Counting Chi-Square Results Across 5% and 1% Thresholds

Summary

The document asks how to report counts of calculated chi-square values against two critical values: 3.84 for the 5% level and 6.64 for the 1% level. It gives an example with one count for values between the thresholds and another for values above the higher threshold, then asks whether the 5% count should include both groups. It does not include an answer or explain the underlying test assumptions.

Because values above the higher cutoff also exceed the lower cutoff, the thresholds define nested groups. Thus, a count for results significant at 5% should include all values greater than 3.84, including those also above 6.64; the 1% count is the subset exceeding 6.64. The interval between the cutoffs can be reported separately if useful, but it is not the total 5% count. This interpretation depends on using the appropriate chi-square critical values for the test's degrees of freedom and on the intended significance convention.

Key ideas

• The 1% threshold is higher than the 5% threshold, so results exceeding it also exceed the 5% cutoff.
• The total count above the 5% cutoff includes values in both the interval between cutoffs and the group above the higher cutoff.
• The count above the 1% cutoff is a subset of the 5% significant count.
• Counts between thresholds can be reported separately to distinguish the two significance bands.
• Critical values must match the test's degrees of freedom and significance convention.

Tags

# How to count [and report] the values of significance at 1% and 5%?


# How to count [and report] the values of significance at 1% and 5%?












I am slightly confused with this:

I have calculated the Chi square for the number of funds and the methods description tells me that if the values I have calculated are greater than 3.84 (6.64) that indicates the persistence at 5% (1%) confidence level.

What I have done next is:

I have used an excel formula to count the number of values >3.84 but <6.64 and then counted number of values that are >6.64.

So e.g. between the 3.84-6.64 I have 22 values but >6.64 I have 120 values.

My main question:

Is my counting correct? Shouldn't I rather calculate the number of values >3.84 for 5% [what in effect means 22+120) and report it as 142, and then report values >6.64 at 120 ?

Thank you

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.