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Statistical hypothesis testing – Inferential statistics I. What is hypothesis testing?. Hypothesis : a theoretical statement concerning a certain feature of the studied statistical population . We want to know if our hypotheses are true or not by doing research.
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What is hypothesis testing? • Hypothesis: a theoretical statement concerning a certain feature of the studied statistical population.We want to know if our hypotheses are true or not by doing research. • Hypothesis testing (or significance test): a procedure of assessing whether sample data is consistent with statements (hypotheses) made about the statistical population.Briefly, we make a decision about the hypothesis on the basis of our sample data.We want to get answers to questions starting typically like these: • „Is there a difference between…” • „Is there a relationship between…”
Types of hypotheses: • There are two kinds of hypothesis: • H1: the statement we actually want to test; usually postulates a non-zero difference or relationship (called ‘alternative hypothesis’)E.g: „The mean weight of males and females are different.” • H0: a statement which usually claims a zero difference or relationship against the H1 (called ‘null hypothesis’).E.g: „The mean weight of males and females are not different.” • Test statistic: • It is a numerical value calculated from our sample which forms a link between our sample and the null hypothesis.
Null distribution: • The probability distribution of a test statistic when the null hypothesis is true. • Null distribution of the test statistic is known by e.g. statistical computer programs. • p-value: • This is a probability indicating how likely to get a sample with such a test statistic like ours or with a more extreme one provided that the H0 is true. • p-value comes from the null distribution by contrasting the value of our test statistic with the null distribution. • The smaller the p-value the more unlikely the null hypothesis is true.
Significance level (αalpha): • It is an arbitrarily and a priori declared probability threshold. • If the p-value of the hypothesis test is less than or equals to alpha, then it is agreed that the null hypothesis will be rejected. • The value of alpha in the most biological research is 0.05.
Principle of hypothesis testing: • We have a link between the sample and the null hypothesis, this is the test statistic. • We know the probability distribution of the test statistic when the null hypothesis is true. • Contrasting our test statistic with the null distribution we will get a probability showing how typical this value of the test statistic of the null distribution. • If the probability we got is less than a threshold declared in advance, we will reject the null hypothesis and accept the alternative hypothesis, otherwise we accept the null hypothesis.
Errors in hypothesis testing • Type I error: • we reject H0 although that is true. • Denoted by α. Occurs only when H0 is true. • Pr(type I error) = p-value • Type II error: • we accept H0, although that is false. • Denoted by β. Occurs only when H0 is false.
One- and two-tailed tests(or One- and two-sided tests) • Two-tailed tests: a test in which H0 can be rejected by large deviations from expected in either direction.E.g:H0: the two population means are equal: μ1 = μ2This can be rejected if either population has a greater mean than the other. • One-tailed test: a test in which H0 is tested in a more specific way, it can be rejected by deviation only in one direction.E.g:H0: the mean of population 1 is greater or equal to the mean of population 2: μ1 >= μ2It would be rejected only if the mean of population 1 was significantly less than that of population 2.
Steps of hypothesis testing • Formulate the hypotheses of the test (H0 and H1). • Collect data (i.e. take a random sample). • Declare your significance level (alpha). • Compute your test statistic and p-value. • Make a decision on the H0.
Assumptions of statistical tests • Most of the statistical tests have clear assumptions on the data. • If these assumptions are not met the test can not be done, because it will give an incorrect result. • In this case you have to try an other test that is appropriate for your study design. • To get detailed knowledge on the concrete assumptions of the a certain test, consult a statistical text book.