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Edit: Answer to Question 1: The Cramer's V statistic doesn't show direction. On a 2 x 2 table, phi shows direction with positive or negative sign, but directionality doesn't make much sense in a larger table of nominal categories.

There is no absolute interpretation of an effect size statistic like Cramer's V. It is always relative to the discipline and the expectations of the experiment. For a couple of points about this, see the comments to my answer at this link. That being said, the interpretations from Cohen 1988 are often used as typical interpretations. There is a table of interpretations here.

Edit: Answer to Question 2: To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

It doesn't make much sense to use the omnibus Cramer's V statistic as evidence for e.g. the association within a specific profession.

Edit:Note* It appears the the function to calculate Cramer's V works correctly.

Edit: Answer to Question 1: The Cramer's V statistic doesn't show direction. On a 2 x 2 table, phi shows direction with positive or negative sign, but directionality doesn't make much sense in a larger table of nominal categories.

There is no absolute interpretation of an effect size statistic like Cramer's V. It is always relative to the discipline and the expectations of the experiment. For a couple of points about this, see the comments to my answer at this link. That being said, the interpretations from Cohen 1988 are often used as typical interpretations. There is a table of interpretations here.

Edit: Answer to Question 2: To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

It doesn't make much sense to use the omnibus Cramer's V statistic as evidence for e.g. the association within a specific profession.

Edit:Note It appears that the function to calculate Cramer's V works correctly.

Edit: Answer to Question 2: To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

Edit: Probably no longer relevant with the updated question: Normally for the omnibus test you would calculate a single Cramer's V statistic as an effect size measure. I don't know Python, so I can't tell if you are intentionally calculating a statistic for each Profession or not. And if so, if you doing so correctly. What is helpful here is if you could post a table of counts (not based on random number generation), that all readers could look at.

Edit: Answer to Question 1: The Cramer's V statistic doesn't show direction. On a 2 x 2 table, phi shows direction with positive or negative sign, but directionality doesn't make much sense in a larger table of nominal categories.

There is no absolute interpretation of an effect size statistic like Cramer's V. It is always relative to the discipline and the expectations of the experiment. For a couple of points about this, see the comments to my answer at this link. That being said, the interpretations from Cohen 1988 are often used as typical interpretations. There is a table of interpretations here.

Edit: Answer to Question 2: To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

It doesn't make much sense to use the omnibus Cramer's V statistic as evidence for e.g. the association within a specific profession.

Edit:Note* It appears the the function to calculate Cramer's V works correctly.

Normally for the omnibus test you would calculate a single Cramer's V statistic as an effect size measure. I don't know Python, so I can't tell if you are intentionally calculating a statistic for each Profession or not. And if so, if you doing so correctly. What is helpful here is if you could post a table of counts (not based on random number generation), that all readers could look at.

To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

Edit: Answer to Question 2: To answer the question of which Profession is associated with which Hood, there a few approaches. One is to simply look at the percentage of counts within, say, each Profession. If Painter is 10% Uptown, 20% Downtown, and 70% Burbs, that is helpful information. Sometimes standardized residuals or odds ratio is used for this purpose. You could also break the table into smaller components, such as a 1 x 3 table for each profession, and look at p-value and effect size statistics for each. Graphical representation (spine plot, mosaic plot, bar plot) is also helpful.

Edit: Probably no longer relevant with the updated question: Normally for the omnibus test you would calculate a single Cramer's V statistic as an effect size measure. I don't know Python, so I can't tell if you are intentionally calculating a statistic for each Profession or not. And if so, if you doing so correctly. What is helpful here is if you could post a table of counts (not based on random number generation), that all readers could look at.