Reduced chi-squared statistic
The reduced chi-squared statistic (also called the chi-squared test statistic) is used to tell us if our data matches a certain pattern. We use this statistic to determine if the data we have is likely to have happened by chance or by some other pattern. It's called "reduced" because it takes into account the number of observations we have in our data.
To calculate the reduced chi-squared statistic, we subtract the number of observations we have (n) from the number of parameters that describe our pattern (p). Then we use this new number (called df, degrees of freedom) to divide the chi-squared value we get from our data. This is called the reduced chi-squared statistic.
The reduced chi-squared statistic allows us to compare data to a pattern and tell if our data matches that pattern or not. If the reduced chi-squared statistic is lower than the predetermined value, then our data matches the pattern we tested. If the statistic is higher than the predetermined value, then our data does not match the pattern.
To calculate the reduced chi-squared statistic, we subtract the number of observations we have (n) from the number of parameters that describe our pattern (p). Then we use this new number (called df, degrees of freedom) to divide the chi-squared value we get from our data. This is called the reduced chi-squared statistic.
The reduced chi-squared statistic allows us to compare data to a pattern and tell if our data matches that pattern or not. If the reduced chi-squared statistic is lower than the predetermined value, then our data matches the pattern we tested. If the statistic is higher than the predetermined value, then our data does not match the pattern.