Is the Dart Throwing Data a Gaussian Distribution?

In summary, a Chi Squared Test is a statistical method used to determine if there is a significant difference between two categorical variables. It is commonly used in analyzing data from experiments or surveys to determine if a relationship exists between the variables. In Excel, the CHISQ.TEST function is used to calculate the test and the p-value is compared to a significance level to interpret the results. The null hypothesis in a Chi Squared Test states that there is no significant difference between the observed and expected values. However, Excel has limitations such as only being able to test two categorical variables and assumptions that must be met for accurate results.
  • #1
Dgray101
33
0

Homework Statement



We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.

Dart 1 Dart 2 Dart 3 Dart 4 Dart 5
1 -7 -4 4 4 5
2 -19 -6 -5 -2 0
3 -10 -6 -5 6 7
4 -13 -8 -3 8 11
5 -8 -4 -2 0 7
6 -7 -1 0 1 2
7 -13 -11 -2 -2 0
8 -8 -4 -1 8 9
9 -13 -9 -6 -3 5
10 -6 7 12 12 14
11 9 -8 -2 -2 0
12 -12 -4 -4 3 10
13 -8 -7 -4 -3 4
14 -7 -4 2 4 4
15 -5 -3 0 6 11
16 -16 -5 -3 3 8
17 -11 -3 3 1 20
18 -6 -3 3 5 7
19 -4 -2 3 5 12
20 -4 0 3 4 6
21 -11 -9 -4 -5 3
22 0 1 2 7 11
23 -8 -7 -4 -4 0
24 -2 0 6 11 13
25 -10 -8 0 0 4
26 -2 0 3 5 9
27 -5 -1 -1 0 7
28 -13 -6 -5 5 12
29 -4 -8 -2 0 3
30 -15 -5 0 1 4
31 -10 -2 -2 0 4
32 -4 1 5 7 8
33 -10 1 2 6 -1.5
34 -6 -2.5 -2 -7 6
35 -9 -3 -2 5.5 6
36 -15 -7 1 0 3
37 -6 -1 -1 3 2
38 2 1 1 -7 -8
39 -4 -3 1 4 9
40 -3 -4 -2 1 -1
41 1 -2 -2 3 4
42 -4 -3 -1 3 3
43 -7 -4 -1 3 7
44 0 -1 -1 1 2
45 0 -7 -1 -3 7
46 -7 1 -1 -1 0
47 -6 2 -3 -2 6
48 -11 -8 -1 -3 2
49 -6 -3 -2 2 5
50 -7 -4 -3 1 1
51 -2 -2 4 4 11
52 0 -1 -4 -6 7
53 -3 -3 -1 1 2
54 -1 -1 -2 2 6
55 1 -3 4 4 2
56 -8 -8 -9 8 -3
57 2 6 -7 -3 -1
58 -5 -1 -1 1 2
59 3 1 2 -1 -3
60 2 0 -3 -4 -5



-20 0
-19 1
-18 0
-17 0
-16 1
-15 2
-14 0
-13 4
-12 1
-11 4
-10 4
-9 4
-8 12
-7 13
-6 11
-5 10
-4 21
-3 23
-2 23
-1 24
0 23
1 20
2 17
3 16
4 15
5 8
6 11
7 10
8 5
9 4
10 1
11 5
12 4
13 1
14 1
15 0
16 0
17 0
18 0
19 0
20 1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.





The Attempt at a Solution

 
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  • #2
I'm not intending to address your question, but putting code tags around your data makes it much more readable.

