Explore BrainMass

# F-Test

An F-test is a form of hypothesis testing used for comparing variances using the F-distributions, with varying degrees of freedom. F-distributions were developed by George W. Snedecor in honour of R.A. Fisher. F-tests are used to test whether the variances of two samples are equal; this is the null hypothesis. The advantage of the F-test is that it can be used to compare multiple samples at the same time. Another way to think of the F-test is that it tests how well a particular regression fits the data set. In this case the F-statistic can be calculated by:

F = explained variance / unexplained variance,

or

F = between-group variability / within-group variability

After calculating the F-statistic we can compare it to the critical value to determine whether the null hypothesis can or cannot be rejected at the specified significance level. The explained variance is calculated by taking the sum of the square of the difference between the means for each group of data and the overall mean of the data set multiplied by the number of observations, and divided by one less the number of groups. Hence, it is known as the between-group variability because it compares the variability of each group to the overall level. The unexplained variance is the sum of every group's differences between each observation of each group and that group's mean squared, and then divided by the number of observations less the number of groups. It is the within-group variability because it compares the variance between the observations and the means within each group. Formally the explained and unexplained variances are shown below respectively where: n is the number of observations for the specific group, i is the counter for the groups, j is the counter for observations, Y is the specific observation, Ῡ is the mean, N is the overall sample size, and K is the number of groups.  © BrainMass Inc. brainmass.com June 19, 2021, 8:45 pm ad1c9bdddf

## BrainMass Solutions Available for Instant Download

### Comparing service rates

A financial services institution wants to compare the service rate at two of its branches. Branch 1 was studied for 25 days and it serviced 250 clients per day on average with a standared deviation of 10. Branch 2 was studied for 20 days and it serviced 240 clients per day on average with a standard deviation of 6. Can we concl

### Hypotheses for Two-Sample Tests: Independent Samples vs Dependent Samples

Respond to the following: - Give two examples as follows: o A research situation when you would use a two-sample test with independent samples o A research situation when you would use a two-sample test with dependent samples - Explain why you would choose the specific test. - Define the null hypothesis and the alternate h

### Phatmaceutical Test Groups

Assume that you work for the Food and Drug Administration. A pharmaceutical company has applied for approval to market a new arthritis medication. The research involved a test group that was given the medication and another test group that was given a placebo. Respond to the following: • Describe some ways in which the te

### F-ratio and t statistic Questions

1. Describe the similarities between an F-ratio and a t statistic. a. The basic relationship between t statistic and F-ratios can be stated in an equation. What is that equation? b. These two methods are very similar in calculation (t and F). If you have data from an independent-measures experiment, with only two treatment c

### F test for the difference between two variances

A professor in the accounting department of a business school claims that there is much more variability in the final exam scores of students taking the introductory accounting course who are not majoring in accounting than for students taking the course who are majoring in accounting. Random samples of 13 non-accounting ma

### Two Sample F Tests

Please describe how a health care manager or researcher might be able to use a Two Sample F Test to compare variances. Identify a peer-reviewed journal article that used power and sample size estimation for stratified categorical data. Provide a summary of the topic and how it was used in the article.

### T distribution and F distribution

Please see attached problem, and please explain all aspects of both problems involving T and F distributions. a) Z is a standard normal random variable, and U is distributed as X(v)^2. Z and U are independent. State the distribution of T = Z/sqrt(U/v) . What is the distribution of T^2? b) Y is a random variable distributed

### True or False

Identify each of the following statements as true or false, explain why: A. A parameter is a population characteristic that is estimated by a coefficient derived from a sample of data. B. A one-tailed t-test is used to indicate whether the independent variables as a group explain a significant share of demand variation. C. G

### ANOVA and Turkey test

See data file attached. Correct decision relative to the null hypothesis (F test) Correct description and interpretation of the post hoc Tukey T tests Age results Internet Age results Text message Age results Internet Text message 1 6 1 5 1 6 5 3 6 3 6 3 6 6 2 6 2 6 2 6 6 4 7 4 3 4 7 3 4 7 4 6 4 7 6

### Statistics: F Test for equality of variance

F test for equality of variance conducted. Correct decision relative to the equality of variance F-test for equality of variance 3.61 variance: Text message 2.11 variance: Internet 1.71 F .1542 p-value F-test for equality of variance 3.61 variance: Text message 2.49 variance: E-mail 1.45 F

### Fisher's exact test chart and analysis.

See attached file. Need help to make a simple Fisher's exact test chart/analysis. Need Fisher's exact test for this problem: SAMPLE: 32 people interviewed. People could put either 1 or 2 dimensions. Participants are in two groups, based by age: 18 of them are from the ages of 18-29- I will call these group A 14 of th

### F test: Critical Value

What is the critical value for a two-tailed F-Test with a=0.10, when the sample size from which the variance for the numerator was obtained was 10, and the sample size from which the denominator was obtained was 24?

