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Assignment: t Test

Each of you will be assigned a research question to answer from data that is provided below. You will need to run a t test to answer the research question. The t test is appropriate because the independent variable has just two levels (i.e., male and female). I have created a spreadsheet to calculate the t test for you and a PowerPoint presentation that describes how to use the spreadsheet. Enter the independent variable in the IV column and the dependent variable in the DV column. The spreadsheet will do the rest. The spreadsheet is set for one group to have been labeled 1 and the other group to have been labeled 2.

Type your assignment similar to the sample below.

For this assignment we have set the alpha level (p) at .05. You need to decide whether to read the equal or unequal variance t test on the spreadsheet. If you have a different number of people in the two groups and the F-max test is less than or equal to .05 you read the unequal. If you have the same number of people in both groups OR if you have a different number of subject in the groups and the F-max is greater than .05, you read the equal variance t test. The spreadsheet will tell you which to use.

If the p (two tailed significance) for your t test is less than or equal to .05, you will reject your null hypothesis and state that there was a statistically significant difference between the means of the two groups. If your p > .05, you will fail to reject your null hypothesis and state that there was no statistically significant difference between the means of the two groups.

You also need to state the effect size. EFFECT SIZE is used to calculate practical difference. Effect size is the difference of the two means divided by the standard deviation of the control group (or the average standard deviation of both groups if you do not have a control group). Effect size becomes important if you have statistical significance. An effect size of .2 is considered small, .5 is considered medium, and .8 is considered large. The spreadsheet program will calculate the EFFECT SIZE for you (you just need to select the correct one).

The number in () following the t is the degree of freedom (number of subjects minus the number of groups). The number following the = is the t-value. In the example below, there are 32 degree of freedom (number of subjects minus the number of groups) and the t-value is 4.58. n is the number of subjects. In the example below there are 17 females and 17 males. p is the significance level (a.k.a. probability — the likelihood of finding this difference between the means of the two groups in our sample by chance when there was no difference in the populations from which the sample was drawn). Although it is not written in stone, p < .05 is a commonly used. Don’t forget to underline or italicize M, SD, p, t, and n. We also underline or italicize the title of the table and put a period after the t statement that is under the table. We only say there is a difference in the means of the two groups if the t-value is statistically significant (p < .05). If p is not less than .05 we still report the means for the two groups, but we say they are similar. We will only report the effect size (d) if there is a significant difference between the mean. We will not report it if there is not a significant difference because that would mean that the effect size probably occurred by chance.   I have listed the scoring system throughout the sample assignment in BOLD ITALIC.

 

Sample Assignment (yours will be different, but have these elements)….

Study Design

Independent variable: Student Gender
Dependent variable:  Mathematics Achievement (4 points)

Type of t test and Why

Equal variance independent t test because the subjects in the two groups are different and while the number of subjects in each group is different, the variance of the two groups is similar. (3 points)

Question
Is there a statistically significant difference between boys and girls with respect to mathematics achievement?
–or–
Does mathematics achievement statistically differ between boys and girls? (This will be provided for you.)

Null Hypothesis
Mathematics achievement does not statistically differ between boys and girls. (1 point)

Alternative Hypothesis
Mathematics achievement statistically differs between boys and girls. (1 point)

Answer
There was a statistically significant difference in the mathematics achievement of boys and girls, t(32)=4.58, p=.04. This difference represented a large effect size, d=3.73 (Cohen, 1988). Girls (M=12.3, SD=.56) scored lower than boys (M=14.5, SD=.62). (5 points for correct answer [there was or wasn’t a statistically significant difference], 1 point for italicize t, 1 point for correct degree of freedom, 1 point for correct t-value, 1 point for italicize p, 1 point for correct p value, 1 point for italicize d, 1 point for correct effect size, 2 points for italicize M (twice), 2 points for correct mean values, 2 points for italicize SD (twice), and 2 points for correct standard deviation values)
Table 1

Gender Differences in Mathematics Achievement

————————————————————————————————

Gender                         M                      SD                      n

————————————————————————————————-

Females                      12.3                      .56                      17

Males                          14.5                      .62                      17

————————————————————————————————-

t(32)=4.58, p=.04, d = 3.73.

(1 point for Table 1, 1 point for table title, 1 point for italicize table title, 1 point for line (rule) above category head, 1 point for independent variable name in category head, 1 point for italicize M, 1 point for italicize SD, one point for italicize n, 1 point for line (rule) under category head, 2 points for two levels of the IV, 2 points for correct means, 2 points for correct standard deviations, 2 points for correct number of subjects in each group, 1 point for bottom line (rule), 1 point for italicize t, 1 point for correct degree of freedom, 1 point for correct t-value, 1 point for italicize p, 1 point for correct p value, 1 point for including value of d, 1 point for italicize d, and 1 point for period at end of d statement.)

Hypothetical Data:

An IBM Fifth Year Student collected the following data for her internship project: First Grade Fall Reading Score, First Grade Spring Reading Score, Number of Books in the Home (per hundred), Age Entering First Grade, Student Gender

Fall         Spring     Books     Age          Gender

5              18            4              6              boy

15            20            3              7              girl

15            21            4              7              boy

14            22            5              7              boy

12            15            4              6              girl

10            20            3              6              girl

14            23            3              7              boy

12            25            4              6              girl

16            21            4              7              girl

5              19            5              6              boy

6              18            3              6              boy

14            26            5              7              girl

15            25            4              7              girl

7              28            5              6              boy

9              22            3              6              girl

6              29            4              7              boy

15            24            4              6              girl

11            20            3              6              girl

6              21            5              6              boy

15            23            4              7              girl

15            25            6              7              boy

5              22            4              6              boy

7              24            3              6              girl

16            15            5              7              girl

15            24            5              7              boy

15            23            6              7              boy

 

In class, you will be assigned one of the following research questions:

  1. Is there a significant difference between boys’ and girls’ first grade fall reading scores?
  2. Is there a significant difference between boys’ and girls’ first grade spring reading scores?
  3. Is there a significant difference between 6-year-olds’ and 7-year-olds’ first grade fall reading scores?
  4. Is there a significant difference between 6-year-olds’ and 7-year-olds’ first grade spring reading scores?
  5. Is there a significant difference between boys and girls with respect to the number of books in the home?
  6. Is there a significant difference between 6-year-olds’ and 7-year-olds’ with respect to the number of books in the home?
  7. Is there a significant difference between students’ fall and spring reading scores?