Statistics question on how to find the chi-squared sample value?
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To do this, you basically have to compared the std. residual to the critical values for the corresponding p-value you care about. Here is a link to a powerpoint presentation that describes how to do a post hoc test for chi squared:http://www.utexas.edu/courses/sc...Quoting from that:"One of the problems in interpreting chi-square tests is the determination of which cell or cells produced the statistically significant difference. Examination of percentages in the contingency table and expected frequency table can be misleading.The residual, or the difference, between the observed frequency and the expected frequency is a more reliable indicator, especially if the residual is converted to a z-score and compared to a critical value equivalent to the alpha for the problem.SPSS prints out the standardized residual (converted to a z-score) computed for each cell. It does not produce the probability or significance.Without a probability, we will compare the size of the standardized residuals to the critical values that correspond to an alpha of 0.05 (+/-1.96) or an alpha of 0.01 (+/-2.58). Standardized residuals that have a positive value mean that the cell was over-represented in the actual sample, compared to the expected frequency."
You can look in a table (if you’re old fashioned) or let the computer do it.If you mean, how are the values calculated in the first place, that is done from the inverse cumulative distribution function. The CDF for the chi-squared distribution iswhere [math]\gamma[/math] is an incomplete gamma[math] [/math] function, [math]\Gamma[/math] is the usual gamma function and r is degrees of freedom.
How do I find the P-value for a GOF test when all I have is the test statistic and critical value?
I've searched all through my notes, textbook, and online, and I still can't find how to get the answer on this particular hw problem. This is an interactive online hw assignment and when I choose the "Help me solve this" it says to use technology to find the P-value, but the only way I know on my TI-84 is to plug in an observed list and an expected list in χ²GOF-Test. The problem doesn't give any lists and I've tried researching how to find the P-value without lists but I still can't figure it out. Well here it is. A person purchased a slot machine and tested it by playing it 1,158 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of χ² = 18.146. Use a 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected? I already know: Test statistic = 18.146 The critical value = 16.919 P-value is _____???
Chi-Square goodness of fit test is a non-parametric test that is used to find out how the observed value of a given phenomena is significantly different from the expected value. In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution.
How do I calculate the p-value for a (2x2) Chi Square test when an expected value is zero?
Tables in a Chi-Square test can have two types of 0 values: Structural and functional zeroes. Structural zero are impossible case, value in a table number of strokes per hole n hole 1 is necessarily smaller than any table with a score of the whole round. Functional zeroes are possible but not probable values, if one looks at age of a woman when bearing a child the woman's' ages less than 3 or greater than 80 are possible but improbable. Nonetheless, This is a possible real world solution--outliers as it were. We can change the test so that the cells with possible values in a dimension are so improbable as to be 0, we add .5 to the cell count and we calculate the chi-square test. So your data will be Expected 499.5 No .5 Yes, so your chi-square with 1 degree of freedom calculates to: (450-499.5)^2 + (50-.5)^2 = .25 + 2450.25 = 2450.5 which rejects Ho. This is a rule of thumb used in modeling tables via chi-square tests. You may balk because it's not a natural part of the theory, but that's the case for the whole test. The whole test uses chi-squre for its test statistic since it's easy ti calculate--but the ddistributionof cells has an ASYMPTOTIC Chi sSquare distribution, In the professional world, this works quite well.
It depends on the context. You mostly hear these terms in dealing with chi-square tests. Lets say you wanted to test if a coin is fair:H0: Coin is fair -> P(H)=0.5HA: Coin is not fair -> P(H) != 0.5Then you flip the coin 100 times and record the results. You get 70 heads and 30 tails. These are the observed values. Under the null, you would expect to get 50 heads and 50 tails. These are the expected values. Then you can calculate the chi-square statistic from these values.
Why can't chi-squared be calculated on negative values?The question is not clear, as worded.Do you mean: Can values of chi square ever be negative? The answer is no. The value of a chi square cannot be negative because it is based on a sum of squared differences (between obtained and expected results).Do you mean: Can data values that are used to calculate chi squared be negative? The answer to this question depends on what pieces of the computation you refer to when you ask about possible negative values.Use of Chi Square as a test of association for a contingency table:The application of chi square that is most familiar is comparison of observed cell frequencies (or counts) in a contingency table to the expected cell frequencies implied by a model or null hypothesis. The usual null hypothesis is that the row and column variables are not related.For each cell, O, the observed cell frequency, cannot be negative; it can be 0 or positive.For each cell, the difference between observed and expected value (O - E) can be either zero, negative, or positive. If there are any positive values of (O- E) there must negative values of (O - E). (O - E) must sum to zero across rows and down columns.When you compute a chi square statistic for a contingency table, each (O - E ) term is squared (and divided by E). A squared term cannot be negative, and so the sum of squared terms.A chi square can also be a one-way test between a list of observed values and a list of expected values under some hypothesis (such as the hypothesis of a uniform or normal distribution).Use of Chi Square as Model Goodness of Fit Test (in SEM, for example).There are other applications of chi square in which some observed values can be negative. For example, the goodness of fit of a structural equation model is assessed by comparing the matrix of observed variances and covariances for all the measured variables, to the set of variances and covariances derived from a specific model. Observed covariances can be negative. The final value of chi squared cannot be negative in this situation either.