 Do you need equal amounts of data for a chisquare test?
I'm trying to see if there is a dependent relationship between whether a school is public or private and its student-teacher ratio. I'm not sure if I can use a chi square test for this because there is like a 6 to 1 ratio between the amounts of public and private schools that I have for my data (way more public schools). Can I chi square test still work ... http://mathhelpforum.com/statistics/167154-do-you-need-equal-amounts-data-chi-square-test-print.html Example 28.8: Computing Friedman's Chi-Square Statistic
Friedman's test is a nonparametric test for treatment differences in a randomized complete block design. Each block of the design may be a subject or a homogeneous group of subjects. If blocks are groups of subjects, the number of subjects in each block must equal the number of treatments. Treatments are randomly assigned to subjects within each block. If there is one subject per block, then the subjects are repeatedly measured once under each treatment. The order of treatments is randomized for each subject. In this setting, Friedman's test is identical to the ANOVA (row means scores) CMH statistic when the analysis uses rank scores (SCORES=RANK). The three-way table uses subject (or subject group) as the stratifying variable, treatment as the row variable, and response as the column variable. PROC FREQ handles ties by assigning midranks to tied response values. If there are multiple subjects per treatment in each block, the ANOVA CMH statistic is a generalization of Friedman's test. The data ... http://v8doc.sas.com/sashtml/stat/chap28/sect41.htm 1.3.6.6.6. Chi-SquareDistribution
Gamma(a) = \int_{0}^{\infty} {t^{a-1}e^{-t}dt} \) In a testing context, the chi-square distribution is treated as a "standardized distribution" (i.e., no location or scale parameters). However, in a distributional modeling context (as with other probability distributions), the chi-square distribution itself can be transformed with a location parameter, μ, and a scale parameter, σ. The following is the plot of the chi-square probability density function for 4 different values of the shape parameter. ... http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm ChiSquareDistribution
The Chi Square Distribution is the distribution of the sum of squared standard normal deviates. The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed. Therefore, Chi Square with one degree of freedom, written as χ2(1), is simply the distribution of a single normal deviate squared. The area of a Chi Square distribution below 4 is the same as the area of a standard normal distribution below 2 since 4 is 22. Consider the following problem: you sample two scores from a standard normal distribution, square each score, and sum the squares. What is the probability that the sum of these two squares will be six or higher? Since two scores are sampled, the answer ... http://onlinestatbook.com/2/chi_square/distributionC.html Aortic Size Assessment by Noncontrast Cardiac Computed Tomography: Normal Limits by Age, Gender, and Body Surface Area | JACC:...
All continuous variables were assessed for normality using the Shapiro-Francia test and assessed visually by inspection of histograms and standardized normal probability (P-P) plots. Continuous variables were compared using the t test for 2 groups and categorical variables were compared using the Pearson chi-square statistic.. Using multiple linear regression analysis, we sought to detect parameters that are associated with ascending and descending thoracic aorta size and to exclude patients with these parameters from the final analysis groups; therefore, the final analysis group would include only patients without parameters that influence the aorta size and can be called essentially "normalized." We employed a 2-stage model. A main effects model, which included potentially clinically important predictors (i.e., age, gender, smoking, family history of CHD, diabetes, dyslipidemia, and hypertension), was developed in stage I and a main effects plus interactions model in stage ... http://www.imaging.onlinejacc.org/content/1/2/200 Poisson Regression :: SAS/STAT(R) 13.2 User's Guide
Figure 43.4 displays the "Analysis Of Parameter Estimates" table, which summarizes the results of the iterative parameter estimation process. For each parameter in the model, PROC GENMOD displays columns with the parameter name, the degrees of freedom associated with the parameter, the estimated parameter value, the standard error of the parameter estimate, the confidence intervals, and the Wald chi-square statistic and associated p-value for testing the significance of the parameter to the model. If a column of the model matrix corresponding to a parameter is found to be linearly dependent, or aliased, with columns corresponding to parameters preceding it in the model, PROC GENMOD assigns it zero degrees of freedom and displays a value of zero for both the parameter estimate and its standard error. This table includes a row for a scale parameter, even though there is no free scale parameter in the Poisson distribution. See the section Response Probability ... http://support.sas.com/documentation/cdl/en/statug/67523/HTML/default/statug_genmod_gettingstarted01.htm Poisson Regression :: SAS/STAT(R) 14.1 User's Guide
Figure 44.4 displays the "Analysis Of Parameter Estimates" table, which summarizes the results of the iterative parameter estimation process. For each parameter in the model, PROC GENMOD displays columns with the parameter name, the degrees of freedom associated with the parameter, the estimated parameter value, the standard error of the parameter estimate, the confidence intervals, and the Wald chi-square statistic and associated p-value for testing the significance of the parameter to the model. If a column of the model matrix corresponding to a parameter is found to be linearly dependent, or aliased, with columns corresponding to parameters preceding it in the model, PROC GENMOD assigns it zero degrees of freedom and displays a value of zero for both the parameter estimate and its standard error. This table includes a row for a scale parameter, even though there is no free scale parameter in the Poisson distribution. See the section Response Probability ... http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/statug_genmod_gettingstarted01.htm Heterogeneity in Meta-analysis (Q, I-square) - StatsDirect
Heterogeneity in meta-analysis refers to the variation in study outcomes between studies. StatsDirect calls statistics for measuring heterogentiy in meta-analysis 'non-combinability' statistics in order to help the user to interpret the results.. Measuring the inconsistency of studies' results The classical measure of heterogeneity is Cochran's Q, which is calculated as the weighted sum of squared differences between individual study effects and the pooled effect across studies, with the weights being those used in the pooling method. Q is distributed as a chi-square statistic with k (numer of studies) minus 1 degrees of freedom. Q has low power as a comprehensive test of heterogeneity (Gavaghan et al, 2000), especially when the number of studies is small, i.e. most meta-analyses. Conversely, Q has too much power as a test of heterogeneity if the number of studies is large (Higgins et al. 2003): Q is included in each StatsDirect meta-analysis function ... https://www.statsdirect.com/help/content/meta_analysis/heterogeneity.htm