Establish Whether populations have equal variance

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  • Thread starter Wrightomatic
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In summary, the F-test is used to compare variances and determine if they are equal or different. The F-test statistic is calculated by dividing the larger variance by the smaller variance. The critical value is then looked up in an F-table and compared to the calculated F-value. If the calculated F-value is greater than the critical value, the variances are considered different. If it is lower, the variances are assumed to be equal.
  • #1
Wrightomatic
3
0
day 1
distance equals 52.175m, std = 0.015m and n = 10

day 2
distance equals 52.193m, std = 0.021m and n = 11

Establish whether the two populations have equal variance at the 0.05 signifcance level. Can someone help me out with how to get to the answer and what the answer actually is?
 
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  • #2
Wrightomatic said:
day 1
distance equals 52.175m, std = 0.015m and n = 10

day 2
distance equals 52.193m, std = 0.021m and n = 11

Establish whether the two populations have equal variance at the 0.05 signifcance level. Can someone help me out with how to get to the answer and what the answer actually is?

Welcome to MHB, Wrightomatic! :)

The F-test is the appropriate test to compare variances.
Do you know how to execute it?
 
  • #3
No sorry i don't know how that is why I am asking. Could you please demonstrate how to apply such a test for the given data?

Thanks for your help :)
 
  • #4
Wrightomatic said:
No sorry i don't know how that is why I am asking. Could you please demonstrate how to apply such a test for the given data?

Thanks for your help :)

The F-test statistic is $F=\dfrac{s_1^2}{s_2^2}$, where $s_1^2$ is the larger of the 2 variances.
Can you calculate that?
 
  • #5
Yes I can calculate that but what does the F test mean? Like ill get the value for F then do i need to do anything else. As you can probably tell I have absolutely no idea how to do the test or how to implement it.

Could you possibly give me all the steps/formulas i will need and then I can work through it and check the final answer with you?
 
  • #6
Wrightomatic said:
Yes I can calculate that but what does the F test mean? Like ill get the value for F then do i need to do anything else. As you can probably tell I have absolutely no idea how to do the test or how to implement it.

Could you possibly give me all the steps/formulas i will need and then I can work through it and check the final answer with you?

Well, you can find the steps/formulas for instance here.

The F-test tests if 2 variances are different.
You should look up the critical value in an F-table for the appropriate significance and degrees of freedom (see the article).
If your calculated F-value is greater than this critical value, your variances are different.
If it is lower, the variances are assumed equal.
 

Related to Establish Whether populations have equal variance

1. How do you establish whether populations have equal variance?

In order to establish whether populations have equal variance, you can conduct a statistical test such as the F-test or Levene's test. These tests compare the variances of two or more populations and determine if they are significantly different.

2. Why is it important to determine if populations have equal variance?

Determining if populations have equal variance is important because it affects the results of many statistical tests. If populations have unequal variances, it can lead to inaccurate conclusions and incorrect interpretations of data.

3. What does it mean if populations have equal variance?

If populations have equal variance, it means that the amount of variability within each population is similar. In other words, the data points are spread out in a similar manner.

4. How does unequal variance affect statistical tests?

Unequal variance can affect statistical tests in two main ways. Firstly, it can lead to biased estimates of the difference between two populations. Secondly, it can affect the Type I error rate, which is the probability of incorrectly rejecting the null hypothesis.

5. What if my data violates the assumption of equal variance?

If your data violates the assumption of equal variance, there are a few options you can consider. One option is to use a statistical test that is robust to unequal variances, such as the Welch's t-test. Another option is to transform the data to make the variances more equal. If these options are not feasible, you may need to report the results with caution and acknowledge the potential impact of unequal variances on the conclusions.

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