Analysis of variance test

Reference no: EM13910089

Research Proposal: Project Paper

Write a Research Proposal (1,000-1,500 words) on a topic relevant to the course. To complete the Research Proposal, do the following:

Review the Topic 7 lecture section on The Results and Discussion Sections in the Research Proposal for a brief overview pertaining to "how to" complete the assignment.

1 Introductory section: Include hypothesis and a review of the literature.

2 Methodology section: Include subsections on Participants, Apparatus/Materials/Instruments, Procedure, and Design.

3 Results section: Include statistic, critical values, degrees of freedom, and alpha level.

4 Discussion section: Include interpretation of results, ethical concerns, limitations of study, and suggestions for future research.

5 Appendices section: Include a minimum of two appendices (either two figures, two tables, or a figure and a table).

6 Include at least six to eight scholarly references

Prepare this assignment according to the APA guidelines found in the APA Style Guide, located in the Student Success Center. An abstract is not required.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

The Analysis of Variance Test

The analysis of variance (ANOVA) test examines mean differences among two or more treatment groups (Bluman, 1998). The one-way ANOVA is used in two cases: 1) a one-way between-subjects analysis of variance is used when there is one independent variable with multiple independent groups, and 2) a one-way repeated measures analysis of variance is used when there is one independent variable with multiple matched groups (or a within-subjects design). The two-way ANOVA is used for factorial designs (two or more independent variables), whether the design uses independent groups, matched groups, or a combination of the two (a mixed design). In addition, the data should be measured by interval or ratio scales. Additional criteria are that the variances of the groups' populations are roughly equal (or homogeneous) and that the populations are normally distributed. However, the test is fairly robust,meaning that meaningful results may be obtained even if some of the criteria are unmet (Myers & Hansen, 2006).

Instead of using ANOVA, one could simply calculate a series of t-tests, but that is more cumbersome and, more importantly, increases the chance of committing a type I error. ANOVA examines mean differences indirectly by calculating differences in variance, a statistic called the F ratio (Bluman, 1998). The numerator of the F ratio calculates between-groups variance, actual differences caused by the independent variable plus random chance fluctuations caused by error. The denominator of the F ratio calculates within-groups variance, which is error caused by random chance fluctuations among the subjects. Thus, the F ratio is an attempt to factor out random chance error; what is left over should reflect the impact of the independent variable on subjects' behavior.

Following is an example of working through the ANOVA formulas. The student is encouraged to follow each step outlined in Jackson's text. One-way, between-subjects ANOVA is calculated as follows: Examine Table 20.1 (p. 299) to see the hypothetical raw data, means, and the grand mean for this particular study involving one independent variable and three treatment groups. Next, SSTotal is calculated in Table 20.2 (p. 302), and the denominator of the F ratio, within-groups variability, is calculated in Table 20.3 (p. 303). The denominator, MSW, is the meansquarewithingroups. It is calculated by dividing SSW, or sum of squares for within-groups variability, by dfW, or degrees of freedom for within-groups variability.

Once the denominator is calculated, then the numerator can be calculated for between-groupsvariability. The grand mean is calculated first, followed by calculating deviations of group means from the grand mean, and then calculating the squareddeviations (SSB). Finally, dfB is calculated so that MSB (the meansquarebetweengroups) can be calculated (SSB divided by dfB). The F ratio can now be computed (it is MSB divided by MSW). Once the ratio is obtained, its significance level can be determined (Table B-3, pp. 379-381). There are two df numbers to use. Use dfBfor the column, and dfW for the row. For each pair of df, find the critical F value to beat; the number on top is the .05 value, and below it is the .01 value. Examine Tables 20-5 and 20.6 for tips on how to set up an ANOVA summary table (p. 306).

Because the F test gives results only for the overall pattern of treatment means, sometimes more information is desired (e.g., differences between two of the cells). In this case, post hoc tests may be used such as Tukey's post hoc test; they are like t-tests, except they are more conservative to minimize chances of a type I error (however, because of that stringency, they increase the chance of making a type II error) (Bluman, 1998). If there is good reason before the experiment is run to expect that a t-test will need to be calculated between particular cells, then an a priori comparisoncan be planned; however, it is not as stringent as a post hoc test in determining statistical significance.

