Understand and use the symbols: =, <, <<, >>, >, ∝, ~ (to include:…

The idea

In a Psychology paper these signs are the shorthand a result is reported in, so each one has to be read exactly. Each sign carries one meaning: = states exact equality, < states less than and > states greater than, while the doubled signs << and >> state much less than and much greater than. The sign ∝ marks a proportional relationship between two measures, and ~ marks an approximate or order of magnitude figure, as in a sample of ~ 30 people. The conventional way to report an inferential result is to set the probability against the accepted level, writing p < 0.05 for a significant result and p > 0.05 for one that is not. At the 0.05 level a psychologist accepts a five percent probability that the pattern arose by chance; the stricter 0.01 level cuts that to one percent and is chosen where a false claim would be costly, such as in drug trials.

What earns the marks

• Justifying a move to the 0.01 level where a Type 1 error would be serious, for instance in drug research, and noting that the stricter level raises the risk of a Type 2 error instead.
• Using the remaining signs accurately, so ∝ claims that one measure rises in direct proportion with another and ~ claims only an approximate or rounded size.

Common mistakes and how to put them right

• Reversing the sign and writing p > 0.05 for a significant result.

  Put it right: The probability of a chance finding has to be small, so the significant outcome is always the one where p falls below the stated level.

• Treating 0.05 as though it meant five, and writing the level as p < 5.

  Put it right: The probability runs from zero to one, so five percent is written as 0.05 and one percent as 0.01.

• Claiming that p < 0.05 proves the hypothesis, or that it shows a ninety five percent chance the theory is true.

  Put it right: It states only the probability that the results occurred by chance, and it proves nothing.

• Quoting a level of significance with no mention of the number of tails and no N or degrees of freedom, which leaves the marker unable to check that the right critical value was read.

Exam tips

• When explaining p < 0.05, include probability, the five-percent threshold and the decision about the null hypothesis, all tied to the variables in the study.
• When asked to state whether a result is significant, write one sentence in the conventional form: calculated value, critical value, tails, N or degrees of freedom, level, decision, then p < 0.05 or p > 0.05.
• Which way the comparison runs depends on the test. Chi Square, Spearman’s rho and both the related and unrelated t tests are significant when the calculated value is equal to or greater than the critical value; Mann Whitney U, Wilcoxon T and the sign test are significant when the calculated value is equal to or less than the critical value.