SIGNIFICANCE

BASIC IDEA

Statistical significance tells you if the relationship you observed in your (properly selected) sample is likely to hold up in the population. It is a probability that tells you the likelihood of obtaining a relationship this strong or even stronger just by chance if there was no relationship in the population. By "chance" means that when you selected your sample randomly (every element has an equal chance of being included) the selection may produce a misleading sample, that shows a relationship when there is none in the population.

Statistical significance, therefore, tells you if you can generalize your finding from your sample to your population.

Statistical significance has two components: 1 the strength of the relationship, 2 sample size. A relationship is more significant if the relationship is stronger or the sample size is larger (or both). Weak relationships are significant only in large samples.

In sociology the level of significance we usually employ as a divide between significant and non-significant findings is .05 (for smaller samples .10). A .05 significance level means that there is a 5% probability that the relationship we observe in our sample is due to chance.

Statistical significance is a technical term. It does not mean "significant" in the sense of "important."

To measure statistical significance of a relationship between two

where fo is the observed cell frequency and fe is the frequency expected in the same cell if the two variables were perfectly unrelated (statistically independent).

For a 2X2 table it looks like this:

The Observed Table with the Observed Frequencies

The "Expected"Table with the "Expected" Frequencies (i.e. the Frequencies One would Expect If There Were No Relationship Between the Two Variables

fe₁₁ = (fo₁₁+fo₁₂)*(fo₁₁+fo₂₁)/N

fe₁₂ = (fo₁₁+fo₁₂)*(fo₁₂+fo₂₂)/N

fe₂₁ = (fo₂₁+fo₁₁)*(fo₂₂+fo₂₁)/N

fe₂₂ = (fo₂₁+fo₂₂)*(fo₁₂+fo₂₂)/N

and N= fo₁₁+ fo₁₂+ fo₂₁ +fo₂₂

For an rxc table

fe₁₁ = S fo_1i*S fo_j1)/S fo_ij

fe₁₂ = S fo_1i*S fo_j2)/S fo_ij