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RSM 550 - Introduction to Research Methodology: Testing for Differences Calculators
Standard Error of the Mean
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 (SEM) and other summary statistics (such as mean, variance, and standard deviation) for any set of data:
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 SEM 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:
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":