Dgray101 said:

Homework Statement



We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.
Code: 
	Dart 1	Dart 2	Dart 3	Dart 4	Dart 5
1	-7	-4	4	4	5
2	-19	-6	-5	-2	0
3	-10	-6	-5	6	7
4	-13	-8	-3	8	11
5	-8	-4	-2	0	7
6	-7	-1	0	1	2
7	-13	-11	-2	-2	0
8	-8	-4	-1	8	9
9	-13	-9	-6	-3	5
10	-6	7	12	12	14
11	9	-8	-2	-2	0
12	-12	-4	-4	3	10
13	-8	-7	-4	-3	4
14	-7	-4	2	4	4
15	-5	-3	0	6	11
16	-16	-5	-3	3	8
17	-11	-3	3	1	20
18	-6	-3	3	5	7
19	-4	-2	3	5	12
20	-4	0	3	4	6
21	-11	-9	-4	-5	3
22	0	1	2	7	11
23	-8	-7	-4	-4	0
24	-2	0	6	11	13
25	-10	-8	0	0	4
26	-2	0	3	5	9
27	-5	-1	-1	0	7
28	-13	-6	-5	5	12
29	-4	-8	-2	0	3
30	-15	-5	0	1	4
31	-10	-2	-2	0	4
32	-4	1	5	7	8
33	-10	1	2	6	-1.5
34	-6	-2.5	-2	-7	6
35	-9	-3	-2	5.5	6
36	-15	-7	1	0	3
37	-6	-1	-1	3	2
38	2	1	1	-7	-8
39	-4	-3	1	4	9
40	-3	-4	-2	1	-1
41	1	-2	-2	3	4
42	-4	-3	-1	3	3
43	-7	-4	-1	3	7
44	0	-1	-1	1	2
45	0	-7	-1	-3	7
46	-7	1	-1	-1	0
47	-6	2	-3	-2	6
48	-11	-8	-1	-3	2
49	-6	-3	-2	2	5
50	-7	-4	-3	1	1
51	-2	-2	4	4	11
52	0	-1	-4	-6	7
53	-3	-3	-1	1	2
54	-1	-1	-2	2	6
55	1	-3	4	4	2
56	-8	-8	-9	8	-3
57	2	6	-7	-3	-1
58	-5	-1	-1	1	2
59	3	1	2	-1	-3
60	2	0	-3	-4	-5

Code: 
-20	0
-19	1
-18	0
-17	0
-16	1
-15	2
-14	0
-13	4
-12	1
-11	4
-10	4
-9	4
-8	12
-7	13
-6	11
-5	10
-4	21
-3	23
-2	23
-1	24
0	23
1	20
2	17
3	16
4	15
5	8
6	11
7	10
8	5
9	4
10	1
11	5
12	4
13	1
14	1
15	0
16	0
17	0
18	0
19	0
20	1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.





The Attempt at a Solution

 
  • #3
Dgray101 said:

Homework Statement



We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below.

Dart 1 Dart 2 Dart 3 Dart 4 Dart 5
1 -7 -4 4 4 5
2 -19 -6 -5 -2 0
3 -10 -6 -5 6 7
4 -13 -8 -3 8 11
5 -8 -4 -2 0 7
6 -7 -1 0 1 2
7 -13 -11 -2 -2 0
8 -8 -4 -1 8 9
9 -13 -9 -6 -3 5
10 -6 7 12 12 14
11 9 -8 -2 -2 0
12 -12 -4 -4 3 10
13 -8 -7 -4 -3 4
14 -7 -4 2 4 4
15 -5 -3 0 6 11
16 -16 -5 -3 3 8
17 -11 -3 3 1 20
18 -6 -3 3 5 7
19 -4 -2 3 5 12
20 -4 0 3 4 6
21 -11 -9 -4 -5 3
22 0 1 2 7 11
23 -8 -7 -4 -4 0
24 -2 0 6 11 13
25 -10 -8 0 0 4
26 -2 0 3 5 9
27 -5 -1 -1 0 7
28 -13 -6 -5 5 12
29 -4 -8 -2 0 3
30 -15 -5 0 1 4
31 -10 -2 -2 0 4
32 -4 1 5 7 8
33 -10 1 2 6 -1.5
34 -6 -2.5 -2 -7 6
35 -9 -3 -2 5.5 6
36 -15 -7 1 0 3
37 -6 -1 -1 3 2
38 2 1 1 -7 -8
39 -4 -3 1 4 9
40 -3 -4 -2 1 -1
41 1 -2 -2 3 4
42 -4 -3 -1 3 3
43 -7 -4 -1 3 7
44 0 -1 -1 1 2
45 0 -7 -1 -3 7
46 -7 1 -1 -1 0
47 -6 2 -3 -2 6
48 -11 -8 -1 -3 2
49 -6 -3 -2 2 5
50 -7 -4 -3 1 1
51 -2 -2 4 4 11
52 0 -1 -4 -6 7
53 -3 -3 -1 1 2
54 -1 -1 -2 2 6
55 1 -3 4 4 2
56 -8 -8 -9 8 -3
57 2 6 -7 -3 -1
58 -5 -1 -1 1 2
59 3 1 2 -1 -3
60 2 0 -3 -4 -5



