# "2 Variances" test for Paired Data in Minitab - How to proceed

B

#### Berg.Jlle

Hello.

I could not find any post about my question of using of "2 Variances" test for paired data. Sorry whether a similar thread already exists...
So, can I use "Stat>Basic Statistics>2 Variances" to assess paired data ?

#### Miner

##### Forum Moderator
What is the question to be answered?
1. Is there a difference between the means? Paired t-Test
2. Is there a relationship between the pairs? Correllation and Regression
The Test for Equal Variances is not really appropriate for paired data. If you are testing for the difference in means, you should be concerned that the delta between the paired measurements is normally distributed.

B

#### Berg.Jlle

What is the question to be answered?
1. Is there a difference between the means? Paired t-Test
2. Is there a relationship between the pairs? Correllation and Regression
The Test for Equal Variances is not really appropriate for paired data. If you are testing for the difference in means, you should be concerned that the delta between the paired measurements is normally distributed.
Miner,

My purpose is to answer the following hypotheses for a set of paired data.

H0: σA = σB or σA - σB = 0
H1: σA ≠ σB or σA - σB ≠ 0

So my question is if I can use "Stat>Basic Statistics>2 Variances" to assess differences of standard deviation or variances for paired data ?

Data:

* The same 35 mobile phones were measured in both equipment A and B.
HTML:
``````#	  A		  B
1	9,70		9,29
2	8,72		7,91
3	10,24		9,99
4	11,28		11,10
5	11,20		11,10
6	11,73		11,60
7	7,82		7,08
8	9,77		9,41
9	11,10		11,10
10	8,91		8,92
11	9,31		8,62
12	8,31		7,95
13	8,15		7,93
14	9,02		9,06
15	9,23		9,60
16	7,88		7,65
17	9,43		8,84
18	9,60		9,53
19	10,13		10,20
20	9,63		9,40
21	9,67		9,51
22	9,63		9,14
23	11,34		12,20
24	9,91		10,50
25	9,81		10,10
26	9,49		9,81
27	11,97		12,70
28	10,87		11,50
29	12,38		13,10
30	9,35		8,86
31	11,66		11,80
32	8,39		7,75
33	10,54		10,10
34	10,90		10,70
35	11,92		12,90``````
Best regards.

#### Miner

##### Forum Moderator
The short answer is yes, you can use the Test for Equal Variances on this data. However, there are other tests that will better utilize the information that you have available.

See, the Test for Equal Variances throws out a lot of information contained in your data. That is, it will ignore the fact that you have paired data and treat it the sample as unpaired data. Yes you will have some useful results, but not as useful as others.

For example, you can analyzed this type of paired data using a Bland Altman plot.

If you are a Minitab user, there are macros that will create the Bland Altman plot. If you use Minitab 16, there is a new feature called Orthogonal Regression that is designed for this specific scenario.

B

#### Berg.Jlle

Miner,

Thank you for the reply. By the way I use Minitab 16.

I read about the orthogonal regression in the Minitab ("Bloodpressure.MTW" example), but I didn't understand the interpretation of results neither the Y/X error variance ratio = 0.90. How was this value obtained ?

Please, if it's not asking too much, could you guide me with the orthogonal analysis for my paired data ?

Regards.

#### Bev D

##### Heretical Statistician
Super Moderator
Can you post your data in excel?
Can you tell us more about what you trying to understand? Not which statistical test you are trying to perform but what real world question(s) you are trying to answer

B

#### Berg.Jlle

Can you post your data in excel?
Can you tell us more about what you trying to understand? Not which statistical test you are trying to perform but what real world question(s) you are trying to answer
Hi Bev D,

Surely I can post the data in excel, please see attached.

So, the situation is:
I have two equipment (A and B) measuring the voltage at a certain point of mobile phones. I used a sample of 35 mobile phones that were measured in both equipment A/B and data were recorded in the attached table.

>> What I am trying to answer in the "real world" is as follows:

1) If the equipment are equal (alpha 0.05) about to the means.
To this question I used "Paired t" test that shows no significant difference between the means of A and B.

2) If the equipment are equal (alpha 0.05) about to the variances or standard deviation, i.e. if the variability are equal for A and B.
This is my doubt.

#### Attachments

• 9.8 KB Views: 112

#### Miner

##### Forum Moderator
Take a look at the attached analysis. Ask any specific questions that you may have, and I will respond.

The biggest concern that I would haveover this data is that you would expect the data to fall on either side of a 45 degree line. The Orthogal regression equation should be close to B = A. In this case the slope of the line is close to 1.3 instead of 0. There is also an overall bias greater than -2 for the means. Now, the 2-sample t and the test for equal variances both indicate that this is not significant, and that is true FOR THE RANGE OF VALUES STUDIED. If you exceed this range, there is every indication that it will become significant.

#### Attachments

• 178.6 KB Views: 108
B

#### Berg.Jlle

Take a look at the attached analysis. Ask any specific questions that you may have, and I will respond.

The biggest concern that I would haveover this data is that you would expect the data to fall on either side of a 45 degree line. The Orthogal regression equation should be close to B = A. In this case the slope of the line is close to 1.3 instead of 0. There is also an overall bias greater than -2 for the means. Now, the 2-sample t and the test for equal variances both indicate that this is not significant, and that is true FOR THE RANGE OF VALUES STUDIED. If you exceed this range, there is every indication that it will become significant.
Hi Miner.

I checked the file attached and I have some questions:

1) Using the regression orthogonal, we have the equation B = - 2.854 + 1.280*A. In order to consider that the two instruments (A and B) measure the same thing, the slope must be 1 and the constant 0, instead of 1.280 and -2.854, respectively.
Since these conditions are not met, can I conclude that the instruments A and B do not measure the variability equally. Right ?

2) Using the test for "2 Variances", this shows that there is no significant difference between the devices A and B, contrary to what was stated with regression orthogonal test in item #1.
Can I conclude that the test "2 Variances" does not show the reality and that the variability of instruments A and B are really different ?

3) To make the orthogonal regression analysis you used the "Error Variance Ratio" (B/A) equals to 1.
How did you come to that conclusion/valor ?

#### Miner

##### Forum Moderator
Questions 1 & 2) If you take the results of the orthogonal regression, the Bland Altman Plot, the paired t-Test and the test for equal variances together, I would draw the following conclusion. The slope between tests A and B is not equal to 1 and there is a bias between the two tests. Within the range of data that you evaluated, this difference is not statistically significant and the two test method could be treated as equivalent. HOWEVER, there is a strong indication that if you were to exceed this range of data, that difference would become statistically significant. As I see it you have three options:
1. If you intend to stay within the range of data, use the two tests as equivalent.
2. Expand the range of testing, solidify the orthogonal regression equation, and use it to correct the results of the new test.
3. Reject the new test and try another.
Question 3) That is based on the best information that you have available at the time and was supported by the test for equal variances. If you follow option 2 above, you will have better data, and should revise the Error Variance Ratio to fit your new data.

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