Levene's test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.
What does it mean to assume equal variance?
Statistical tests, such as analysis of variance (ANOVA), assume that although different samples can come from populations with different means, they have the same variance. Equal variances (homoscedasticity) is when the variances are approximately the same across the samples.
When you choose to compare the means of two nonpaired groups with a t test, you have two choices: Use the standard unpaired t test. It assumes that both groups of data are sampled from Gaussian populations with the same standard deviation. Use the unequal variance t test, also called the Welch t test.
The assumption of homogeneity of variance is that the variance within each of the populations is equal. This is an assumption of analysis of variance (ANOVA). ANOVA works well even when this assumption is violated except in the case where there are unequal numbers of subjects in the various groups.
Use a test for equal variances to test the equality of variances between populations or factor levels. Many statistical procedures, such as analysis of variance (ANOVA) and regression, assume that although different samples can come from populations with different means, they have the same variance.
If the variances are relatively equal, that is one sample variance is no larger than twice the size of the other, then you can assume equal variances. By looking at the output of the Levene's test you decide which row to use. If the significance is .05 or below, use the bottom row, or “equal variances not assumed.”
Assuming Equal. Variance (Enter Means) Introduction. This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of the two groups (populations) are assumed to be equal. This is the traditional two-sample t-test (Fisher, 1925).
The Wikipedia page on ANOVA lists three assumptions, namely:
- Independence of cases – this is an assumption of the model that simplifies the statistical analysis.
- Normality – the distributions of the residuals are normal.
- Equality (or "homogeneity") of variances, called homoscedasticity
The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.
The assumption of independence is a foundation for many statistical tests. The assumption of independence is used for T Tests, in ANOVA tests, and in several other statistical tests. The observations between groups should be independent, which basically means the groups are made up of different people.
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value.
In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part.
Homoscedasticity. This assumption means that the variance around the regression line is the same for all values of the predictor variable (X). The plot shows a violation of this assumption. For the lower values on the X-axis, the points are all very near the regression line.
Equal variances across samples is called homogeneity of variances. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Bartlett test can be used to verify that assumption. Bartlett's test is sensitive to departures from normality.
The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. The Independent Samples t Test is a parametric test. This test is also known as: Independent t Test.
Sphericity is an important assumption of a repeated-measures ANOVA. It refers to the condition where the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal.
Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable. Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out.
Sphericity is the measure of how closely the shape of an object approaches that of a mathematically perfect sphere. Sphericity applies in three dimensions; its analogue in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft, is called roundness.
Abrasion- Rocks collide causing the rocks to chip and become smooth. resistance- the sand creates resistance and acts like sand paper to smooth the rocks. motion of the water- The motion of the water pushes the rocks and causes the rocks to collide with the rocks and stream beds.
Rounding, roundness or angularity are terms used to describe the shape of the corners on a particle (or clast) of sediment. Such a particle may be a grain of sand, a pebble, cobble or boulder.