lowry--to determine the standard error of the mean (*SE _{M}*) and other summary statistics (such as mean, variance, and standard deviation) for any set of data:

**http://vassarstats.net/basic.html**

As noted in *Making Sense of Statistics *(on page 103), the standard error of the mean can be used to build a 68% confidence interval for a mean. First add the* SE _{M}* to the mean, then subtract it from the mean. These two values represent the limits of the 68% confidence interval for the mean. Use this calculator from VassarStats to determine the 95% and 99% confidence intervals for any set of data:

Use this calculator from VassarStats to perform a *t*-test on any two sets of data:

**http://vassarstats.net/tu.html**

Be sure to specify whether the data you are testing is independent (or uncorrelated/unpaired) or dependent (or correlated/paired) using the buttons in the box labeled "Setup":

Use this calculator from VassarStats to perform a one-way ANOVA or *f*-test on up to five sets of data:

**http://vassarstats.net/anova1u.html**

Click on the Graph Maker in the "ANOVA Summary" area of the page after you perform your calculation to graph your results:

Use this calculator from VassarStats to perform a two-way ANOVA for independent samples with up to four columns and rows:

**http://vassarstats.net/anova2u.html**

A number of additional calculators are available from VassarStats that you can use to perform other kinds of two-way ANOVAs:

Use this calculator from VassarStats to calculate the value of chi-square for a one-way test "goodness of fit" test for up to eight categories:

**http://vassarstats.net/csfit.html**

**Important: **You must enter both observed and expected frequencies. To obtain expected frequencies, simply divide *n *by the number of categories you're working with (since the null hypothesis indicates that each category should be equally represented in your results). So, to perform a chi-square test for the data in Example 1 on page 141 of *Making Sense of Statistics*, you would enter the following:

110 voters indicated that they plan on voting for Candidate Smith, so that's the number you enter as your first observed frequency. 90 candidates indicated that they plan on voting for Candidate Doe, so that's the number you enter as your second observed frequency. Since the null hypothesis states that there is no true difference in the population--that is, that the population of registered voters is evenly split--the number you enter as your expected frequency in each case is 100.

Use this calculator from VassarStats to perform a two-way chi-square "test of independence":