Question

1. What does Levene’s test do? How do we know which line to use for this test when writing up the results?

2. How can we use confidence intervals to do hypothesis testing?

Answer 1

ANSWER 1

LEVENE’S TEST

- For a given set of sample data arising out of a non normal type of distribution , Levens’s test is used to check and ensure that variances are equal for all of the presented data

- This equality of variances amongst the data presented is known as homogeneity of the variances

- Levene’s test is also used for verifying the assumptions that in types of statistical tests being
Analysis of variance it is assumed that value of variances falls equal amongst the group of sample data

- Levene’s test is generally used as an alternative to the Bartlett's test because , Levene test is less sensitive than the Bartlett test to the factor of departures from normality.

- Levene’s test is presented as

H0: σ12 = σ22 = … = σk2.

H1: σ12 ≠ σ22 ≠… ≠ σk2. ( for at least one pair )


What needs to be checked while writing up the results


- If in the case the given distribution is skewed distribution or there is not much surety about the particular underlying shape of the distribution then Median is the best option to be chosen

- If in the case the given distribution is symmetric or can also tag along with some moderately tailed distribution , in that particular scenario Mean should be checked





ANSWER 2

Using confidence intervals to do hypothesis testing

- Both of the methods mentioned in the question be it confidence intervals and hypothesis text work on the same fundamental ground and are similar in ways like they both depend upon approximated sampling distribution as both of them are inferential methods

- For any Hypothesis testing a hypothesized parameter is a necessity to be there in the data , and hypothesis tests generally test the data from a sample to test a particular hypothesis.

- On the contrary , Confidence intervals use data from a particular sample for estimating a specific population parameter

- Generally confidence intervals maintain a specific range of reasonable estimates of the given population parameter , the two-tailed confidence interval works well with a two-tailed hypothesis

- Any conclusion drawn from a particular confidence interval be it a two tailed confidence interval would be usually the same as a particular conclusion drawn from any other hypothesis test be it a two-tailed hypothesis test