Response 1 (Josh)
Chi-Square Goodness-of-Fit
The Chi-Square Goodness-of-Fit is a statistical test used to determine if a distribution is
suitable for a given dataset, or how a model actually represents the data used. This test is nonparametric and measures the probability that an observed distribution of data or model is due to
chance alone. It finds many uses in datasets that are not quantitative.
The main difference of the Chi-Square Goodness-of-Fit test from the t-test and ChiSquare test of independence is the fact that it is non-parametric. The two tests mentioned in the
latter are both parametric, and the dataset almost always follows the normal distribution or tdistribution.
To clarify the Chi-Square Goodness-of-Fit’s use, below is an equation for the calculation
of the Chi-Square Goodness-of-Fit statistic:
The test statistic computed using this equation will tell how “fit” the set of values are to
the model: if the statistic is too large, then the fit is very poor. In hypothesis testing, the test
evaluates the null hypothesis H0, that the data follows the assumed distribution, against the
alternative.
References
http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm
http://www.ruf.rice.edu/~bioslabs/tools/stats/chisquare.html
Response 2 (Lisa)
1. Describe the Chi-Square goodness-of-fit test?
"The first test is called the 1 x k ("one by kay"), or the goodness-of-fit chi-square test."
(Tanner 2011, Ch. 10.2) This test is like the one-way ANOVA because it only uses one variable.
The one question that many researchers ask when using this type of test is the hypothesis that
comes from this type of test accurate or did it happen by chance.
2. 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?
The goodness-of-fit test can accommodate one variable whereas the chi-square of
independence accommodates two variables; the independent T test refers to samples in the
analysis itself. When it comes to possible negatives there is some draw back but from what I
have read they tend to be the same; when we look at the goodness-of-fit there is no comparison
of means or the two groups because nominal data tend to not yield any means. The chi-square of
independence tends to tell us that the null hypothesis lets us know that the two variables have no
relation as you can see we see draw backs but they are related.
References:
Tanner, David (2011) Statistics for the Behavioral and Social Sciences. Bridgepoint Education,
Inc.
Response 3 (Nich)
Describe the chi-square goodness-of-fit test.
The chi-square goodness-of-fit test is also known as the 1 x k chi-square test. The test is
commonly used to test the association of variables in two-way tables. According to the text,
“It sounds like most of the other statistical tests of significant difference and, except for the scale
of the data involved, there are some important similarities.” (Tanner 2011, Ch. 10.2)
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.
According to Marczyk, DeMatteo and Festinger, (2005) “Chi-square summarizes the discrepancy
between the observed and expected scores, the smaller the value of the chi-square will be.
Conversely, the larger the discrepancy is between the observed and expected scores, the larger
the value of the chi-square will be.” The test is different from the T test by the chi-square test
determines if the result will be different from what we expect, while the independent t-test
compares the mean difference between the two independent groups. The tests are similar by they
both require
How do you know when to use one analysis over the other? Provide a real-world example.
The time that I would use the chi-square test of independence is when I am attempting to
determine the difference between two different populations from a single population. An
example that I would use is a poll of 2000 residence broken down by gender and political parties
to see if there is a preference between the voter’s genders and public party.
References:
Marczyk, G., DeMatteo, D., & Festinger, D. (2005). Essentials of research design and
methodology. Hoboken, NJ: John Wiley & Sons.
Tanner, David (2011) Statistics for the Behavioral and Social Sciences. Bridgepoint Education,
Inc.
Response 4 (Instructor based on initial post)
John,
Thank you for your thoughtful and detailed description of chi-square. I like
your example. How might your data be set up in a table? What might your
expected values be?
Here is a link to some nice examples:
http://math.hws.edu/javamath/ryan/ChiSquare.html
What do you think of that website?
thanks,
Jeral
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