Levene's Test Calculator

How to Use the Levene’s Test Calculator

This Levene’s test calculator allows you to check whether two or more independent groups have equal population variances. The calculator accepts raw data entered manually or uploaded from Excel or CSV files.

However, before entering the data, you need to specify:

• Test Method: Choose Levene’s Test (Mean) or Brown–Forsythe Test (Median). The calculator uses the mean-based method by default.
• Significance Level (α): Enter your preferred significance level. The default is 0.05.

Option 1: Enter Data Manually

If you have the individual observations for each group, follow these steps:

1. Select Enter Data under Data Input.
2. Enter the group name and observations in the corresponding fields. Separate the values using commas, spaces, or new lines.
3. Click Add Group if you have more than three groups. To delete an unwanted group, click the × button next to its name.
4. Click Calculate to perform the test.

Tip. Each group must contain at least two numerical observations.

Option 2: Upload Data from Excel or CSV

If your dataset is in Excel or CSV format, follow these steps:

1. Select Upload Excel / CSV under Data Input.
2. Click Choose File and upload your dataset.
3. Review the data preview and choose the appropriate worksheet if your Excel file contains multiple sheets.
4. Select how your data are arranged:
   • Grouping column + numeric variable(s): Choose the categorical variable that identifies the groups, followed by the numerical variable or variables you want to test.
   • Each group in a separate column: Select the columns containing observations for the groups you want to compare.
5. Click Calculate to run the test.

In both cases, the calculator displays the F statistic, degrees of freedom, p-value, critical F value, and hypothesis-testing decision. It also provides an APA-style report of the results, which you can copy and paste in your research notes or data analysis report.

Note. This levene’s test calculator also allows you to select multiple numerical variables from an uploaded dataset. In this case, the calculator displays a separate result for each variable in a summary table.

What Is Levene’s Test?

Levene’s test is a statistical hypothesis test used to determine whether two or more independent populations have equal variances. In statistics, the assumption that population variances are equal across groups is known as homogeneity of variance, or homoscedasticity.

For example, suppose a researcher wants to compare examination scores among students taught using three different teaching methods. Before performing a conventional one-way ANOVA, the researcher may want to determine whether the variability in examination scores is similar across the groups. Levene’s test helps assess this assumption by comparing the variation within each group.

A statistically significant result provides evidence that the population variances are not all equal. On the other hand, a non-significant result indicates that the test did not detect sufficient evidence of unequal variances.

Researchers commonly use Levene’s test when checking assumptions for the Independent Samples T-Test Calculator and ANOVA Calculator.

Levene’s Test Formula

In most cases, you will not need to calculate Levene’s test manually. Your main task will be to perform the test and interpret the results. However, it is useful to understand how the test statistic is obtained.

The original Levene’s test begins by finding the absolute deviation of each observation from its group mean, using the following formula:

Zᵢⱼ = |Xᵢⱼ − x̄ᵢ|

Where:

• Zᵢⱼ = Absolute deviation of observation j in group i
• Xᵢⱼ = Individual observation
• x̄ᵢ = Mean of group i

These deviations are also used when calculating the mean absolute deviation, which measures the average distance of observations from their mean.

However, for the Brown–Forsythe test, we use the group median instead of the mean. The formula is:

Zᵢⱼ = |Xᵢⱼ − Mᵢ|

Here, Mᵢ represents the median of group i.

This approach is related to the median absolute deviation, but the two are not exactly the same. Median absolute deviation takes the median of the absolute deviations, whereas the Brown–Forsythe test compares their means.

Therefore, unless your assignment specifically requires manual calculations, you can use our Levene’s test calculator to perform the test and focus on interpreting the results.

Assumptions

Before performing Levene’s test, the data must meet the following assumptions.

• Independent observations: Each observation should be independent of the others. The standard test is not suitable for repeated measurements collected from the same participants.
• Independent groups: Every observation should belong to one of the groups being compared.
• Numerical outcome variable: The dependent variable should contain quantitative measurements for which variance has a meaningful interpretation.
• Distribution shape: Strict normality is not required. However, substantial skewness, outliers, and differences in distribution shape can influence the test results.

Pay particular attention to independence. Even when the data are not normally distributed, the observations must still satisfy the independence requirements of the test.

Levene’s Test Hypotheses

Like other hypothesis tests, Levene’s test involves a null hypothesis and an alternative hypothesis. The hypotheses are:

• Null hypothesis (H₀): The population variances are equal across all groups (Homogeneity of variance is met).
• Alternative hypothesis (H₁): At least one population variance differs from the others (Homogeneity of variance is not met).

