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Analysis of Variance

Analysis of variance, ANOVA, is a collection of statistical models used to analyze the differences between group means and their associated procedures. In ANOVA, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. It provides a statistical test of whether or not the means of several groups are equal. Therefore it generalizes t-test to more than two groups. Doing multiple two-sample t-tests would result in an increased change of committing a type 1 error. Analysis of variance is useful in comparing three or more means for statistical significance.

ANOVA is a particular form of statistical hypothesis testing heavily used in the analysis of experimental data. A statistical hypothesis test is a method of making decisions using data. A test result is called statistically significant if it is deemed unlikely to have occurred by change, assuming the truth of the null hypothesis. A statistically significant result is less than a threshold justifies the rejection of the null hypothesis. In an application of ANOVA, the null hypothesis is that all groups are simply random samples of the same population.

The terminology of ANOVA is largely from the statistical design of experiments. The experimenter adjusts factors and measures responses in an attempt to determine an effect. Factors are assigned to experimental units by a combination of randomization and blocking to ensure the validity of the results. ANOVA is the synthesis of several ideas and it is used for multiple purposes. ANOVA is a statistical tool used in many ways to develop and confirm an explanation for the observed data.

Conduting a Two Factor ANOVA

ANOVA An experiment is designed to measure the effect of detergent brand and washing cycle time on the amount of dirt removed from standard household laundry loads. Four brands and four levels of washing cycles are selected for the analysis. The results, in pounds of dirt removed are as follows 18 20 22 24 A 0.11 0.13 0

Scatter Diagram & Correlation Problems

1. The three problems in the attached file to be solved are #10, #14 and #24. They are circled and hi-lited in yellow. 2. The least-squares regression line is a model that describes the relationship between two variables. Now that you have read about regressions and hypothesis tests, you will collect data to create a least-s

Factorial ANOVA: Music and Age

Conduct two-way independent ANOVA on the data attached. The first independent variable is age. The second independent variable is music. The variable is called liking. Please provide me the step by step guide for this assignment to master the procedure.

Repeated Measures ANOVA

A researcher has been hired by a pizzeria to determine which type of crust customers prefer. The restaurant offers three types of crust: hand tossed, thick, and thin. Following are the mean number of 1 inch pieces of pizza eaten for each condition from 10 subjects who had the opportunity to eat as many pieces with each type of

Reaction time study

A study is made regarding the reaction times (in seconds) to danger among four groups of professional drivers: bus drivers, cab drivers, truck drivers, and race car drivers. The results are as follows: Reaction Time (Seconds) Cab Drivers Bus Drivers Truck Drivers Race Car Drivers 3.4 4.5

Generating Hypotheses for t-Tests and ANOVAS

Please help with the following problem. In doing the test for the ANOVA one-way or two-way, how would you describe the F ratio of ANOVA as compared to a two-way or is there a difference?

Two Way ANOVA: Gender, Marital Status, and Happiness

Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100): What is/are the independent varia

Variance Comparison and Analysis

11.8 Students in a business course performed a completely randomized design to test the strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until the bag broke. A total of 40 bags, 10 for each brand, were used. The data in the trashbags.xls file gives the weight (in lbs.) required t

Analysis of Variance (ANOVA) - F Test

See the attached file. Happy Fund's manager believes that the return on Airline shares is dependent the fluctuations in oil prices and interest rates. He collects the weekly data on the share prices, oil prices, and interest rates. Use the data provided and regression analysis and show whether oil prices and interest rate affec

Analysis of variance involving experimental treatment

In a completely randomized design, 12 experimental units were used for first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance at 0.05 level of significant difference between the treatment. Source of variation Sum of Squares Degree of freedom Mean S

Cell Condition/Means

What is the difference between a cell (condition) mean and the means used to interpret a main effect?

Statistics: ANOVA Tables

Complete each of the following ANOVA summary tables. In addition, answer the following questions for each of the ANOVA summary tables: a. What is the factorial notation? b. How many conditions were in the study? c. How many subjects were in the study? d. Identify significant main effects and interaction effects. Source df

How to interpret an ANOVA table

Additional info is attached. See attached for table: Answer the following questions in an analysis of whether level of stress and gender has an impact on caffeine consumption (measured as cups of coffee per day). Copy and paste your results below. a. Is there a difference between the levels of caffeine consumption for

2x3 ANOVA Experimental Design

Create a drawing or plan for a 2 x 3 experimental design that would lend itself to a factorial ANOVA. Be sure to identify the independent and dependent variables.

