STAT 217
Lab 7

1: Background 2: Explore Data 3: Inference: MAD 4: Inference: Max-Min 5: Inference: Chi-square 6: Theory-Based 7: Estimation 8: Conclusions 9: Extension 10: Summary

Statistical Inference - Chi-Square Statistic

Another possible statistic is the Chi-square statistic. Here is one version of how to calculate the statistic for a binary response variable:

where is the overall proportion of successes for the entire sample and the n_i are the sizes of the three treatment groups. Note: The summation symbol S stands for "sum all the values." You can consider this statistic as the sum of the squared z-statistics from the (common) overall proportion of successes.

(h) Calculate the overall proportion of successes (donors) for all 161 responses.

 

This overall proportion represents what we would expect to see in each group if there was no effect from the default option wording provided to the participants.

(i) Compare each conditional proportion to this overall proportion and standardize by dividing by the standard error using the overall proportion and that group's sample size. Then square each of these values. Then sum these three values together. (Show the details in your lab report.)

 

 

(j) Now use the Statistic pull-down menu to select the X² to show the results of 1000 repetitions of this statistic. Confirm your calculation of the observed chi-square statistic (in black). Describe the shape, center, and spread of the resulting null distribution of the chi-square statistic.

 

(k) Use the applet to estimate the p-value corresponding to this chi-square statistic for our study. Include a screen capture of the null distribution with the count samples output. Is this p-value similar to the previous two?