The purpose of this discussion is to allow you to consider how various non-param
ID: 3126467 • Letter: T
Question
The purpose of this discussion is to allow you to consider how various non-parametric tests are used and how they compare to other tests with similar variables. To do this, you will need to identify the appropriate application of course-specified statistical tests, examine assumptions and limitations of course-specified statistical tests, and communicate in writing critiques of statistical tests. Describe the chi-square goodness-of-fit test. Provide a detailed explanation of what this test measures, and how it is similar to and different from the independent t-test and the chi-square test of independence. How do you know when to use one analysis over the other? Provide a real-world example.Explanation / Answer
Solution:
the appropriate application of course-specified statistical tests, examine assumptions and limitations of course-specified statistical tests, and communicate in writing critiques of statistical tests
Research Report. Write a research report based on a hypothetical research study. Conducting research and writing a report is common practice for many students and practitioners in any of the behavioral sciences fields.
A research report, which is based on scientific method, is typically composed of the different sections listed below:
• Introduction: The introduction states a specific hypothesis and how that hypothesis was derived by connecting it to previous research.
• Methods: The methods section describes the details of how the hypothesis was tested and clarifies why the study was conducted in that particular way.
• Results: The results section is where the raw uninterpreted data is presented.
Discussion: The discussion section is where an argument is presented on whether or not the data supports the hypothesis, the possible implications and limitations of the study, as well as possible future directions for this type of research.
Together, these sections should tell the reader what was done, how it was done, and what was learned through the research. You will create a research report based on a hypothetical problem, sample, results, and literature review. Organize your data by creating meaningful sections within your report. Make sure that you:
• Apply key concepts of inferential hypothesis tests.
• Interpret the research findings of the study.
• Examine the assumptions and limitations of inferential tests.
• Develop a practical application of the research principles covered in this course.
Chi-Square Test
generally speaking, the chi-square test is a statistical test used to examine differences with categorical variables. There are a number of features of the social world we characterize through categorical variables - religion, political preference, etc. To examine hypotheses using such variables, use the chi-square test.
The chi-square test is used in two similar but distinct circumstances:
a. for estimating how closely an observed distribution matches an expected distribution - we'll refer to this as the goodness-of-fit test
b. for estimating whether two random variables are independent.
The Goodness-of-Fit Test
One of the more interesting goodness-of-fit applications of the chi-square test is to examine issues of fairness and cheating in games of chance, such as cards, dice, and roulette. Since such games usually involve wagering, there is significant incentive for people to try to rig the games and allegations of missing cards, "loaded" dice, and "sticky" roulette wheels are all too common.
Example and explanation:
So how can the goodness-of-fit test be used to examine cheating in gambling? It is easier to describe the process through an example. Take the example of dice. Most dice used in wagering have six sides, with each side having a value of one, two, three, four, five, or six. If the die being used is fair, then the chance of any particular number coming up is the same: 1 in 6. However, if the die is loaded, then certain numbers will have a greater likelihood of appearing, while others will have a lower likelihood.
The chi-square statistic can be used to estimate the likelihood that the values observed on the blue die occurred by chance.
The key idea of the chi-square test is a comparison of observed and expected values.
Lastly, to determine the significance level we need to know the "degrees of freedom." In the case of the chi-square goodness-of-fit test, the number of degrees of freedom is equal to the number of terms used in calculating chi-square minus one. There were six terms in the chi-square for this problem - therefore, the number of degrees of freedom is five. O
recap the steps used in calculating a goodness-of-fit test with chi-square:
1. Establish hypotheses.
2. Calculate chi-square statistic. Doing so requires knowing:
o The number of observations
o Expected values
o Observed values
3. Assess significance level. Doing so requires knowing the number of degrees of freedom.
4. Finally, decide whether to accept or reject the null hypothesis.
Testing Independence
The other primary use of the chi-square test is to examine whether two variables are independent or not. What does it mean to be independent, in this sense? It means that the two factors are not related. Typically in social science research, we're interested in finding factors that are related - education and income, occupation and prestige, age and voting behavior. In this case, the chi-square can be used to assess whether two variables are independent or not. A two variable Chi-square test or test of independence is similar to the test for an interaction effect in ANOVA, that asks: Is the outcome in one variable related to the outcome in some other variable
More generally, we say that variable Y is "not correlated with" or "independent of" the variable X if more of one is not associated with more of another. If two categorical variables are correlated their values tend to move together, either in the same direction or in the opposite.
Chi-square analysis for real world
Any business situation where you are essentially checking if one variable, K is related to, or independent of, another variable, L. The use of chi-square test is indicated in the following business scenario.
Suppose you want to determine if certain types of products sell better in certain geographic locations than others. A simple example: the type of shoes sold in winter depends strongly on whether a retail outlet is located in the upper mid-west versus in the south.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.