With computers being used more and more to calculate results (e.g., Statistical Packages for the Social Sciences); it is very rare to see anyone calculate by hand a two-way ANOVA anymore. It is important to note that, with a factorial design, not only do independent variables (or main effects) need to be checked for possible statistical significance, but also possible interaction effects need to be checked as well (Martin, 1977). For example, for a design with two independent variables, three F ratios would be calculated (two main effects and one interaction). For a design with three independent variables, six F ratios would be calculated. Since interaction effects are often tricky to decipher, this is yet another reason for keeping the design simple.

The Results and Discussion Sections in the Research Proposal

Since you will not typically be carrying out your research proposal, you may be wondering how you will fill out your results section. There are four items that can be included. 1) Since you created the design for the Method section, you can select the appropriate statistic. 2) You can include the alpha level (of .05). 3) You know how many subjects you need, so df can be calculated. 4) Thus, you can also calculate the critical value needed to reject the null hypothesis.

The Discussion section should explain three aspects: 1) what the results mean, in "everyday" language (practical versus research significance), 2) the strengths and the limitations of the study, and 3) future possibilities for research (Martin, 1977). In addition, for this class' project, a discussion of ethics is needed (e.g., how ethical issues were dealt with).

Following the body of the paper is the References page; see the American Psychological Association (APA) Manual for the correct format (pp. 49-51). The last two items are Tablesand Figures.The research project must contain one of each (or two tables or two figures). Tables are columns of data (if you do not carry out the project, do not make up data; the table format can still be set up). Figures include pictures, graphs, or drawings.

DQ 1

How do descriptive, predictive, and explanatory methods of research differ from each other? In what ways are they similar?

Goal Met Research Methods Advantages/Disadvantages

Description Observational method Descriptive methods allow description of behavior(s)

Case study method Descriptive methods do not support reliable predictions

Survey Method Descriptive methods do not support cause-and-effect

Explanations

Prediction Correlational method Predictive methods allow description of behavior(s)

Quasi-experimental method Predictive methods support reliable predictions of one

variable based on another

Predictive methods do not support cause-and-effect

explanations

Explanation Experimental method Allows description of behavior(s)

Supports reliable predictions of one variable based on

another

Supports cause-and-effect explanations

DQ 2

How does the scientific method point towards truth? What is truth, and how do you know when you have found it?

Assignment

Complete the even-numbered problems for the designated chapter(s) in the textbook. Students are highly encouraged to complete all problems in each chapter, as odd-numbered problems increase understanding of even-numbered problems (answers to odd numbered problems are located in appendix A at the back of the text.

Provide an argument for the idea that basic research is as important as applied research.

Some psychologists conduct research because they enjoy seeking knowledge and answering questions. This work is referred to as basic research- the study of psychological issues to seek knowledge for its own sake. Most basic research is conducted in university or laboratory settings. Its intent is not immediate application but the gaining of knowledge. However, many treatments and procedures that have been developed to help humans and other animals began with researchers asking basic research questions that later led to applications. Examples of basic research include identifying differences in capacity and duration in short-term memory and long-term memory, identifying whether cognitive maps can be mentally rotated, determining how various schedules of reinforcement affect learning, and determining how lesioning a certain area in the brains of rats affects their behavior.

A second type of research is applied research , which involves the study of psychological issues that have practical significance and potential solutions. Scientists who conduct applied research are interested in finding an answer to a question because the answer can be immediately applied. Much applied research is conducted by private businesses and the government. Examples of applied research include understanding how stress affects the immune system, determining the accuracy of eyewitness testimony, determining the relationship between watching violent TV and aggression in children, and determining whether cell phone use while driving negatively affects driving performance.

Some people think that most research should be directly relevant to a social problem or issue. That is, they favor only applied research. However, much of what started out as basic research has eventually led to some sort of application. If researchers stopped asking questions simply because they wanted to know the answer (i.e., stopped engaging in basic research), they would undoubtedly lose many great ideas and eventual applications.

An infomercial asserts, " A study proves that Fat-B-Gone works, and it will work for you also." What is wrong with this statement?

