Combining Probabilities Across Studies

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It is possible to combine the probabilities obtained from independent studies into one overall probability level. The formula is: χ² = -2Σ Ln(p).

The chi square ( χ²) is based on 2k degrees of freedom where k is the number of probabilities being combined. This test is typically conducted using one-tailed probability values.

Consider a researcher who conducted three experiments comparing an experimental and a control condition. None of the three studies revealed significant differences (one-tailed p's = 0.08, 0.21, and 0.11). Combining the three p's into one,

χ² = -2(-2.53 -1.56 - 2.21) = 12.6.

A Table of the Chi Square distribution can be used to find that the probability value for a chi square of 12.6 with 6 df is 0.0498.