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:

• 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?

• 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?