Hypothesis testing

Null hypothesis Alternative (experimental) hypothesis

Example Der Mann, der dich gesehen hat.21 Der Mann, den du gesehen hast.6 Der Film, der dir gefallen hat.12 Der Film, den du gesehen hast.17 Null hypothesis: There is no relationship between the animacy of the head noun and the syntactic role of the relative pronoun. Alternative hypothesis: There is a relationship between the animacy of the head noun and the syntactic role of the relative pronoun.

PopulationSample

AnimateInanimate Subject50 Object50 AnimateInanimate Subject2112 Object617

Statistical tests determines the probability that the relationship we observe has arisen from sample error. If that probability is very low (i.e. > 5%), we can reject the null hypothesis, i.e. the hypothesis that there is no relationship between variables. Statistical hypothesis testing does not prove that the (explanation for the) alternative hypothesis.

p-value The p-value indicates that, given that there is no relationship between x and y, what is the probability that we obtain the distribution in our sample. If there is no relationship (correlation) between X and Y in the true population, then there is a less than 5% chance (i.e. 1 out of 20 chance) that there is a correlation in the sample. The p-value is a conditional probability.

p-value P = What does that mean? The probability of the null hypothesis to be true is 5%. False Given that the null hypothesis is true, there is a 5% chance of obtaining the distribution in the given sample. Correct The probability of the alternative hypothesis to be true is 95%. False

Type 1 and type 2 errors Type 1 error: The p-value is significant (p <.05) and you reject the null hypothesis although there is no correlation between X and Y. Type 2 error: The p-value is not significant (p >.05) and you accept the null hypothesis although there is a difference between X and Y.

The p-value indicates the probability of making a type 1 error. It does not say anything about the probability of a type 2 error occurring. While a type 2 error is as fatal as a type 1 error, in practice it is less dramatic. Why? Type 1 and type 2 errors If p > 0.05 and you accept the null-hypothesis, it is not automatically assumed that there is no correlation (or difference) between conditions. Why? Because sample error is only one possible source for the non-significant p-value. Other sources: experimental design.

A researcher wants to find out if sex influences language development during childhood. He has collected MLU values from a group of 3 year-old boys and 3 year-old girls. – State the hypotheses. One-tailed and two-tailed tests Sex does not influence development (i.e. MLU). Sex influences development (i.e. MLU) Girls have a higher MLU. Boys have a higher MLU.

One-tailed and two-tailed tests

Statistical measures p-value Confidence intervals Effect size