In reporting the results of a statistical test authors give degrees of freedom, an F statistic and a p-value.
1) As a reader, what am I to learn from the F statistic?
2) If I want to use a reported result in a meta-analysis is there a use for the F statistic?
3) Is the answer any different for a chi-square value, or a t value (t-test)?
Not sure if this is what you are after, but
1. F is the ratio of two variance estimates and is used in relation to the F distribution and can result from different statistical procedures. What you learn from it will depend on the test.
2. Meta-analyses usually use effect sizes. If given enough additional information, you can calculate effect sizes from test statistics like F. SInce in older papers people did not always report effect sizes (or report different ones than you want), you might have to do this.
3. t^2 is an F value where the F has 1 df in the numerator. If the denominator df is infinite (or in practice very large), F times the numerator df is Chi^2.
The p is the probability of observing an F this high, or higher, conditional on the null hypothesis being correct. For a less abstract interpretation, say how you are using the F statistic.
Hello Timothy,
I agree with Daniel Wright 's points, but would like to add to his second statement.
The reason that effect sizes (ESs) are the data points for meta-analyses is that they are independent of sample size, whereas statistical tests (t, F, chi-square, etc.) are dependent on sample size, effect size, and (of course) alpha level. A common critique of relying solely on statistical significance is that trivially small effects can be significant (given sufficient N) and enormous effects can fail to be declared statistically significant (because of too-small N). Furnishing confidence intervals for parameter estimates (even effect sizes!) can be a useful way of honestly declaring the precision with which anything is being estimated.
Obviously, the precision of an ES estimate does vary with N (bigger n = better precision, all else equal). But, we tend to take a wider view of ES values than "significant" vs. "non-significant," as is the case with hypothesis testing.
Finally, I suppose the value of including p-values for significance tests is that you, the reader, can apply your own alpha level to making judgments of whether an effect is statistically dependable or not. We needn't all dance to the .05 tune if it's not reasonable for our situation!
I am reviewing a manuscript wherein they have some large tables that take up an entire page. The tables are missing some data, in part because there is no room for more. The table gives a mean, a standard error, degrees of freedom, an F or chi-square value depending on if the variables are counts or measurements, and a p-value.
Thank you for your answers, they were helpful. While it would make things easier to remove the F values, it would seem like that is a mistake.
Re-phrasing your question, I am not sure what the p-values add to that table.
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