T-Test Explanation
Statistical analysis was done on the data from the tests to determine the improvement caused by chewing gum and if it is significant. For each grade, and for each gender the scores from tests while chewing gum and while not chewing gum were compared to find a Percentage of Improvement. This was found by the equation:
(Gum-NoGum) / NoGum x 100
In this equation ‘Gum’ represents the number of words repeated correctly during the gum test and ‘NoGum’ represents the number of words repeated correctly during the test while not chewing gum. This established a percentage based upon the number of words repeated for the test without gum, such that a positive percentage means an increase when chewing gum.
Of these percentages, the Standard Deviation was taken for both groups, boys and girls. The standard deviation is a representation of how spread apart the data is from each other point and the mean. This number is later used to calculate the significance of the difference statistically. The Variation is the square of the standard deviation.
The number of people tested in each group is the sample size, n. We tested 10 boys and 10 girls, from each grade, for their memory of the words. The Critical Value is a value which is determined by one less than the sample size, and by the confidence interval which was selected to be 95%, it was previously determined and found in appendix III of Schaum's Outlines (1998). In the left-tailed test which was done on the set of data, the critical value is how far left the t value can be before the Null Hypothesis is rejected.
For each gender, a t-statistic value was determined. This value is to be as close to the critical value while not being less than or equal to it, it must be greater than the critical value. The t value is found by the t-test equation:
t = (x – (mu)) / (s / sqrt(n))
In this equation, the x with a line represents the sample mean of which is the average of the percentages of improvement for either boys or girls. The Mu is the Hypothesized Mean for the population. This is the improvement which is statistically expected for the entire population if they were to chew gum. The population would be the larger group which the sample is supposed to model. In the equation, s is equivalent to the standard deviation of the group and n represents the sample size.
The same t-test was then used to calculate the significance of the larger samples such as the whole middle and upper school, all boys and all girls and all of the test subjects. The sample sizes changed because of the larger groups for these tests and because of this the critical values change slightly, becoming larger as the sample size increased.