-20 0
-19 1
-18 0
-17 0
-16 1
-15 2
-14 0
-13 4
-12 1
-11 4
-10 4
-9 4
-8 12
-7 13
-6 11
-5 10
-4 21
-3 23
-2 23
-1 24
0 23
1 20
2 17
3 16
4 15
5 8
6 11
7 10
8 5
9 4
10 1
11 5
12 4
13 1
14 1
15 0
16 0
17 0
18 0
19 0
20 1

I graphed it, and I did a gaussian distribution and all the data fits fine and dandy. But when I perform the Chi squared test in excel, what ends up happening is that I will get CHITEST = 0
and then when I do CHIINV I get that the number isn't recognized by excel. Or when I mess around with bins I end up getting a number that's roughly around 300...


I honestly have no idea why I am not getting that this data is a gaussian distribution.





The Attempt at a Solution


You need to include more details. How did you obtain the Chi-squared values; that is, what are the individual "bins" that you used in submitting the data to the Chi-squared package?

I looked at your data in maple, and found that in some ways of presenting the data the normality hypothesis was rejected (at some reasonable level of significance), while in other ways of presenting the data the normality hypothesis was accepted at the same level of significance. The point is that it is easy to "misuse" the Chi-squared test if you don't really know what you are doing. There are certain rule of thumb restrictions that typically accompany descriptions of chi-squared usage, and we have no way of knowing whether or not you paid attention to these restrictions. If you violate the restrictions the chi-squared test simply does not apply; that is, the use of a Chi-squared table is inaccurate and ill-advised.
 

1. What is a Chi Squared Test and how is it used?

A Chi Squared Test is a statistical method used to determine if there is a significant difference between two categorical variables. It is commonly used to analyze data from experiments or surveys and determine if there is a relationship between the variables being studied.

2. How is the Chi Squared Test calculated in Excel?

In Excel, the CHISQ.TEST function is used to calculate the Chi Squared Test. The function takes in two arrays of data, representing the observed and expected values, and returns the p-value for the test. The p-value is then compared to a significance level to determine if the results are statistically significant.

3. What is the null hypothesis in a Chi Squared Test?

The null hypothesis in a Chi Squared Test states that there is no significant difference between the observed and expected values. This means that any differences in the data can be attributed to chance and not a relationship between the variables.

4. How do you interpret the results of a Chi Squared Test in Excel?

In Excel, the p-value returned by the CHISQ.TEST function is used to interpret the results of a Chi Squared Test. If the p-value is less than the chosen significance level (usually 0.05), then the null hypothesis is rejected and it can be concluded that there is a significant difference between the variables being studied. If the p-value is greater than the significance level, then the null hypothesis cannot be rejected and it is likely that any differences in the data are due to chance.

5. Are there any limitations to using the Chi Squared Test in Excel?

While Excel is a convenient tool for performing Chi Squared Tests, it does have some limitations. One limitation is that it can only be used for two categorical variables, and not continuous variables. Additionally, the assumptions of the Chi Squared Test, such as having a large enough sample size and independent observations, must be met for the results to be accurate. It is important to carefully consider these limitations before using Excel for a Chi Squared Test.

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