Wheelchair Bowling and SPSS

For a psychology degree at my university, you need to take two statistics classes. I'm currently awaiting my final exam in the first of those two. In the course of this class, I was introduced to Statistic Package for Social Sciences (SPSS), a computer program for doing statistical analysis. (And something I desperately wished to have when I was 14!)

My best friend and classmate invited me to go bowling with her last Friday. She has CP and uses a wheelchair. In case you don't know, the usual accomodation for someone bowling in a wheelchair is to give them a T-shaped wooden thing they can put on their lap, and let the ball roll down that thing to propell it along.

Anyway, my brother claimed that using the T-shaped thing would make the game considerably easier, so I decided to test that. Half of the time I bowled standing up, and half of the time I bowled sitting down with the T-shaped thing. My friend, of course, used the T-shaped thing every time. I kept records on our scores, and plugged it into SPSS.

Here's what I found:

T-test for my scores sitting vs standing:

N was 10 for both groups. My mean score while sitting was 10.3, with a standard deviation of 2.79 and a standard error (mean) of .88; for standing, the mean was 4.6, standard deviation 4.35 and standard error 1.38. On the face of it, then, it seems like my sitting scores are higher.

SPSS does two forms of the T-test - one assuming the standard deviations of the two groups are equal, and one assuming they're not. It also runs a test to decide if they are equal or not, and based on this test, we decide which set of data to pay attention to. In this case, the variances were equal (significance .277) so I used the data for the equal-variances form of the T-test.

Mean difference between my score sitting vs standing was 5.7. The 95% confidence interval for this mean was 2.27 to 9.13 - this means I'm 95% certain that the true difference in mean score between my sitting and standing scores is between these two values. Since 0 is not within the confidence interval, the probability that there is no difference between sitting and standing scores must be below 5%. This is confirmed by the p-test, which gives the value of .003 (in other words, 0.3%).

So I can reject the null hypothesis - my scores are significantly higher when I'm sitting than when I'm standing.

T-test for my scores vs my friend's scores:

N was 20 for both groups, since I lumped together my sitting and standing scores. My mean score was 7.45, with a standard deviation of 4.61 and a standard error of 1.03; my friend's mean score was 6.15, with a standard deviation of 4.32 and a standard error of .97. On the face of it, my score is slightly higher, but it's awfully close. (Incidentally, this is bunched together from two games - my friend won the first and I won the second.)

The test for equal variances spit out .817, so it's very likely that both me and my friend had the same standard deviation of scores. (As you can see by simply glancing, the standard deviations are very close.)

Mean difference was 1.3, with a 95% confidence interval of -1.56 to 4.16. This range includes 0, so I'm more than 5% certain that there's no difference in mean score between me and my friend. The p-test confirms this with a value of .363 - well above .05.

I can't reject the null hypothesis - we don't have any evidence to claim our overall scores were different.

T-test for my sitting scores vs my friend's scores:

Remember, my friend was sitting for every round, and I've already shown that my sitting scores were higher than my standing scores. So, if we only compare rounds done while sitting, what do we get?

This is actually pretty tricky to tell SPSS to do. I had each data point marked both by who was bowling and whether they were sitting or standing. There's an option to split the file by a certain variable, so you calculate multiple groups as separate data sets - I told it to split by sitting/standing. Then I ran the t-test by person bowling. It actually tried to run separate t-tests on both sitting and standing, and spat out an error for standing because my friend didn't have any standing data points. But I didn't care about that.

I'm not going to review the means, standard deviations and standard errors, because I've already reported those. So let's get on to the equal variances measure. This is interesting - it spat out .011. That's lower than .05, so the standard deviations are probably not equal. My friend's standard deviation was about twice my standard deviation (even though it should've been smaller since she had a larger sample size). This indicates that her scores were more variable than mine.
Mean difference was 4.15, with a 95% confidence interval of 1.46 to 6.84. That doesn't include 0, so our means are unlikely to be the same - the p-test reported .004.

So I can reject the null hypothesis - when both bowling the same way, my scores were significantly higher than my friend's scores.

Conclusion:

What have I found out? Bowling with a T-shaped thingy is easier than normal bowling, and I'm better at bowling than my friend is. (Then again, she does have significant upper-body impairment, which is why she uses a motorized chair rather than a manual.) Neither of us is particularly good at bowling, not that it matters since we both like playing regardless.

And SPSS is really fun to play around with. I'm going to love being able to do actual psychological research, which I'm apparently going to start doing in 3rd year.