The test produces an F statistic and a corresponding p-value, which we use to determine whether there is sufficient evidence to reject the null hypothesis.

To determine whether the homogeneity of variance assumption is met using the generated outputs, we compare the p-value with the chosen significance level (α). The decision is as follows:

• If the p-value is less than the significance level (p < α), we reject the null hypothesis. This means that there is sufficient evidence to conclude that the population variances are not equal. In other words, a significant result means that the homogeneity of variance assumption is violated.
• If the p-value is greater than or equal to the significance level (p ≥ 0.05), we fail to reject the null hypothesis. This means that the data did not provide sufficient evidence to conclude that the population variances differ. In this case, we conclude that the homogeneity of variance assumption is met.

Alternatively, you can also use the critical F value to make the decision. In this case, we compare the calculated F statistic and the F critical value and reject the null hypothesis if the F-statistic exceeds the critical value. Otherwise, we fail to reject the null hypothesis.

Example: Levene’s Test for Equality of Variances

A researcher conducted a study to compare the examination performance of students taught using three different teaching methods. As part of the analysis, the researcher wanted to determine whether the population variances in examination scores were equal across the three groups.

The table below presents the examination scores for six students selected from each teaching group. Assume that all observations are independent.

Required:

Using the mean-centered Levene’s test at the 5% significance level, determine whether there is sufficient statistical evidence to conclude that the population variances in examination scores differ across the three teaching methods. Follow the six steps of hypothesis testing and report your findings in APA style.

Solution

To perform Levene’s test of homogeneity of variance for the dataset, follow these steps:

Step 1: State the Null and Alternative Hypotheses

The hypotheses are:

• Null hypothesis (H₀): The population variances in examination scores are equal across the three teaching methods.
• Alternative hypothesis (H₁): At least one population variance differs from the others.

Step 2: Specify the Significance Level

The question specifies a 5% significance level. Therefore, α = 0.05.

Step 3: Select the Appropriate Statistical Test

Since we want to determine whether the population variances are equal across three independent groups, the appropriate statistical test is Levene’s test for equality of variances.

For this example, we will use the original mean-centered Levene’s test.

Step 4: Calculate the Test Statistic and P-Value

To perform the test using our Levene’s test calculator:

1. Select Levene’s Test (Mean)
2. Set α = 0.05 as the significance level.
3. Select the “Enter Data” option
4. Enter the observations from the three teaching methods.
5. Click Calculate

The calculator instantly returns complete results as summarized in the table below.

Step 5: Make the Statistical Decision

Since the p-value (0.000650) is less than 0.05, we reject the null hypothesis. Similarly, the calculated F statistic (12.452731) is greater than the critical F value (3.682320), which suggests that we reject the null hypothesis.

Step 6: State the Conclusion

At the 5% significance level, there is sufficient statistical evidence to conclude that the population variances in examination scores are not all equal across the three teaching methods. The result suggests that the assumption of homogeneity of variance is not supported by the data.

You may also report the complete results in APA style as follows:

Levene’s test indicated that the population variances in examination scores differed significantly across the three teaching methods, F(2, 15) = 12.45, p < .001.

Levene’s Test vs. Brown–Forsythe Test

Levene’s test and the Brown–Forsythe test are both used to test the equality of population variances across two or more independent groups. The main difference between the two methods is how they calculate the absolute deviations of observations within each group.

The original Levene’s test uses the group mean, whereas the Brown–Forsythe test uses the group median. Since the median is less affected by extreme values, the Brown–Forsythe test is generally more robust when the data are skewed or contain outliers.

So, which method should you use?

You should use Levene’s test when the group distributions are reasonably symmetric and do not contain influential outliers. However, if the data are skewed, contain outliers, or depart substantially from normality, use the brown-forsythe test.

Levene’s Test vs. F-Test for Equality of Variances

Both Levene’s test and the classical F-test for equality of variances examine whether population variances are equal. However, they use different methods and have different assumptions.

While Levene’s test can examine two or more groups, the classical variance-ratio F-test compares exactly two populations. Additionally, the classical F-test assumes that the underlying populations follow normal distributions, making it more sensitive to violations of this assumption. However, Levene’s test is less dependent on normality, particularly when you use the median-centered Brown–Forsythe version.

The table below summarizes their main differences.

What to Do If Levene’s Test Is Significant

A significant Levene’s test indicates that the data provide evidence against the equal-variance assumption. Your next step depends on the type of statistical analysis you want to perform.

• If you’re performing an independent t-test and the homogeneity of variance assumption is violated, you should use Welch’s T-Test instead.
• However, if you were testing whether three or more independent groups differ, you should use Welch’s ANOVA instead.

Frequently Asked Questions