1. Beyond the Formula 2005 Investigating Statistical Assumptions Using Fathom 2
Sponsored by Key Curriculum Press
Tom Short
Indiana University of Pennsylvania

2. Outline + Introduction + Inference for one proportion
+ Visualizing confidence intervals
+ Simulation studies of coverage
+ Inference for means
+ Questions and discussion

3. Inference for One Proportion
What is the true proportion, p, of BTF participants who are currently high school classroom teachers?
Collect a sample of size n
Count the proportion of “successes,” x
Compute the sample proportion,

4. Confidence Interval for p
An approximate 95% confidence interval for the true proportion, p, is given by:
Note that for 95% confidence, z* = 1.96

5. Rules for Sample Proportions
+ Number of trials, n, is fixed
+ Trials are independent
+ There is a constant probability of success on each trial, p
+ The number of observed successes, np >= 10 (or 5 or 15 or …)
+ The number of observed failures, n(1-p) >= 10 (or 5 or 15 or …)

6. Quantifying Skewness
Skewness
Large negative values indicate a tail to the left.
Large positive values indicate a tail to the right.
Skewness is the third moment about the mean.

7. What are the consequences?
+ Misleading or incorrect coverage percentages
+ Inflated Type I error probabilities