### F distribution: Probability & Raw score

F distribution Use the calculator provided to solve the following problems: ?Consider an F distribution with 9 numerator degrees of freedom and 8 denominator degrees of freedom. Compute P (0.73 < F < 1.05). Round your answer to at least three decimal places. ?Consider an F distribution with 17 numerator degrees of free

### Using the F-Ratio

Scenario: A researcher reports an f-ratio with degrees of freedom (df) = 3,36 from an independent-measures research study. Questions: How many treatment conditions were compared in the study? What was the total number of participants in the study?

### ANOVA analysis: Treatment conditions, F-ratio, Migrating birds,

Estimation/Analysis of Variance 1. The following data are from an experiment comparing three treatment conditions with a separate sample of n = 4 in each treatment. a. Use an ANOVA with a = .05 to determine whether there are any significant differences among the three treatments. b. Compute eta2 for these data Treatment

### F test for equality of variance of two populations

An automobile manufacturer claims the variance in the fuel consumption for its vehicles is less than the variance of similar type vehicles from another competitor. A random sample of 19 of the manufacturer's vehicles has a variance of 16.2 mpg. A random sample of 21 of the competitor vehicles has a variance of 32.5. At a signifi

### Statistics: Values of the F-statistic

Case A: If all the sample means were exactly the same, what would be the value of the numerator of this F-statistic? Case B: If all the sample means were very spread out and very different from each other, how would the variation between the sample means compare to the value in Case A? So what values could the F-statistic

### Null hypothesis and alternate hypothesis

According to a high-profile realtor, houses in the sleepy town of Sun Beach have shown higher appreciation over the past three years than have houses in the bustling town of North Arden. To test the realtor's claim, an economist has found fourteen recently sold homes in Sun Beach and fourteen recently sold homes in North Arden t

### F test of a multiple regression model

To help schedule staffing equipment needs, a large hospital uses a multiple regression model to predict its 'bed census' y, the number of beds occupied at the end of each day. Using hospital records from the most recent 28 days, a total of 3 independent variables are used to find the estimated regression model. Let B1, B2 and B3

### Assumptions for the F Test

Which of the following assumptions is not made for the F test for comparing three or more means? A) The populations from which the samples were obtained must be normally distributed B) The samples must be independent of each other C) The sample sizes must be equal. D) The variances of the populations must be equal

### Post Hoc Analysis for an F-Test

What are post hoc comparisons, and why do researchers make them? Why do researchers not use the Bonferroni procedure of procedures for post hoc comparisons? What is the advantage over the Bonferroni procedure of procedures such as the Tukey and Scheffe tests? Is Scheffe preferred over others if so, why and what are the advant

### F test: Five Step Approach

A random sample of five observations from the first sample resulted in a standard deviation of (12). A random sample of seven observations from the second sample gave a standard deviation of (7) at the (.01) significance level. Is there more variation in the first population? And is the null hypothesis rejected or not, and why?

### P value for F test

The calculated value of F in a one-way analysis is 8.23. The numerator degrees of freedom and denominator degrees of freedom are 4 and 8, respectively. The most accurate statement to be made about the p-value is: a. p-value > 0.05 b. 0.05 > p-value > 0.025 c. P-value > 0.01 d. 0.01 > p-value One-way ANOVA is performed

### Critical Value for F-Test

a) Given the significance level 0.01, the F-value for the degrees of freedom, d.f. = (7,3) is? b) In a completely randomized design for ANOVA, the number of degrees of freedom for the numerator and denominator are 4 and 25, respectively. The total number of observations must equal?

### Hypothesis Testing for Variances: F Test

For two samples from what are assumed to be normally distributed populations, the sample size and standard deviations are n1 = 10, s1 = 23.5, n2 =9 and s2=10.4. At the 0.10 level of significance, test the null hypothesis that the population variances are equal. Would your conclusion be different if the test had been conducted at

### Independent Sample/F Distribution/Type I Error

a. What is an independent sample? What is a related sample? When should researchers use different hypothesis tests for independent and related samples? Is one type of sample preferable over the other? b. What is a Type I error? Explain how the cumulative Type I error affects your decision making. How is the two independent sa

### A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent.

I am clueless on these 3 problems. Please help. See attached. 6. A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation

### Hypothesis testing :F test for Variance

The mean age of 25 randomly selected college seniors was found to be 23.5 years, and the standard deviation of all college seniors was 1.3 years. Which of the following is the correct symbol for 1.3 years? A. u B. s C. o D. A researcher wishes to compare two different groups of students with respect to their mean tim

### ANOVA and the F statistic at the 0.01 significance level.

Please see attached file for full problem description. Please help with the areas in red, thanks! ANOVA and the F statistic at the 0.01 significance level. #3) The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is

### Degrees of Freedom for F Statistic

Please help with the areas in red, thanks! Please see attached file for full problem description. #2) Cris Turlock owns and manages a small business in San Francisco, California. The business provides breakfast and brunch food, via carts parked along sidewalks, to people in the business district of the city. Being an ex