Chi-square goodness-of-fit test power analysis

Let’s use an example where a phone vendor sells four popular models of phones, models A, B, C, and D. We want to determine how many samples are required to produce a power of 0.8 so we can understand whether there is a statistically significant difference between the popularity of different phones so the vendor can more properly invest in phone acquisitions. In this case, the null hypothesis asserts that 25% of phones from each model were sold. In reality, 20% of phones sold were model A, 30% were model B, 19% were model C, and 31% were model D phones.

Testing different values for the nobs argument (number of observations), we find that a minimum of 224 samples produces a power just greater than 0.801. Adding more samples will only improve this. If the true distribution were more divergent from the hypothesized 25% even split, fewer samples would be required. However, since the splits are relatively close to 25%, a high volume...