Manuals/calci/LEVENESTEST
LEVENESTEST(xRange,ConfidenceLevel,NewTableFlag)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle xRange} is the set of values for the test.
- is the value from 0 to 1.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LogicalValue} is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.
is the value from 0 to 1.Description
- This function used to test the Homogeneity of variances.
- Levene's test is used to test the Samples have equal variances.
- Equal variances across samples is called homogeneity of variance or homoscedasticity.
- To do the Levenes test we need the following assumptions:
1.The Samples from the populations are independent of one another. 2. The population under consideration are Normally Distributed.
- For three or more variables the following statistical tests for homogeneity of variances are commonly used:
1.Levene's Test. 2.Bartlett Test.
- Levene's test is an alternative to the Bartlett test.
- If the data surely is of normally distributed or nearly to normally distributed then we can use the Bartlett test.
- The Levene's test is defined as
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0 = \sigma_1^2 = \sigma_2^2=...... = \sigma_t^2}
.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_1}
=Not all of the variances are equal.
- Normally there are three versions of the Levenes test.
- There are
- 1.Use of Mean.
- 2.Use of Median.
- 3.Use of 10% of Trimmed Mean.
- The Levene test statistic is:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W=\frac{(N-k)\sum_{i=1}^k N_i(Z_i-Z)^2}{(k-1)\sum_{i=1}^k \sum_{i=1}^k \sum_{j=1}^{N_i} (Z_{ij}-Z_i)^2}} .
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W} is the result of the test.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} is the number of different groups to which the sampled cases belong.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is the total number of cases in all groups.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N_i} is the number of cases in the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} group.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y_{ij} is the value of the measured variable for the <math>j^{th}} case from the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} group.
- Zij is satisfying the one of the following conditions:
- 1.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_{ij}=|y_{ij}-\bar{y_i}|} ,Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{y_i}} is the Mean of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} subgroup.
- 2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_{ij}=|y_{ij}-\bar{y_i}|} ,Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{y_i}} is the Median of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} subgroup
- 3. ,Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{y_i}} is the 10%Trimmed Mean of the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} subgroup.
- Levene's Testing Procedure:
- 1. checking the assumptions.
- 2.State the Null(H0) and alternative(H1) hypothesis.
- 3.Decide on the Significance level (α).
- 4.Finding the Critical value and Rejection Region.Here Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle df_1=t-1} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle df_2=N-t} .
- 5.Compute the Levenes statistic using the formula.
- 6.Then decision of the value of the test statistic,W is falls in the rejection region or if p-value ≤ α, then reject Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} .Otherwise, fail to reject Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} . For the computation p-value we have to use the value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle df_1} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle df_2} .
- 7. Finally we have to conclude that the rejection of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} or fail to rejection Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H_0} according to the test statistic at the significance level.
Example
| X1 | X2 |
| 3067 | 3200 |
| 2730 | 2777 |
| 2840 | 2623 |
| 2913 | 3044 |
| 2789 | 2834 |
- =LEVENESTEST(B1:C5,.05,0)
| Stats | Data1 | Data2 |
|---|---|---|
| Median | 2840 | 2834 |
| Mean | 2867.8 | 2895.6 |
| Variance | 16923.7 | 51713.3 |
| Count | 5 | 5 |
| df | 4 | 4 |
| SUMMARY OUTPUT
|
LevenesTest | Statistics |
|---|---|---|
| W | 1.0439235110342522 | |
| F-Test | 0.38245649772919 | |
| a | 0.05 | |
| F | 0.32726010523405 | |
| p 1 & 2 Tail | 0.1524069466470822 | 0.3048138932941644 |