As discussed in Assignment 11A, a common type of association study is one in which two or more different groups of phenomena (group membership being a qualitative property (X)) are suspected of having significantly different values for some co-existing quantitative property (Y). For example, one may suspect:

• men and women may have different drinking habits ("number of weekend drinks"); or
• Democrats, Republicans, and Independents might have different television watching habits ("daily minutes of watching TV news").

In such cases, we collect a set of relevant observations, sort the observations into groups according to the qualitative property (X), calculate the mean value of the quantitative property (Y) for each group, and compare the means. If the means are similar, we would interpret this to signify that the groups are not different with regard to the co-existing quantitative property. Conversely, if the group means are different, we would suspect that these differences are due to the different values of the qualitative property. If the qualitative property has two attainable values, we employ the t-Test to assess the significance of the observed differences between the two group means. In those projects in which the qualitative property has more than two attainable values, we employ what is said to be an analysis of variance (ANOVA) to assess the statistical significance of the different group means. However, unlike the t-Test, ANOVA proceeds by comparing the variances of the different groups. More precisely, ANOVA compare the mean for the variances when sorted into groups to the overall variance of the observations when not sorted into groups. If the variance due to sorting differs considerably from the variance without sorting, we suspect the sorting makes a difference, thus suggesting the group observations are significantly different.

This Assignment

For this assignment, you are to design and execute a research project in which you suspect two properties of some set of phenomena of interest to be related in an association.

• One of the properties is to be qualitative. This is to be the independent property (X), and this property is to have at least three but no more than five attainable values (i.e., different groups).

• The other is to be quantitative. This property, (Y), will be the dependent property.

Property X (Qualitative)
Value 1 (Group 1)
Value 2 (Group 2)
Value 3 (Group 3)
Value 4 (Group 4) (If necessary)
Value 5 (Group 5) (If necessary)

Property Y (Quantitative)
Units of Measurement

Collect observations of 50 phenomena. The number of phenomena in each of the groups need not be the same but should not be too different.

Observation number	Property X (Group) Value	Property Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

Sort the observations into groups according to the values of property (X).

Then, find the mean value of Y for each group, and calculate the Variance among the observations for that group.

Group 1:

(Use as many rows as necessary)

Observation	Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOTAL Y

Calculation of the Mean Value:

Total of all observed values for Property (Y)	Number of Observations	Mean = Total of Values Number of Observations

Calculation of the Variance:

Observation	Y Value	Mean	= Diff	Diff2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total	NA	NA	NA

Total of all Diff2	Number of Observations	Mean Diff2 = Variance = Total of Diff2 Number of Observations

Group 2:

(Use as many rows as necessary)

Observation	Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOTAL Y

Calculation of the Mean Value:

Total of all observed values for Property (Y)	Number of Observations	Mean = Total of Values Number of Observations

Calculation of the Variance:

Observation	Y Value	Mean	= Diff	Diff2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total	NA	NA	NA

Total of all Diff2	Number of Observations	Mean Diff2 = Variance = Total of Diff2 Number of Observations

Group 3:

(Use as many rows as necessary)

Observation	Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOTAL Y

Calculation of the Mean Value:

Total of all observed values for Property (Y)	Number of Observations	Mean = Total of Values Number of Observations

Calculation of the Variance:

Observation	Y Value	Mean	= Diff	Diff2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total	NA	NA	NA

Total of all Diff2	Number of Observations	Mean Diff2 = Variance = Total of Diff2 Number of Observations

Group 4 (If necessary):

(Use as many rows as necessary)

Observation	Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOTAL Y

Calculation of the Mean Value:

Total of all observed values for Property (Y)	Number of Observations	Mean = Total of Values Number of Observations

Calculation of the Variance:

Observation	Y Value	Mean	= Diff	Diff2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total	NA	NA	NA

Total of all Diff2	Number of Observations	Mean Diff2 = Variance = Total of Diff2 Number of Observations

Group 5 (If necessary):

(Use as many rows as necessary)

Observation	Y Value
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOTAL Y

Calculation of the Mean Value:

Total of all observed values for Property (Y)	Number of Observations	Mean = Total of Values Number of Observations

Calculation of the Variance:

Observation	Y Value	Mean	= Diff	Diff2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total	NA	NA	NA

Total of all Diff2	Number of Observations	Mean Diff2 = Variance = Total of Diff2 Number of Observations

Compare the group Values:

1. Compare the group Means:

Group 1 Mean
Group 2 Mean
Group 3 Mean
Group 4 Mean
Group 5 Mean

Are the group means similar or different?

n

1. Compare the group Variances:

Group 1 Variance
Group 2 Variance
Group 3 Variance
Group 4 Variance
Group 5 Variance

Are the group Variances similar or different?

this below can be used for the first part of the question Let's go through the steps outlined in your project.

Below are the 50 observations:

| Observation Number | X Value (Religious Affiliation) | Y Value (Party Affiliation) | |--------------------|---------------------------------|-----------------------------| | 1 | Christian | Republican | | 2 | Jewish | Democrat | | 3 | Hindu | Independent | | 4 | Islamic | Other | | 5 | Other | Democrat | | 6 | None | Republican | | 7 | Christian | Democrat | | 8 | Jewish | Republican | | 9 | Hindu | Independent | | 10 | Islamic | Democrat | | 11 | Other | Republican | | 12 | None | Independent | | 13 | Christian | Republican | | 14 | Jewish | Democrat | | 15 | Hindu | Other | | 16 | Islamic | Democrat | | 17 | Other | Republican | | 18 | None | Democrat | | 19 | Christian | Independent | | 20 | Jewish | Republican | | 21 | Hindu | Democrat | | 22 | Islamic | Independent | | 23 | Other | Republican | | 24 | None | Democrat | | 25 | Christian | Republican | | 26 | Jewish | Democrat | | 27 | Hindu | Independent | | 28 | Islamic | Other | | 29 | Other | Republican | | 30 | None | Democrat | | 31 | Christian | Independent | | 32 | Jewish | Republican | | 33 | Hindu | Democrat | | 34 | Islamic | Independent | | 35 | Other | Republican | | 36 | None | Democrat | | 37 | Christian | Republican | | 38 | Jewish | Democrat | | 39 | Hindu | Independent | | 40 | Islamic | Other | | 41 | Other | Republican | | 42 | None | Democrat | | 43 | Christian | Independent | | 44 | Jewish | Republican | | 45 | Hindu | Democrat | | 46 | Islamic | Independent | | 47 | Other | Republican | | 48 | None | Democrat | | 49 | Christian | Republican | | 50 | Jewish | Democrat |

I am not sure