testing for improvement over time

[JackSwan]

A company kept record of contacts and sales during 20 consecutive periods. The results are listed in the file xx. According to these data, can there be shown a significant improvement of the success rate over time? (significance level of 1%)

How do i test for improvement over time? I believe a t-test isn't applicable here because we're not testing for changes from mean. I believe it has something to do with regression. Could someone give some pointers please?

The file contains a number of contacts and sales made in each period.
f.ex.
Period 1: contacts (120), sales (10)
Period 2: contacts (122), sales (12)
...

[JackSwan]

Would it be possible to split them into three or four samples, take the mean of the samples and test with ANOVA (one-tailed F-test) whether there is an increase?
Another option is to do a regression and check the coefficient and if it's more than 1 then there's an increase over time. Could this be the right solution?

[Dragan]

Would it be possible to split them into three or four samples, take the mean of the samples and test with ANOVA (one-tailed F-test) whether there is an increase?

I think that if you're going to use the means, you might also want to consider testing for Trend (i.e. trend analysis using orthogonal polynomial coefficients).

[JackSwan]

Thanks for the answer. This is an intermediary statistics course and we haven't had any trend analysis using orthogonal polynomial coefficients in our lectures so I really don't know what that is but I will check it out.

[trinker]

I'm just shooting ideas here. Take what looks good and run with it. You haven't given a full picture of the scenerio so...

A repeated measures analysis could work here but that's a lot of trials. Regression could work but that's getting into territory you said you haven't covered with trend analysis as Dragen suggests. You have appears to be two DV's. You could possibly turn the 2 DVs into a proportion of contacts to sales and put that into a simple regression model.

[JackSwan]

Actually this is the full picture of the scenario. After thinking long and hard the answer was actually very simple. First calculate the success rate: sales/contacts
Then run regression with x= period and y=success rate. From this one can figure out that the coefficient *period is positive and significant at a = 0.01 . Thus, we can reject the null and conclude that there is significant improvement of the success rate over time.

Thanks to all who contributed