Q270
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Here is another way to intuit why it is better to compare the means and variances of 12 pairs of data points than to compare the means and variances of one sample of 12 to that of another sample of 12. | Here is another way to intuit why it is better to compare the means and variances of 12 pairs of data points than to compare the means and variances of one sample of 12 to that of another sample of 12. | ||
| − | When squaring numbers, you will notice that numbers become bigger much faster as they grow. 2^2 is 4 (twice as large) but 20^2 is 400 (twenty times as | + | When squaring numbers, you will notice that numbers become bigger much faster as they grow. 2^2 is 4 (twice as large) but 20^2 is 400 (twenty times as large). Since variance is the square of a value's distance from the average value, this property of squaring means that big differences have more influence in determining the variance than small differences. |
| − | The two independent samples will inevitably have more points that are further from their two means than each paired sample will, because there are only two means to | + | The two independent samples will inevitably have more points that are further from their two means than each paired sample will, because there are only two means to fit all of your data to, instead of twelve means, each of which controls for many factors (like individual differences). As a result, the variance must be much higher, making it more likely that the natural variance in the estimates will be able to account for the difference in the means that were caused by your experimental condition (which is bad). |
If this additional way of thinking about it makes it easier, good. Otherwise, you have permission to forget it. | If this additional way of thinking about it makes it easier, good. Otherwise, you have permission to forget it. | ||
Revision as of 00:51, 27 September 2009
Course Site: http://cognitrn.psych.indiana.edu/rgoldsto/courses/q270.html
Contents |
Paired vs Ind Samples T-Test
Here is another way to intuit why it is better to compare the means and variances of 12 pairs of data points than to compare the means and variances of one sample of 12 to that of another sample of 12.
When squaring numbers, you will notice that numbers become bigger much faster as they grow. 2^2 is 4 (twice as large) but 20^2 is 400 (twenty times as large). Since variance is the square of a value's distance from the average value, this property of squaring means that big differences have more influence in determining the variance than small differences.
The two independent samples will inevitably have more points that are further from their two means than each paired sample will, because there are only two means to fit all of your data to, instead of twelve means, each of which controls for many factors (like individual differences). As a result, the variance must be much higher, making it more likely that the natural variance in the estimates will be able to account for the difference in the means that were caused by your experimental condition (which is bad).
If this additional way of thinking about it makes it easier, good. Otherwise, you have permission to forget it.
Special Note: Location
We were very fortunate to get hooked up at the Simon Hall lab, with the musical equipment, and I think I can safely say that we will be meeting there for the rest of the semester.
Part One of Class
Lab One
Assignment One
Note: The assignment was written with Mac in mind. Where it asks you to go to preferences, go instead of "Options" under "Edit" and find the Viewer tab from there. That said, the little box should be checked by default. Please provide me with clean printouts, not too much line noise if you can help it.