ANOVA Effect Size

Independent variable: Teaching methods (here we have three teaching methods so we have three levels of independent variable) Dependent variable: Mathematics scores Null Hypothesis (Ho): There is no significant difference between the population average scores of mathematics among these three groups with different teaching m

One-way Analysis of Variance (ANOVA) done by the SPSS program

Can someone help me to condense the statistical results of the attached "One-way Analysis of Variance (ANOVA) done by the SPSS program? The test looks at: Are there any Ethnic difference in level of education. Also, can you help me with answering the following? 1. State the statistical assumptions of this test. 2. Select a

ANOVA - Lowering Cholesterol

A medical researcher wants to try three different techniques to lower cholesterol levels. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subject's cholesterol level is

Statistics: Regression, Correlation, ANOVA

1. Find the equation of the regression line for the given data. What is the predicted value of Y when X = -2? What is the predicted value of Y when X = 4? X -5 -3 4 1 -1 -2 0 2 3 -4 Y -10 -8 9 1 -2 -6 -1 3 6 -8 2. The data below

ANOVA and Least Squares Regression

For the purposes of this session long project, I tracked my driving time to work on a daily basis for 15 days. During this 15 day period, I took the same route to work and left my house at 6:45 every morning. The total driving distance from my residence to my office is 5.5 miles, and the speed limit for the majority of the rou

ANOVA: Analysis of Variance

The original concepts of analysis of variance came from the work of Sir Ronald A. Fisher, an English statistician. This technique, better known as ANOVA, has become one of the most commonly used research methods for testing differences among several population means. If only two populations are in question, ANOVA can be used; ho

The Dial Switching Problem: Analysis of Variance

2. Dial Switching Problem #2: The Beavis Panel Company manufactures porcelain metal panels for the appliance industry. The porcelain is set under conditions of heat, pressure and thickness. The company is presently having a problem with porcelain brittleness (...the stuff cracks too easily). The ideal brittleness is measured

Measuring the Media using Statistics

Table: Sales RadioTV Newspaper 973 0 40 1119 0 40 875 25 25 625 25 25 910 30 30 971 30 30 931 35 35 1177 35 35 882 40 25 982 40 25 1628 45 45 1577 45 45 1044 50 0 91

ANOVA Model and Degrees of Freedom

A professor of statistics at a large Midwestern university designed an experiment to evaluate the effectiveness of four methods of online instruction: (1) providing students with a set of PowerPoint slides with no audio; (2) providing a slideshow of the PowerPoint slides with audio of the professor reading through the notes; (3)

Repeated-Measures Analysis of Variance

The repeated-measures analysis of variance can be viewed as a two-stage process. What is the purpose for the second stage? Compare the repeated-measures analysis of variance with the regular ANOVA.

One-Way Analysis of Variance with SPSS.

One-Way Analysis of Variance with SPSS. o State the statistical assumptions of this test. o Given a data set, select an independent variable with two or more levels and a dependent variable. o Develop the null hypothesis and the alternative hypothesis for main effects. o Using SPSS, calculate an ANOVA. Include a post hoc t

Sample Mean, Variance, Standard Deviation and Quartiles

Problem 1: Calculating sample mean, sample variance and sample standard deviation 7 8 7 8 8 11 7 9 10 12 9 10 12 10 10 9 8 11 11 11 9 9 12 10 11 10 The table above gives the shoes sizes of 26 members of a football club. Tasks: - Enter the data into column A in an Excel sheet. Use the first rows for titles/description

ANOVA, F Scores and Hypothesis Testing

14. Foofy obtained a significant Fobt from an experiment with five levels. She therefore concludes that changing each condition of the independent variable. (a) Is she Correct? Why or why not? (b) What must she do now? 16. A report says that the between-subjects factor of participants' salary produced significant differences i

Analysis using One-Way ANOVA

1) What is the difference between the means of employees' length of experience within their organizations and their decisions of staying or leaving their current job? 2) What is the difference between the means of employees' length of experience with their managers and their decisions of staying or leaving their current job? B