Hypothesis testing Hypothesis testing Null hypothesis Alternative experimental

Hypothesis testing

Hypothesis testing • Null hypothesis • Alternative (experimental) hypothesis

Example Der Mann, der dich gesehen hat. Der Mann, den du gesehen hast. Der Film, der dir gefallen hat. Der Film, den du gesehen hast. 21 6 12 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.

Population Sample

Animate Inanimate Subject 50 50 Object 50 50 Animate Inanimate Subject 21 12 Object 6 17

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 is a conditional probability. 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.

p-value P = 0. 05. What does that mean? The probability of the null hypothesis to be true is 5%. False The probability of the alternative hypothesis to be true is 95%. False Given that the null hypothesis is true, there is a 5% chance of obtaining the distribution in the given sample. Correct

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.

Type 1 and type 2 errors 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? 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.

One-tailed and two-tailed tests 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. • 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