LIS 504 - Statistical tests

Chi-square test

For example, in a series of experiments, people were asked to write abstracts using computer assistance. Before they wrote the abstracts, they were asked how how much experience they had with the computer operating environment. Afterwards, the abstracts were examined to see if they contained any spelling errors. The results can be summarized in the following table:

Experience with operating environment	No misspellings	One or more misspellings	Total
Little or none	6	17	23
Some or a lot	18	17	35
Total	24	35	58

It looks as though people with more experience are more likely to avoid spelling errors. But is the difference statistically significant?

To use the chi-square test, we need expected counts, too. In this case, these are calculated on the assumption that experience and spelling are not correlated at all. The formula to use for each expected value is

(Row Total) * (Column Total)

(Grand Total)

For example, the expected value for the top left cell is

(23) * (24)	= 9.517
58

Applying the formula gives the following table, which keeps the same totals:

Experience with operating environment	No misspellings	One or more misspellings	Total
Little or none	9.517	13.483	23
Some or a lot	14.483	20.517	35
Total	24	35	58

Applying the CHITEST function in Excel gives a result of about 0.055, which is just short of the critical value of 0.050 for minimal statistical significance. Even though a relationship between experience and spelling is plausible, therefore, for these data, based on the chi-square test, we should accept the null hypothesis that the observed differences could have arisen by chance.

Like most statistical tests, the chi-square test provides only an approximate value, especially for small numbers of observations.

T test

For example, in a series of experiments, people were asked to write abstracts of an article. The distributions of the lengths of the abstracts produced by males and females respectively looked like this:

Excel was used to run a two-tailed t test (the usual kind) on the original lists of abstract lengths for males and females respectively. The result was about 0.696*, indicating no statistical significance, and supporting the null hypothesis that the difference is due to sampling error.

*For unequal variance, the safer option, which also makes sense here since the variances are quite different, at 3,568,221 and 904,922 respectively.

Other tests

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