What is PHI in Chi-Square?

Phi is a chi-square based measure of association. The chi-square coefficient depends on the strength of the relationship and sample size. Phi eliminates sample size by dividing chi-square by n, the sample size, and taking the square root.

What does a negative phi coefficient mean?

The phi coefficient ranges from −1 to +1, with negative numbers representing negative relationships, zero representing no relationship, and positive numbers representing positive relationships.

What information does the phi coefficient provide and under what circumstances should it be used?

The Phi Coefficient is used to understand the strength of the relationship between two variables. To use it, your variables of interest should be binary.

What does Phi Coefficient tell you?

The Phi Coefficient is a method for determining the strength of association between two categorical variables (e.g., sex, ethnicity, occupation), each of which is or is measured as binary, that is, they only have two groups (male/female or employed/unemployed).

How do you interpret phi coefficients?

The interpretation for the phi coefficient is similar to the Pearson Correlation Coefficient….The range is from -1 to 1, where:

  1. 0 is no relationship.
  2. 1 is a perfect positive relationship: most of your data falls along the diagonal cells.
  3. -1 is a perfect negative relationship: most of your data is not on the diagonal.

What is a strong phi coefficient?

The same rule of thumb can be used for the Phi coefficient. Note that these are “crude estimates” for interpreting strengths of relationships. r value = +.70 or higher. Very strong positive relationship.

What happens if PHI is negative?

Similar to a Pearson Correlation Coefficient, a Phi Coefficient takes on values between -1 and 1 where: -1 indicates a perfectly negative relationship between the two variables. 0 indicates no association between the two variables. 1 indicates a perfectly positive relationship between the two variables.

What does chi-square tell you SAS?

SAS Chi-Square test of Independence is used to determine if there is a significant relationship between two categorical variables. Chi-Square Testing independence determines whether two or more observations across two populations are dependent on each other (that is, whether one variable helps to estimate the other).

What is Phi Coefficient with example?

The phi coefficient is the product-moment correlation coefficient when both variables are coded (0, 1). For example, the phi coefficient could be used to examine the relationship between gender (male [0] and female [1]) and left- (0) or right-handedness (1).

Why do we use Phi Coefficient?

The Phi Coefficient provides a measure of the strength of association, which can also be used to test the statistical significance (with which that association can be distinguished from zero, or no-association).

What is the range of the phi coefficient?

The phi coefficient is a measure of association derived from the Pearson chi-square. The range of the phi coefficient is for tables. For tables larger than , the range is (Liebetrau, 1983 ). The phi coefficient is computed as

What is the relationship between the chi-squared and the phi coefficient?

The phi coefficient is related to the chi-squared statistic for a 2×2 contingency table (see Pearson’s chi-squared test) where n is the total number of observations.

What is the Pearson correlation coefficient and Phi coefficient?

Introduced by Karl Pearson, this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient.