If sample sizes are equal
, the pooled and unpooled standard errors are equal. If sample standard deviations are similar, assumption of equal population variance may be reasonable and the pooled procedure could be used.
How do you know if population variances are equal?
If the variances are equal,
the ratio of the variances will equal 1
. For example, if you had two data sets with a sample 1 (variance of 10) and a sample 2 (variance of 10), the ratio would be 10/10 = 1. You always test that the population variances are equal when running an F Test.
What does it mean when population variances are equal?
What Is the Assumption of 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.
What is meant by equal and unequal variance?
The Two-Sample assuming Equal
Variances test
is used when you know (either through the question or you have analyzed the variance in the data) that the variances are the same. The Two-Sample assuming UNequal Variances test is used when either: You know the variances are not the same.
How do you compare two population variances?
- The F-test: This test assumes the two samples come from populations that are normally distributed.
- Bonett’s test: this assumes only that the two samples are quantitative.
- Levene’s test: similar to Bonett’s in that the only assumption is that the data is quantitative.
Can variance and mean be equal?
In poisson distribution mean and variance are equal i.e.,
mean (λ) = variance (λ)
.
Why do we need equal variances?
It is important because it is
a formal requirement for statistical analyses
such as ANOVA or the Student’s t-test. The unequal variance doesn’t have much impact on ANOVA if the data sets have equal sample sizes. However, if the sample sizes are different, ANOVA will end up with inaccurate results.
When comparing the variance of two or more populations what statistical test should be used?
A z-test
is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large.
What is equality of variance in t tests?
When running a two-sample equal-variance t-test, the basic assumptions are that
the distributions of the two populations are normal, and that the variances of the two distributions are the same
.
What is variance of population?
Population variance (σ
2
) tells
us how data points in a specific population are spread out
. It is the average of the distances from each data point in the population to the mean, squared.
Which of the following is used to compare two variances?
Explanation:
F – Distribution
is used when we require for comparing two variances. It uses a f-Test to compare two values of variances.
What distribution is used to test for equality of variances between two populations given that data was collected independently?
In order to compare two variances, we must use
the F distribution
. In order to perform a F test of two variances, it is important that the following are true: The populations from which the two samples are drawn are normally distributed. The two populations are independent of each other.
How do you compare the variance of the population and the variance of the sampling distribution of the sample means?
That is, the variance of the sampling distribution of the mean is
the population variance divided by N, the sample size (the number of scores used to compute a mean)
. Thus, the larger the sample size, the smaller the variance of the sampling distribution of the mean. … The variance of the sum would be σ
2
+ σ
2
+ σ
2
.
Which is equal to variance?
Informally, variance estimates how far a set of numbers (random) are spread out from their mean value. The value of variance is equal to
the square of standard deviation
, which is another central tool. Variance is symbolically represented by σ
2
, s
2
, or Var(X).
Which of the following is equal to variance?
The standard deviation
for a given distribution is equal to the variance.
Is population variance the same as standard deviation?
The variance is the average of the squared differences from the mean. … Standard deviation is the
square root of the variance
so that the standard deviation would be about 3.03. Because of this squaring, the variance is no longer in the same unit of measurement as the original data.
How do you test a hypothesis to determine whether the variances of two populations are equal?
| Two-Tailed Test One-Tailed Test One-Tailed Test | H 1 : σ 1 2 ≠ σ 2 2 H 1 : σ 1 2 > σ 2 2 H 1 : σ 1 2 < σ 2 2 |
|---|
When dealing with two independent means when is it appropriate to assume equal variances?
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.
What statistical technique when you want to test more than population means?
In order to compare the means of more than two samples coming from different treatment groups that are normally distributed with a common variance,
an analysis of variance
is often used. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal.
When running a test of equal variance for normal data which test statistic is read when you are comparing several samples?
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.
Why do we assume unequal variances?
Your prime goal is not to ask whether two populations differ, but to quantify how far apart the two means are. The unequal variance t test reports a confidence
interval for the difference between two means that is usable even if the standard deviations differ
.
What is population variance and sample variance?
Summary:
Population variance refers to the value of variance that is calculated from population data
, and sample variance is the variance calculated from sample data. … As a result both variance and standard deviation derived from sample data are more than those found out from population data.
How do I calculate the coefficient of variation?
The formula for the coefficient of variation is:
Coefficient of Variation = (Standard Deviation / Mean) * 100
. In symbols: CV = (SD/x̄) * 100. Multiplying the coefficient by 100 is an optional step to get a percentage, as opposed to a decimal.
How do you find population variance and standard deviation?
Since population variance is given by σ2, population standard deviation is given by σ. So when you want to calculate the standard deviation for a population, just
find population variance, and then take the square root of the variance
, and you’ll have population standard deviation.
When population standard deviation is unknown what can you use instead of?
When the population standard deviation, σ, is unknown, the
sample standard deviation
is used to estimate σ in the confidence interval formula. The quantity 1.96σ/ √n is often called the margin of error for the estimate.
Is there a difference between the mean of the population and mean of the sampling distribution of the sample means?
The sampling distribution of the mean is the distribution of ALL the samples of a given size. The mean of the
sampling dist is equal to the mean of the population
.
When you test for a difference between two population means from small samples when should a pooled variance be calculated?
When you test for a difference between two population means from small samples, when should a pooled variance be calculated?
When the sample sizes are different.
What test is used when a population variance is unknown?
Explanation: If the population variance is unknown, which is usually the case, then use
a t-test
rather than a normal or z-test.
When the T-test is used for testing the equality of two means the populations must be?
The t -test provides an exact test for the equality of the means of two
normal populations with unknown, but equal, variances
.
How do you find the sample variance of differences?
- Find the mean of the data set. Add all data values and divide by the sample size n. …
- Find the squared difference from the mean for each data value. Subtract the mean from each data value and square the result. …
- Find the sum of all the squared differences. …
- Calculate the variance.
What assumption has to be made about the two populations in order to justify the use of the F-test?
Explanation: An F-test
assumes that data are normally distributed and that samples are independent from one another
.
Which distribution is used to test the equality of population means?
| Alternative Hypothesis Rejection Region | H a : μ 1 < μ 2 T < t α , ν |
|---|
