Cross Validated Asked by yaynikkiprograms on December 10, 2020

For example, if I am a scientist evaluating 2 methods to determine blood glucose and I want to compare if one is more variable, I would take, say, 6 samples from each person (subject) and use Method A on 3 and Method B on the other 3. So now I have data that looks like

```
Subject Replicate Method Glucose
1 1 A 80
1 2 A 80
1 3 A 79
1 1 B 90
1 2 B 91
1 3 B 93
..... etc
```

and I can calculate the standard deviation within method for each subject and then compare them for Method A vs. Method B. What test is appropriate for this? I think ANOVA is not because it is a parametric test and if I want to know if one standard deviation is greater than the other, we violate homoscedasticity.

Thank you.

You can use an F-test of $H_0: sigma_1^2=sigma_2^2$ against $H_a: sigma_1^2nesigma_2^2$. Sometimes this is written in terms of ratios of variances: $H_0: sigma_1^2/sigma_2^2 = 1$ against $H_a: sigma_1^2/sigma_2^2 ne 1.$

However, you will find that three observations in each group (method) is usually not enough for helpful testing---unless the population variances are hugely different.

For example, there is no statistically significant difference between
variances in your two samples, according to the procedure `var.test`

in R.

```
x1 = c(80,80,79); x2 = c(90,91,93)
var.test(x1, x2)
F test to compare two variances
data: x1 and x2
F = 0.14286, num df = 2, denom df = 2, p-value = 0.25
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.003663004 5.571428571
sample estimates:
ratio of variances
0.1428571
```

If there is a 4:1 ratio of population standard deviations (that's a 16:1 ratio for variances), then the power of this F-test (ability to reject $H_0,$ indicating a significant difference) for only three observations in each group is less than $0.3 =30%.$ (Such F-tests are notorious for their poor power.)

```
set.seed(2020)
pv = replicate(10^5, var.test(rnorm(3,0,4), rnorm(3,0,1))$p.val)
mean(pv <= 0.05)
[1] 0.28955
```

Ten observations in each group would give power above 95% detecting such a large difference between population variances. (There are online 'power and sample size' procedures for this test, and many statistical program also have such procedures.)

```
set.seed(915)
pv = replicate(10^5, var.test(rnorm(10,0,4), rnorm(10,0,1))$p.val)
mean(pv <= 0.05)
[1] 0.97468
```

Answered by BruceET on December 10, 2020

(You're so close when you mention ANOVA!)

Remember that ANOVA works by comparing two variances: the "between" variance and the "within" variance. Then we calculate the F-statistic and compute a p-value.

While we use the F-test to do ANOVA and compare means, the F-test is a test of variances (just in a particular way when we do ANOVA). We can use the F-test to compare any two variances. Then, if we reject that the variances are equal, we reject that the standard deviations are equal.

(Do not make the mistake of thinking that the F-test compares that variances of multiple groups, however.)

I am concerned about you taking multiple measurements from individuals, however, as that violates the independence assumption of most tests.

Answered by Dave on December 10, 2020

1 Asked on November 2, 2021 by data-man

0 Asked on November 2, 2021 by franziska

1 Asked on November 2, 2021 by s_haring

3 Asked on March 9, 2021 by pythonnoob

0 Asked on March 4, 2021 by bmurray

0 Asked on March 2, 2021 by pluviophile

1 Asked on March 2, 2021 by sleepy

chi squared test contingency tables ecology hypothesis testing statistical significance

0 Asked on March 1, 2021 by sedi

2 Asked on February 28, 2021 by peterbe

0 Asked on February 27, 2021 by user2991421

categorical data categorical encoding continuous data machine learning random forest

1 Asked on February 27, 2021 by mathslover

1 Asked on February 27, 2021 by misologie

1 Asked on February 25, 2021 by mcgurck

0 Asked on February 25, 2021 by la_haine

0 Asked on February 24, 2021 by zge

0 Asked on February 24, 2021 by diricksen

1 Asked on February 24, 2021 by zvisofer

Get help from others!

Recent Answers

- Peter Machado on Why fry rice before boiling?
- haakon.io on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP