Can you please provide the Chi Squared formula given the helper formulas provided SELECT Bet = COUNT(*) OVER (), Collect = SUM(CASE WHEN Result = 1 THEN ([BetfairWinSP ] - 1) * 0.95 + 1 END) OVER (), Profit = SUM(CASE WHEN Result = 1
To calculate the Chi-Squared statistic using the provided helper calculations, you will need observed frequencies and expected frequencies for the categories of your data. The general formula for the Chi-Squared statistic (\( \chi^2 \)) is:
\[
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\]
Where:
- \( O_i \) = Observed frequency for category \( i \).
- \( E_i \) = Expected frequency for category \( i \).
### Given your context:
Assuming that:
- Your observed frequencies can be derived from the results of bets (where `Result = 1` indicates a win and another value indicates a loss).
- Expected frequencies could be calculated based on the proportion of wins and losses or based on a theoretical distribution.
### Using SQL to implement Chi-Squared calculation might look like this:
Assuming we have two categories (wins and losses) for simplicity:
1. **Calculate Observed Frequencies**:
- Wins (from your `Wins` calculation)
- Losses (Total bets - Wins)
2. **Calculate Expected Frequencies**:
- This could be a uniform distribution based on the total bets or a theoretical proportion based on prior data.
```sql
WITH BettingData AS (
SELECT
COUNT(*) OVER () AS TotalBets,
COUNT(CASE WHEN Result = 1 THEN 1 END) OVER () AS Wins,
COUNT(CASE WHEN Result <> 1 THEN 1 END) OVER () AS Losses
)
SELECT
(POWER(Wins - ExpectedWins, 2) / NULLIF(ExpectedWins, 0)) +
(POWER(Losses - ExpectedLosses, 2) / NULLIF(ExpectedLosses, 0)) AS ChiSquared
FROM
BettingData
CROSS JOIN (
SELECT
TotalBets / 2.0 AS ExpectedWins, -- e.g., assume equal distribution of wins and losses
TotalBets / 2.0 AS ExpectedLosses
FROM
BettingData
) AS Expected
```
### Explanation:
1. The `WITH BettingData AS` Common Table Expression (CTE) computes the total number of bets, the total number of wins, and infers the losses.
2. We simultaneously compute expected wins and losses using a simple hypothesis of equal distribution.
3. The final `SELECT` statement computes the Chi-Squared statistic based on the observed and expected frequencies derived from `BettingData` and the hypothetical expected values.
### Notes:
- Modify the logic of calculating `ExpectedWins` and `ExpectedLosses` based on your actual expected distribution.
- NULLIF is used to prevent division by zero.
- Ensure your categories match the expectations from your data (e.g., if multi-category then expand accordingly).
This formula serves as a suitable guide, but you should ensure that assumptions about expected distributions align with your specific analysis objectives.