In a research project intended to gather data on the effects of type of study method on examination performance, subjects are randomly assigned to one of two conditions. In one condition, they study alone, using notes they took during class lectures. In a second condition, subjects study in interactive groups with notes from class lectures. The amount of time spent studying is held constant. All students then take the same exam.

In this study:

a. What is the independent variable?
b. What is the dependent variable?
c. Identify the control and experimental groups.
d. Is the independent variable manipulated, or is it a participant variable?

Gerontologists interested in

DQ 1

Using Stevens's four levels of measurement, give an example of nominal, ordinal, interval, and ratio scales (do NOT use examples from the text or lecture).

DQ 2

Stanley Milgram's obedience to authority experiment is one of the most controversial studies in psychology's history. Considering this example as well as others, critique such experiments from an ethical standpoint.

Assignment

When you arrive for your psychology exam, you are flabbergasted to find that all of the questions are on calculus and not psychology. The next day in class, students complain so much that the professor agrees to give you all a makeup exam the following day. When you arrive at class the next day, you find that, although the questions are different, they are once again on calculus. In this example there should be high reliability of what type? What type(s) of validity is the test lacking? Explain your answers.

While APA format is not required for the body of this assignment, solid academic writing is expected and in-text citations and references should be presented using APA documentation guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

DQ 1

Discuss the advantages and disadvantages of the following nonexperimental research methods: (a) naturalistic observations, (b) surveys, and (c) correlational studies. If you were asked to use one of these designs in a study next week, which nonexperimental design would you select and why?

DQ 2

Discuss examples of when a naturalistic observational study would be the most appropriate design to select.

Assignment

1. Explain the difference between participant and nonparticipant observation and disguised and undisguised observation.

2. Explain how qualitative research differs from quantitative research.

3. Explain the difference between an interview and a focus group interview.

4. Draw a scatterplot indicating a strong negative relationship between the variables of income and mental illness. Be sure to label the axes correctly.

DQ 1

Explain the circumstances when a quasiexperimental design would be preferable to a between-subjects design, but also discuss why an explanatory research method is superior to a predictive method.

DQ 2

Compare and contrast:
1. Between-subjects with within-subjects designs
2. Small N designs with large N designs.
3. In what circumstances would you use the within-subjects design and in what circumstances would you use the large N design?

Assignment

1 Chapter 6 (pg 173), module 12, exercises 2 and 4

2. You read in a health magazine about a study in which a new therapy technique for depression was examined. A group of depressed individuals volunteered to participate in the study, which lasted 9 months.

There were 50 subjects at the beginning of the study and 29 at the end of 9 months. The researchers claimed that of those who completed the program, 85% improved. What possible confounds can you identify in this study?

4. What are internal validity and external validity? Why are they so important to researchers?

DQ 1
One of the best-known longitudinal designs is Lewis Terman's study of giftedness. He began tracking gifted children into adolescence and adulthood in 1925; the study is supposed to conclude in 2020. Explain the unique benefits of such a study, and then explain the problems caused by this type of design.

DQ 2
Lay out the design for two between-subjects experiments: (a) an experiment involving an experimental group and a control group, and (b) a factorial design with three independent variables that have 3, 2, and 2 levels, respectively.

Assignment

2 Chapter 7 (pg 221), module 15, exercises 4 and 6

4. Calculate the mean, median, and mode for the data set in Exercise 1. Is the distribution normal or skewed? Which measure of central tendency is most appropriate for this distribution? Why?

6. Calculate the range and standard deviation for the following five distributions:

a. 1, 2, 3, 4, 5, 6, 7, 8, 9

b. - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4

c. 10, 20, 30, 40, 50, 60, 70, 80, 90

d. 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9

e. 100, 200, 300, 400, 500, 600, 700, 800, 900

This is a CLC assignment.

Each CLC team will design a correlational and experimental study investigating the relationship between these two variables-time spent playing video games and aggression.

To complete this assignment, read the designated chapter readings in the textbook for Topic 2 (chapter 2 (module 4), chapter 3 (modules 5 and 6), chapter 5 (modules 9, 10, 11) and chapter 6 (module 12)), as the readings contain pertinent information for successful assignment completion. Address the following:

1 Submit a filled-in copy of the "CLC Group Projects Agreement."

2 Consider the hypothesis and how the group will define operationally and measure the variables.

3 How will the group obtain a random sample of participants?

4 Assume the study produces a correlation of .56 between the variables. What are three possible causal reasons for the relationship?

