• 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 ( α alpha):
– 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.

• 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.

• 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: μ
1
= μ
2
This 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: μ
1
>= μ
2
It would be rejected only if the mean of population 1 was significantly less than that of population 2.

1. Formulate the hypotheses of the test (H0 and H1).
2. Collect data (i.e. take a random sample).
3. Declare your significance level (alpha).
4. Compute your test statistic and p-value.
5. Make a decision on the H0.

• 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.