Below are several data sets that will be used in a few basic statistical analyses. Please follow the directions and contact me if you have any questions. You will need Microsoft Excel 2000 to perform the analyses or calculate them by hand. If you chose to calculate them by hand, please refer to your STA 270 Basic Statistics textbook or any basic statistics text for the t-test formulas and df tables.
Submit this assignment to the course facilitator as an
email message.
Central Tendencies
1. Mean
Formula: mean = sum of all scores / the number of scores.
Calculate the mean for the following data set.
Money spent by youth at a little league concession
| Youth | Amount Spent |
| 1 | $2.56 |
| 2 | $1.25 |
| 3 | $3.25 |
| 4 | $1.15 |
| 5 | $1.01 |
| 6 | $1.27 |
| 7 | $2.12 |
| 8 | $1.01 |
| 9 | $3.62 |
| 10 | $0.79 |
2. Median
The median is the point that divides a distribution of scores exactly in half. Remember, the median is a point in the distribution, it may or may not be an actual score.
Calculate the median using the same data set. First, arrange the scores from highest to lowest, then determine the median.
Scores
| $2.56 |
| $1.25 |
| $3.25 |
| $1.15 |
| $1.01 |
| $1.27 |
| $2.12 |
| $1.01 |
| $3.62 |
| $0.79 |
3. Mode
The mode is the most frequently occurring score - the score with the greatest frequency.
Calculate the mode using the previous data set.
Tests of Differences
4. t-Test
The t distribution tells you the probability that the difference you observe is due to chance is the null hypothesis is true. The t-test is a ratio of a statistic over a measure of variability.
Using the t distribution to test a hypothesis is very similar to using the normal distribution. The null hypothesis is that the two populations have the same mean, and thus any difference between the two sample means is due to chance.
The t distribution tells you the probability that the difference you observe is due to chance if the null hypothesis is true. You simply establish a Type 1 error level, and if your observed difference is less probable than the Type 1 error level, reject the null hypothesis and conclude that the two means came from populations with different means.
Calculate the t score for the following Independent-Samples t-test data set.
Self-esteem scores for a challenge course research study
| Experimental Group (X1) | Control Group (X2) |
| 74 | 39 |
| 52 | 51 |
| 48 | 68 |
| 39 | 79 |
| 62 | 49 |
| 57 | 49 |
| 40 | 43 |
Tips for working with
Microsoft Excel
create the data set shown above (Experimental Group in Column A and Control Group in Column B)
click on Tools from the menu bar at the top of the screen.
click on Data Analysis
NOTE: If the Data Analysis command is not on the Tools menu, you need to install the Analysis ToolPak in Microsoft Excel. This is an optional program in your existing Microsoft Excel 2000 software. It should be in the Microsoft Excel '98 software without having to install the ToolPak.
 | On the Tools menu, click Add-Ins.
If Analysis ToolPak is not listed in the Add-Ins dialog box, click Browse and locate the drive, folder name, and file name for the Analysis ToolPak add-in, Analys32.xll — usually located in the Microsoft Office\Office\Library\Analysis folder — or run the Setup program if it isn't installed. |
| Select the Analysis ToolPak check box. |
| On the Tools menu, click Data Analysis. |
| In the Analysis Tools box, click the tool you want to use. |
| Enter the input range and the output range, and then select the options you want. |
Note Add-ins you select in the Add-Ins dialog box remain active until you remove them.
select t-test paired Two Sample for Means;
select New Worksheet Ply;
on the box that appears, for variable 1: drag a box around Column A; then drag a new box around Column B for variable 2; then
Click OK
Formula
for calculating the Independent t-test (If you do not use Excel)
 |
Key
= Sum (add)
= Scores
= Number of
scores
= Standard
error of the mean for a sample
= Standard
error of the difference between means
df (degrees of freedom) = N1 + N2 - 2
Reject the null if the t is 2.447 (at .05 Confidence Level) or lower.
From the Data Analysis Sheet, submit the following
information:
 |
4a. the df (degrees of freedom) |
|
4b. the t Stat |
|
4c. the t Critical o (one-tail test) |
|
4d. depending on, if the t Stat is less than the t Critical o number, WOULD YOU REJECT THE NULL HYPOTHESIS? Yes or No |
Submit this assignment to the course facilitator as an
email message.
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