The Independent Samples T-Test

The Chi Square Goodness-of-Fit Test

The Chi Square Goodness-of-Fit Test determines if it is reasonable to assume that your sample came from a population where, for each category, the actual proportion of outcomes is equal to some hypothesized proportions.

Assumptions and Conditions

Counted Data Condition - You must have observed COUNTS to use chi square if they give you percentages or proportions you have to be able to convert them into counts. Do not use quantitative data!!!!

Random Condition – the individuals who have been counted and whose counts are available for analysis should be a random sample from some population.

Large Sample Assumption – The sample is large enough if we check the…. Expected Counts Condition – every cell has an expected count of at least 5 (similar to the 10% condition)

Hypotheses

the actual proportions in the population are equal to those in your model

at least one actual proportion in the population is not equal to that in your model.

The test statistic () needs the following:

1. Make a Chi Square Table! ( This is not an “actual” thing its just something I use to keep my frequencies straight!)

Outcomes
Observed
Frequencies
Expected
Frequencies

2. You must be given information to calculate expected frequencies or be given contextual information to know that the expected frequencies are equally distributed.

3. The test statistic is:

4. The Degrees of Freedom for your data are found by

5. The P-Value for your data is the probability of getting a value of as extreme as or even more extreme than the one in the sample, assuming the null is true. Approximate the P-Value by comparing the value of to the appropriate value of in the table in the back of the book or use your calculator and put in cdf (, 9999, df) which you find in the distributions section.

Conclusion in Context

If the P-Value is smaller than the alpha level or if the value is larger than the value in the back of the book then reject the null hypothesis. If not, there is no evidence that the null is false and you don’t reject it.

Calculator STAT TESTS GOF-Test

You must have your observed frequencies stored in L1 and your expected stored in L2 and you must know the degrees of freedom to do this.

Ok so you might not have this command on your calculator……if you don’t you will have to do chi square goodness of fit by hand but it’s ok! The rest of the chapter you should be able to do via calculator!!! Sorry!!! You can try to get an upgrade……

Example:

Suppose in a random sample of 75 peanut M&M’s you get the distribution of colors shown in the table. We know that plain M&M’s have 30% brown, 20% red, 20% yellow, 10% green, 10% orange and 10% blue. Is the distribution of peanut M&M’s the same as the distribution of plain M&M’s?

Colors
red / yellow / green / orange / brown / blue
11 / 16 / 8 / 5 / 17 / 18