# Levine Test Assignment Help

The Levine test is a statistical test designed to measure the reliability of a decision or hypothesis by means of two independent tests. The first test (the “robustness” test) is based on finding an upper and lower confidence level; the second (the “relevance” test) is based on finding the probability that the data would be different if one decision were true. If you are a statistics student looking a statistician assignment tutor, we are also looking forward to helping you. Get a clearer picture of Levine test assignment help by hiring our services. Place your ORDER NOW.

## Why use Levine test statistic?

Levine test is a statistical method used in the context of data collection and analysis. The method is named after its creator, Leon Levin. The Levin test is a statistical procedure that involves the measurement of the tendency to reject a null hypothesis. It is widely used in many fields, including statistics and computing. A Levine test for equality of variances is a statistical test that can be used to identify different kinds of error.

A Levine test is a type of statistical test that measures the equality or difference between two values. In most cases the test is used to assess the equality of variances, a condition known as homoscedasticity. In other words, it tells us whether one value lies on the left side or right side of an inequality line. A good way to tell whether two values are equal is to check if they have the same magnitude so as not to confuse small changes with large differences. For example, if the first value has a larger magnitude than the second value by a certain percent, then it’s considered equal – for example if 1% and 2% have equal magnitudes, then they are equal and we can say “1% = 2%” or “2% = 1%”.

## Levine Test for Equality of Variances

The Levine test for equality of variances is widely used in statistics to compare two groups. The difference between the two groups is measured by the standard deviation or standard error. The standard deviation or standard error, measures the amount of variation that exists between an observation and its mean. The Levine test for equality of variances is used to test the equality of variances between two independent samples. It is also known as the t-test for normality.

## Levine Test Description

The Levine test for equality of variances is used to test the equality of variances between two independent samples. If our sample size (N) and variance (σ2) are given, we can calculate the correlation coefficient (r). The r values range from -1 to +1 and provide us with important information about how closely our data series match each other. An r value less than 1 means that their values are very close to each other, while an r value greater than 1 means that they are far apart!

The Levine test for homoscedasticity is defined as:

H0:      σ1222=…=σn2

Ha:      σi2≠σj2  for at least one pair (i,j).

Test Statistic:  Given a variable X with sample of size N divided into M subgroups, where Ni is the sample size of the ith subgroup, the Levine test statistic is defined as:

where Zij can have one of the following three definitions:

where  is the mean of the ith  subgroup.

are the group means of the Zij and  is the overall mean of the Zij

The three choices for defining Zij determine the reliability and accuracy power of Levine’s test. By reliability, we mean the ability of the test to not falsely detect unequal variances when the underlying data are not normally distributed and the variables are in fact equal. Such an error of  rejecting the null hypothesis when it is actually true is known as the type I error. By accuracy power, we mean the ability of the test to detect unequal variances when the variances are in fact unequal. Failing to reject the null hypothesis when it is actually false would lead to the type II hypothesis error.

## Improvement on the Levine Test Statistic

The early work by Levine simply suggested using the mean. In addition to the mean, Brown and Forsythe (1974)) modified Levine’s test to include the median or trimmed mean. The trimmed mean fared well whenever the data set followed a Cauchy distribution (i.e., heavy-tailed), and the median performed best when the underlying data followed a  skewed distribution, according to Monte Carlo studies. For homogeneous, moderate-tailed distributions, using the mean offered the most power. Thus, the mean method would not be the most suitable for platykurtic or leptokurtic distributions. It is more feasible for normally distributed data with medium tails.

## Decision Criteria

After calculating the test statistic L, its significance is tested against the F statistic using M -1 and N -M as degrees of freedom and the chosen level of significance α (usually 0.05 or 0.01). The decision criteria is to reject the null hypothesis when Levine test statistic is greater than the F-Distribution statistic. If L is higher than the critical F value, Levine’s test rejects the null hypothesis that the variances of the data sets are equal.

## Importance of the Levine statistical test

The Levine statistical test is one of the most important tools in statistical analysis.

The Levine test is used to test if two given data sets are statistically significant or not. It also compares two means of two different populations with each other. For instance, if you are testing whether five out of five people in a certain group are smokers, you need to compare the mean (average) smoking rate in that group with the mean overall smoking rate.

The Levine statistical test is used to determine the significance of differences between two variables. It is commonly used for the analysis of data like sales, customer satisfaction, product quality etc.

The Levine statistical test can be used for finding out whether there are significant differences between two variables or not. This test can also be used to find out if there is a significant difference between two sets of data. It can also be applied to find out if there are any differences in results when comparing two different sets of data.

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