Daily DAX : Day 277 CHISQ..DIST

 The **CHISQ.DIST** function in Power BI's DAX (Data Analysis Expressions) calculates the probability associated with the chi-squared distribution, which is commonly used in statistical analysis to test the independence of two variables or the goodness of fit of an observed distribution to an expected one. 

### Syntax

```

CHISQ.DIST(x, deg_freedom, cumulative)

```

- **x**: The value at which to evaluate the chi-squared distribution (must be non-negative).

- **deg_freedom**: The degrees of freedom (a positive integer).

- **cumulative**: A logical value (`TRUE` or `FALSE`):

  - `TRUE`: Returns the cumulative distribution function (CDF), giving the probability that a chi-squared random variable is less than or equal to `x`.

  - `FALSE`: Returns the probability density function (PDF), giving the probability density at `x`.

### Return Value

- A probability value between 0 and 1, representing either the cumulative probability (CDF) or the density (PDF) of the chi-squared distribution.

### Use Case

The **CHISQ.DIST** function is primarily used in statistical hypothesis testing, particularly in:

1. **Chi-Squared Test for Independence**: To determine if two categorical variables are independent by comparing observed and expected frequencies.

2. **Goodness of Fit Test**: To check if an observed distribution matches an expected theoretical distribution.

3. **Power BI Applications**: It’s useful in scenarios where you’re analyzing categorical data in Power BI, such as survey responses, customer segmentation, or quality control metrics, to compute p-values or probabilities for chi-squared tests.

### Example

Suppose you’re analyzing survey data in Power BI to test if customer satisfaction (categorical) is independent of product type (categorical). You calculate a chi-squared test statistic of 10.5 with 4 degrees of freedom. You want to find the p-value to determine if the result is statistically significant.

**DAX Formula**:

```dax

P_Value = CHISQ.DIST(10.5, 4, TRUE)

```

- **x = 10.5**: The chi-squared test statistic.

- **deg_freedom = 4**: Based on the number of categories in the data.

- **cumulative = TRUE**: To get the cumulative probability (p-value).

This formula returns the probability that a chi-squared random variable with 4 degrees of freedom is less than or equal to 10.5. If the result is low (e.g., < 0.05), it suggests the variables are not independent.

### Practical Example in Power BI

1. **Data Setup**: You have a table with observed and expected frequencies for a chi-squared test.

2. **Calculate Test Statistic**: Use DAX to compute the chi-squared statistic based on your data (e.g., `(Observed - Expected)^2 / Expected` summed across categories).

3. **Apply CHISQ.DIST**: Use the calculated statistic in `CHISQ.DIST` to compute the p-value.

4. **Interpretation**: Add the p-value to a report visual to assess statistical significance (e.g., p < 0.05 indicates significance).

### Notes

- **Non-negative x**: Ensure the input `x` is non-negative, as the chi-squared distribution is defined only for non-negative values.

- **Degrees of Freedom**: Must be a positive integer, typically derived from the number of categories minus 1 in your data.

- **Limitations**: If `x` is negative or `deg_freedom` is not a positive integer, the function returns an error.

For more complex chi-squared testing, you might combine **CHISQ.DIST** with other DAX functions or use it alongside Power BI’s statistical visuals to interpret results effectively. If you need to automate the chi-squared test, consider pre-calculating the test statistic in a measure before applying **CHISQ.DIST**.