How do I compare pre and post test answers using statistics when a different number of tests were returned?

i need to compare pre and post tests but there were a different number of pre tests than post test. I thought there was a statistical calculation for this type of problem but I can't remember it. I need to make the calcs as accurate as possible because it is for evaluating a program.

How do I compare pre and post test answers using statistics when a different number of tests were returned?
because you are looking at paired data you should only use the pre and post test scores from subjects who have provided both and then use a hypothesis tests for paired data.





Let (X1, Y1) ... (Xn, Yn) be a sample of ordered pairs.


Let D1, D2, ... , Dn be the differencs Yi - Xi = Di


Let Dbar be the mean difference


Let sD be the standard deviation of the difference





to test the null hypothesis


H0: μD = Δ or


H0: μD ≤ Δ or


H0: μD ≥ Δ





find the test statistic t = (Dbar - Δ) / (sD / sqrt(n))





The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.





H1: μD ≠ Δ; p-value is the area in the tails greater than |t|


H1: μD %26gt; Δ; p-value is the area in the tails to the right of t


H1: μD %26lt; Δ; p-value is the area in the tails left of t.





the t statistic follows the student t distribution with n - 1 degrees of freedom.





if the sample size is large then the test statistic follows the standard normal distribution.














If you were tracking more variables than just the test scores, such as age, gender, etc. then use only the data where both pre and post scores and exist and set up a regression analysis with the difference between the scores as a function of all other tracked variables. Using a step-wise model selection and analsysi of variance or analysis or covariance you will be able to determine which factors are important in producing a differece in the scores.
Reply:Compare "pre and post test answers"





1. Comparison of Means: utilize Confidence Interval (t-statistic)





2. Comparison of Variations: utilize ANOVA (F-statistic)