Assignment # 5 - Statistical Analyses

Grading Basis: Each of the seven (7) questions/calculations are worth 14 points each out of 100 possible points. This assignment is worth 5 points of your final grade. See Syllabus Grading System.

Example: 100 (possible total assignment points) - 14 points (one wrong answer) = 86 (assignment grade) x .05 = 4.3 total grade points

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Assignment Guidelines

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Please review all of the Kaltura assignment videos in the PRM 447 BbLearn site.

If you cannot view the video, contact the Student Technology Center at (928) 523-9294 or (888) 520-7215

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The data set in the Assignment 5 Kaltura video in NOT the same data set required for the assignment.

For many research and evaluation projects, statistics are used to understand the numeric relationship of variables. Most beginner evaluators and researchers conduct basic descriptive and inferential statistics for their analyses. Software such as Excel provides these basic statistics in easy-to-learn procedures. This assignment is an example of the basic statistical analyses using descriptive statistics (mean, median and mode) and a t-test.

The t score is a ratio between the difference between two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t test, the bigger the t-value, the more likely it is that the results are repeatable.

Terminology you need to understand:

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 2011 or 2016 to perform the analyses.

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.


Tips for working with Microsoft Excel - PC & MAC
 

PC 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 software.

To install the Analysis ToolPak for Excel 2011 or 2016

bulletClick the File tab, click Options, and then click the Add-Ins category, then
bullet In the Add-ins list, select the Analysis ToolPak-VBA, and then click Go.
bullet In the Add-Ins available box, select the Analysis ToolPak, and then click OK.
Tip: If Analysis ToolPak is not listed in the Add-Ins available box, click Browse to locate it.
If you are prompted that the Analysis ToolPak is not currently installed on your computer, click Yes to install it.
bulletAfter you load the Analysis ToolPak , the Data Analysis command is available in the Analysis group on the Data tab.

To install the StatPlus:mac LE ToolPak for Excel 2010 or 2011

MAC NOTE: MAC with Excel 2004 or 2016, Go to Tools; Select Excel Addins; Select Analysis ToolPak; OK

This will show the Data Analysis icon in the Top Navigation Bar.

Assignment 5 Statistical Analyses

Descriptive Statistics Items 1-3 and t-Test Items 4-7

 DO NOT ROUND ANY ANSWERS AND INCLUDE THREE DECIMAL PLACES (0.456)

Central Tendencies


 Note: The mean, median and mode can be calculated using the descriptive statistics in the Data Analysis options. See below.
 

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

Amount Spent
12.15
8.33
14.27
10.89
6.50
7.61
8.88
17.29
10.89
12.03
13.41
11.83
8.49
3.55
11.29
5.89
13.52

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.

Amount Spent
12.15
8.33
14.27
10.89
6.50
7.61
8.88
17.29
10.89
12.03
13.41
11.83
8.49
3.55
11.29
5.89
13.52

3. Mode

The mode is the most frequently occurring score - the score with the greatest frequency.

Calculate the mode using the previous data set.

To use the Analysis ToolPak

1. Click on the Data tab,

2. Click on Data Analysis.

3. In the Analysis Tools box, select Descriptive statistics, click OK

4. In the Input Range box: drag a box around Column A; then

5. Select Summary statistics, click OK

6. This will calculate all the required answers.

Tests of Differences

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. The scores below are Self-esteem scores from a challenge course research study


 Directions: To get your answers for items 4-7, Calculate the t score for the following data set.,
 

Group (X)
Group (Y)
77 54
94 45
71 58
88 78
64 75
46 69
89 67
68 49

79

68
79 58
97 67
85 50
95 53
69 66
94 56
99 79
86 65

84

63
79 58
80 40
67 51
86 62

From the Data Analysis Sheet, submit the following information:

4. The df (degrees of freedom)

5. The t-Stat or Test Statistic for the StatPlus Mac

6. The t Critical two-tail

7. WOULD YOU REJECT THE NULL HYPOTHESIS? Yes or No
Note: If  the t-Stat (Test Statistic for the StatPlus Mac) number is less than the t Critical two-tailed number, (at .05 Confidence Level), accept the null.
There is no difference between the two groups.

If  the t-Stat (Test Statistic for the StatPlus Mac) number is larger than the t Critical two-tailed number, (at .05 Confidence Level), reject the null. There is a significant difference between the two groups.

email icon Submit your answers for this assignment in the body of an email and send to the course facilitator.

PC: To use the Analysis ToolPak

1. Click on the Data tab,

2. Click on Data Analysis.

3. In the Analysis Tools box, select t-Test Paired Two Sample for Means, click OK

4. In the box that appears, for variable 1: drag a box around Column A; then drag a new box around Column B for variable 2;

5. Select New Worksheet Ply; then

6. Click OK

7. This will calculate all the required answers.

MAC: To use the StatPlus;mac LE Program

bulletDownload the StatPlus program at: http://www.analystsoft.com/en/products/statplusmacle/     (no upgrade is required)

Once you have downloaded the StatPlus program

bullet

Select Statistics from the top menu bar

bullet

Select Basic Statistics and Tables

bullet

Select Descriptive (to calculate the mean, median and mode)

bullet

This will calculate all the required answers for 1 through 3.

bullet

Select Comparing Mean (T-Test)

bullet

In 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

bullet

Select t Test: Paired Two-Sample T-Test

bullet

This will calculate all the required answers for 4a through 4c.


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

[Unit 3]

 

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