How do I compare a list of observed frequencies with a list of my own expected frequencies?

This can be done in two ways: a chi-square calculator may be found [http://www.graphpad.com/quickcalcs/chisquared1.cfm here.] Note: There have been instances where this software incorrectly claims the total of the observed and expected frequencies are not equal when, in fact, they are.

Alternatively this may be performed in SPSS. The observed frequencies need to be entered in the spreadsheet using two columns: the first column specifying the category and the second the observed frequency. Input the observed frequency into the weight cases box using Data:weight cases . We are now ready to use the chi-square procedure located under nonparametric tests>chi-square. The columns containing the observed categories is entered in thetest variables window. The expected frequencies may be entered in the menu window by clicking values under expected frequencies and entering the list of expected frequencies in the window. Note: SPSS cannot handle zero observed frequencies for a category even when the analogous expected frequency is non-zero.

[SPREADSHEET TO BE ADDED].