How is the binomial test direction determined when the test proportion is not .5?
I'm using the binomial test in SPSS. When I specify a test value different than the default .5 value, it seems that which observed proportion is tested against the specified value is arbitrary. How is SPSS determining which value to test?
The BINOMIAL test option in the SPSS NPAR TESTS procedure allows three different ways to specify how to determine the two groups and which one is used as the comparison when doing a one-sided test with the test proportion other than .5. If a cutpoint is specified, all values up to and including the cutpoint are included in the first group, and that group's proportion is tested against the specified value. If two values are specified using command syntax, all cases having the first value go into the first group and all other values go into the second group. Again, the first group's proportion is used in the test. If the dichotomy is determined by the data (which is the default in the menus and if nothing is specified in command syntax), then the first group is determined by which value is observed first in the data. All cases with that value are in the first group. Cases with a second value go into the second group. Again, the first group's proportion is the one tested.
The direction of the alternative hypothesis is always the direction in which the observed proportion of the first group departs from the null-hypothesized proportion.