Lecture
The experimental hypothesis (EH) is placed under such conditions of testing that the chances of obtaining data both «for» and «against» are equal. To choose between the EH and the counter-hypothesis (CH), the results of statistical decisions (inferences) must be taken into account.
The level of statistical hypotheses is needed for the quantitative assessment of the probability of errors in making decisions about experimental facts.
Decisions about whether a significant difference between the DV indicators occurred, whether a significant relationship between the IV and the DV was established – that is, here there is no longer an assertion about the causal nature of the IV's influence.
Statistical hypotheses are hypotheses about the sample values of psychological indicators (indicators of the DV).
On their basis an assertion is made about accepting or rejecting the statistical null hypothesis, which makes it possible to return to the evaluation of the psychological hypotheses.
A distinction is drawn between the formulation of the null hypothesis H0 – as a hypothesis of the absence of differences between the values of a variable under different conditions (the absence of a relationship) – and directional hypotheses H1.
It is also necessary to distinguish between detected differences and actual differences.
Statistical decisions clarify the degree of confidence in the decisions concerning experimental facts.
Confidence finds formal expression in the significance level – p.
The significance level is chosen arbitrarily; it is connected with the assessment of the number of experiments or the size of the samples.
On the basis of the data, H0 may or may not be rejected, but it cannot be proved.
When a decision about H0 has been made, the next step is a return to the level of psychological hypotheses – to accepting the EH, the CH, or accepting neither of them.
H0 may be rejected with a certain probability of error (a Type I error, usually α=0.05).
If H0 was not rejected but is in fact false, this is a Type II error.
There are two traditions of testing statistical hypotheses:
1) The Fisher tradition. A decision about whether H0 is rejected is sufficient. Data from this point of view were regarded as testifying, or not, in favor of the EH. The use of this scheme is possible when the researcher knows little about the problem.
2) The Neyman–Pearson tradition. Type I and Type II errors are introduced, and the formulation of H1 presupposes a relationship opposite in direction to that of H0. Here one can make a choice between two opposing statistical hypotheses – H1 and H2. Here the CH may be formulated not simply as a negation of the EH but as an assertion about a new kind of relationship.
Transitions between the levels of hypotheses taking into account the old (Fisher) and new (Pearson) traditions.
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Levels of hypotheses |
Making a decision about the hypothesis |
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Empirical hypotheses |
The EH is accepted |
Neither hypothesis is accepted; a third is sought |
The CH is accepted |
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Statistical decisions (old tradition) |
Reject H0 at the significance level p=0.05 |
A choice between H0 and H1 cannot be made |
Do not reject H0 at the significance level p=0.05 |
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Statistical decisions (new) |
The effect corresponds to H1 (α=0.05) |
A choice between H1 and H2 cannot be made |
The effect corresponds to H2 (α=0.05) |
Popper's paradox: assertions about causal dependencies are evaluated probabilistically!
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