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 equal population standard deviation?

As a rule of thumb, the condition of equal population standard deviations is met, if the ratio of the larger to the smaller sample standard deviation is less than 2 (Weiss 2010). Let us assume that the data of the students data set is a good approximation for the population.

How do you know if two samples are the same population?

The two-sample t-test (Snedecor and Cochran, 1989) is used to determine if two population means are equal. A common application is to test if a new process or treatment is superior to a current process or treatment. There are several variations on this test. The data may either be paired or not paired.

What does equal mean in statistics?

Equal Sign – Definition with Examples The equal sign in mathematics describes equality between the values, equations, or expressions written on both sides. The symbol for equal to is two small horizontal lines placed parallelly. We place the ‘equal to’ sign is between two things that are the same or equal.

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 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.

When mean and standard deviation are equal?

One situation in which the mean is equal to the standard deviation is with the exponential distribution whose probability density is f(x)={1θe−x/θif x>0,0if x<0. The mean and the standard deviation are both equal to θ. for all positive numbers x and y.

When can we assume equal population variances?

Two sample standard deviations are very similar so we will assume equal population variances. 95% confidence interval contains 0 so cannot rule out that the population means may be equal. If sample sizes are equal, the pooled and unpooled standard errors are equal.

Do the samples appear to be from the same population?

It is clear that almost all of the standard statistics are different across samples. If sample size = population size, all statistics would be the same across all samples (obviously, because each of the samples would be the same ).

What is equal number?

Equivalent means equal in value, function, or meaning. In math, equivalent numbers are numbers that are written differently but represent the same amount.

What is the meaning of its equivalent?

1 : equal in force, amount, or value also : equal in area or volume but not superposable a square equivalent to a triangle. 2a : like in signification or import. b : having logical equivalence equivalent statements. 3 : corresponding or virtually identical especially in effect or function.

When is the difference between two populations equal?

In this case, we can state the null hypothesis in the form that the difference between the two populations means is equal to some constant where the constant is the desired threshold. where N1 and N2 are the sample sizes, and are the sample means, and and are the sample variances.

Is the mean of a sample equal to the population mean?

There is no way that the mean area of a biased sample will equal the mean area of the population. Bias means, by definition, that the statistics of the sample will not match the statistics of the population. Your question was whether the mean of a sample is equal to the population mean.

Are there districts that are of equal population?

Blue shaded districts are under the ideal population; gold shaded districts are above. In the 1960s the U.S. Supreme Court ruled in a series of cases that congressional and state legislative districts must be of equal population.

When to use standard deviation to compare two populations?

When the sample sizes are nearly equal (admittedly “nearly equal” is somewhat ambiguous, so often if sample sizes are small one requires they be equal), then a good Rule of Thumb to use is to see if the ratio falls from 0.5 to 2. That is, neither sample standard deviation is more than twice the other.