5 Design an experimental study to investigate the variables. What is the hypothesis? What kinds of hypotheses with respect to testing, does the experimental method allow that the correlation design does not?

6 What is the independent variable? What is the dependent variable?

7 How will the group ensure the study has high internal validity? Will the group use random assignment conditions?

8 Are there any ethical concerns about the treatment of participants emerging from the experiment?

Include at least three to four scholarly sources.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

You are required to submit this assignment to Turnitin. Please refer to the directions int he Student Success Center.

DQ 1

Suppose that, for a t test, your computed value for t is +3.28. The critical value of t is +2.048. Explain what this means. Do you reject the null hypothesis or not? Now suppose that you have 28 degrees of freedom and are using a two-tailed (nondirectional) test. Draw a simple figure to illustrate the relationship between the critical and the computed values of t for this result.

DQ 2

Explain the purpose of a null hypothesis. Why are both a research/alternative hypothesis and a null hypothesis necessary in statistics?

Assignment

1 Chapter 8 (pg 267), module 17, exercises 2 and 4

2. To test the hypothesis in Exercise 1, the admissions counselors select a random sample of freshmen and compare their scores on the SAT to those of the population of upperclassmen. They find that the freshmen do in fact have a higher mean SAT score. However, what they are unaware of is that the sample of freshmen was not representative of all freshmen at Brainy University. In fact, the sample overrepresented those with high scores and underrepresented those with low scores. What type of error (Type I or Type II) did the counselors make?

4. What are the appropriate H0 and Ha for each of the following research studies? In addition, note whether the hypothesis test is one- or two-tailed.

a. A study in which researchers want to test whether there is a difference in spatial ability between left- and right-handed people.

b. A study in which researchers want to test whether nurses who work 8-hour shifts deliver higher- quality work than those who work 12-hour shifts.

c. A study in which researchers want to determine whether crate-training puppies is superior to training without a crate.

2 Chapter 8, module 18, exercises 2 and 4

2. What is the standard error of the difference between means?

4. A college student is interested in whether there is a difference between male and female students in the amount of time spent studying each week. The student gathers information from a random sample of male and female students on campus. Amount of time spent studying is normally distributed. The data follow.

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute the effect size and interpret.

f. If significant, draw a graph representing the data.

DQ 1

A researcher computed the F ratio for a four-group experiment. The computed F is 4.86. The degrees of freedom are 3 for the numerator and 16 for the denominator.
1 Is the computed value of F significant at p < .05? Explain.
2 Is it significant at p < .01? Explain

DQ 2

Explain the difference between a t test for independent groups and a t test for matched groups.

Assignment

1 Chapter 9 (293), module 19, exercise 2, 4, and 6

2. What are the assumptions of a correlated groups t test?

3. What measure of effect size is used for a correlated-groups t test?

4. The student in Question 5 from Module 18 decides to conduct the same study using a within-subjects design in order to control for differences in cognitive ability. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. The data appear below. As before, they are measured on an interval ratio scale and are normally distributed.

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute the effect size and interpret.

f. If significant, draw a graph representing the data.

DQ 1

Explain how you would show each of the following in a report:
1 The results of a t test with 38 degrees of freedom, where the obtained value of t was 1.38, and the significance level was p < .20.
2 The proper placement of a figure within the text.
3 The proper placement of a table within the text.

DQ 2

How can internal and external validity be increased in an experiment?

Assignment

Briefly describe the type of information that should be in an introduction.

Introduction

The introduction begins on page 3. It is not labeled "Introduction"; instead, the title of the manuscript, exactly as it appears on the title page, is centered at the top of the page. The introduction has three basic components. The first part introduces the problem under study. The second part contains relevant previous research to provide an appropriate history and cites works that are pertinent to the issue but not works of marginal or peripheral significance. When summarizing earlier works, emphasize pertinent findings, relevant methodological issues, and major conclusions. Do not include nonessential details. The third part of the introduction states the purpose and rationale for the study. You should explain your approach to solving the problem, define the variables, and state your hypotheses along with the rationale for each hypothesis.

Reference no: EM13910089

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