Perform an ANOVA test and observe that the P-Value is 0.081. Now remove the Socks data and perform the test again. What is the P-Value when we remove the Socks data?

See explanations

Step-by-step explanation:

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means. In this post, I’ll show you how ANOVA and F-tests work using a one-way ANOVA example.

But wait a minute...have you ever stopped to wonder why you’d use an analysis of variance to determine whether means are different? I'll also show how variances provide information about means.

As in my posts about understanding t-tests, I’ll focus on concepts and graphs rather than equations to explain ANOVA F-tests.

What are F-statistics and the F-test?

F-tests are named after its test statistic, F, which was named in honor of Sir Ronald Fisher. The F-statistic is simply a ratio of two variances. Variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion.

F is for F-test

Variance is the square of the standard deviation. For us humans, standard deviations are easier to understand than variances because they’re in the same units as the data rather than squared units. However, many analyses actually use variances in the calculations.

F-statistics are based on the ratio of mean squares. The term “mean squares” may sound confusing but it is simply an estimate of population variance that accounts for the degrees of freedom (DF) used to calculate that estimate.

Despite being a ratio of variances, you can use F-tests in a wide variety of situations. Unsurprisingly, the F-test can assess the equality of variances. However, by changing the variances that are included in the ratio, the F-test becomes a very flexible test. For example, you can use F-statistics and F-tests to test the overall significance for a regression model, to compare the fits of different models, to test specific regression terms, and to test the equality of means.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents