# Equality of Variance for Paired Data- alternative for Leven's Test?

#### kingsna1

##### New Member
Hello,

I have set up an experiment that tests 3 instruments on 35 different people. Each person gets tested three times with each instrument (see below). Now i understand this is paired data, i was just wondering whether there is a statistical test to check for equality of variance. From Googling i understand Levene's test is generally used for independent samples but i can't find any test that can do the same for comparing paired data.

At the moment i have used the pooled std Dev for each instrument to say that with 95% confidence (1.97 SD) that any measure i take will be within say 3cm with instrument 1 , 2cm with instrument 2 and 1cm with instrument 3. But i would like to statistically test whether my data has equality of variance.

I hope to be able to say something along the lines of ...... their is decreased variability between measures with instrument 3 than 1 and 3. Therefore choose instrument 3.
Now i have plotted some Bland Altman plots of the first and third repeated measures for each instrument and these show the variability. Is that enough to show variability or do you think i should do some sort of significance test?

$$\begin{tabular}{cccc|ccc|ccc} Instrument & & 1 & \multicolumn{1}{c}{} & & 2 & \multicolumn{1}{c}{} & & 3 & \tabularnewline Subject-Reps & 1 & 2 & \multicolumn{1}{c}{3} & 1 & 2 & \multicolumn{1}{c}{3} & 1 & 2 & 3\tabularnewline \hline Tom & 4 & 4 & 5 & 7 & 8 & 6 & 4 & 5 & 5\tabularnewline Alec & 13 & 14 & 16 & 11 & 11 & 11 & 12 & 17 & 10\tabularnewline \end{tabular}$$

#### rogojel

##### TS Contributor
hi,
this is a very interesting question. Maybe there are more sophisticated methods but a quick solution could be to calculate the range for each subject on each machine. So, you would get three data sets, one for each machine, and you could use a non-parametric test to check for significant differences between the machines. I would pick a non parametric test because the ranges are definitely not normally distributed - but an ANOVA could also work if the residuals are normal.

regards
rogojel

#### rogojel

##### TS Contributor
hi Karabiner,
I think if we take the range of the three measurements on a given machine for a given person then the dataset consisting of the ranges will not be correlated, unless there is a really weird interaction between the subjects and variation of the measurement on all machines.

what do you think?

regards
rogojel

#### Karabiner

##### TS Contributor
Oops. Obviously my reading of the first posting was too sloppy.
I would do the same as you proposed, i.e. I'd use some measure of
dispersion (intra-individual range or standard deviation) as DV and
compare the three instruments using Friedman and/or Wilcoxon
signed rank test.

With kind regards

K.

#### Hossein SA

##### New Member
Hello kingsna1;
I know that Brown-Forsythe test is a modification of Levene test, I know how work this test and i think U can use this test for pairwise test on Instruments. A good property of this test is that does not depend on normality of the error terms.
Check it and tell me do this test work true. THanks