Question

What are the characteristics of an F Distribution?

Name the tests that the F distribution is used for in this chapter.

In a one way ANOVA we are comparing:

What assumptions underly ANOVAs:

What are the benefits of considering other factors using ANOVA

Answer 1

1) The F distribution graph is always positive and skewed right, though depending on the combination of numerator and denominator degrees of freedom the shape may be mounded or exponential. The F statistic is the ratio of a function of the group mean variance to a related measure of variance within the groups. If the null assumption is right, then the numberer should be small compared to the denominator. This will result in a small F statistic, and the area under the F curve to the right will be large, indicating a high p-value. If the null hypothesis of equal group means is false, then relative to the denominator, the numerator will be large, giving a large F statistic and a small area (low p-value) to the right of the statistic under the F curve. When the data have unequal group sizes (unbalanced data), then techniques need to be used for hand calculations.  However, simplified calculations based on group mean and variances may be used in the case of balanced data (the groups are the same size). Naturally software is typically used in the analysis of operation. Graphs of various kinds can be used in combination with numerical methods, as with any study. Look always at your data. . The curve is not symmetrical but skewed to the right. 2. There is a different curve for each set of dfs. 3. The F statistic is greater than or equal to zero. 4. As the degrees of freedom for the numerator and for the denominator get larger, the curve approximates the normal. 5. Other uses for the F distribution include comparing two variances and Two-Way Analysis of Variance. Comparing two variances is discussed at the end of the chapter. Two-Way Analysis is mentioned for your information only.

2) there is two taste one is annova and second is test of two varaince

The purpose of an ANOVA test is to determine the existence of statistically significant difference between means of multiple group. The test also uses variances to help determine whether or not the mean is equal.

There are three basic assumptions to be fulfilled for carrying out an ANOVA test:
• Each population from which a sample is taken shall be considered normal.
• Each specimen is chosen randomly and is autonomous.

• Equal standard deviations (or variances) are assumed for the populations.

None of the distribution F uses measures two variances. Comparing two is always wünschenswert Variances, not 2 averages. University administrators for example want two college professors Grading tests will have the same variability in their gradation. The variation so that a lid can fit a container The container and the lid should be identical.

In order to perform a F test of two variances, it is important that the following are true: 1. The populations from which the two samples are drawn are normally distributed. 2. The two populations are independent of each other.

3) A one-way ANOVA is a type of statistical test that compares the variance within a sample in the group mean while only considering a single independent variable or factor. It is a hypothesis-based test, meaning it aims to evaluate multiple theories about our data which are mutually exclusive. We need to have a question about our data before we can generate a hypothesis that we want an answer to. A single-way ANOVA compares three or more categorical categories to decide whether there is any difference between them. There should be three or more observations within each category (here, this means walruses), and the sample media are compared. There are two plausible theories in a single-way ANOVA. The null hypothesis ( H0) is that there is no difference between the groups and the means equality. (Walruses, in separate months, weigh the same) The alternative hypothesis (H1) is that the mean and the groups vary. (The walruses weigh differently in different months) .

4)  There are three basic assumptions to be fulfilled for carrying out an ANOVA test:
• Each population from which a sample is taken shall be considered normal.
• Each specimen is chosen randomly and is autonomous.

• Equal standard deviations (or variances) are assumed for the populations.

5)  Multivariate ANOVA (MANOVA) expands variance analysis capabilities (ANOVA) by simultaneous evaluation of multiple dependent variables. Statistically, ANOVA measures the differences between means of three or more classes. For example, if you have three different methods of teaching and want to compare the mean scores for these classes, you can use ANOVA. ANOVA has one drawback, though. iT can only evaluate one dependent variable at a time. In other cases, this limitation can be a major issue, as it can keep you from identifying symptoms that actually occur. For some studies MANOVA provides a solution. This statistical procedure simultaneously tests multiple dependent variables. In doing so, MANOVA will deliver a range of benefits over ANOVA. In this post, I explain how MANOVA functions, its advantages compared to ANOVA, and when to use it. I'll also use an example from MANOVA to show you how to analyze the data and interpret the results.