28. Biostatistics II: t-distribution, confidence interval. Hypothesis testing: null-hypothesis, type-I and type-II errors. t-test for a single sample, for two samples, and for correlation.

Question 1

What is hypothesis testing?

Answer 1

methods used for deciding about the acceptance or rejection of a hypothesis.

Question 2

How to calculate a confidence interval?

Answer 2

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

→ This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence.

Question 3

What does it mean when confidence interval is 95%?

Answer 3

This means that from 100 arbitrarily chosen similar samples it may happen only 5 times that the corresponding confidence interval does not include expected value

Question 4

What s STUDENT’S t -TESTS?

Answer 4

statistical tests used for examining the hypothesis about the expected values of one or more variables of the normal distribution.

Question 5

The exact shape of the distribution depends ___

Answer 5

• On the distribution of the initial variable,
• n the parameter or statistical characteristic (it can be the correlation coefficient r as well) considered
• on the number of elements in the sample, or more exactly the degree of freedom.

Question 6

What is null hypothesis?

Answer 6

The initial hypothesis that needs to be tested and about which the decision will be made

→ E,g. the further sales of the medication cannot be banned, because the active ingredient content does not differ from the specified value (“presumption of innocence”, not guilty).

Question 7

What is An alternative hypothesis H₁ ?

Answer 7

An alternative hypothesis H₁must also be specified.H₁ is valid if the null hypothesis is rejected.

Question 8

What is one-tailed test?

Answer 8

The null hypothesis remains the same H₀:(µ - 􏰀􏰒􏰀µ₀ 􏰈= 0), but the alternative hypothesis is formulated as H₁:(µ - 􏰀􏰒􏰀µ₀ 􏰈> 0)

→ H₀ is rejected only if 􏰀 􏰒 􏰀µ - 􏰀􏰒􏰀µ₀ 􏰈< 0 .

→ This is called the one-tailed test (and a directional alternative hypothesis).

Question 9

What is two-tailed test?

Answer 9

if H₀:(µ - 􏰀􏰒􏰀µ₀ 􏰈= 0), then H1: (􏰀􏰒􏰀0 􏰢0). This statement is true in most of the

cases, hence H0 is rejected both if􏰀􏰒􏰀0 􏱁0and if 􏰀􏰒􏰀0 􏱀0.

Question 10

Main purpose of t-test

Answer 10

the measurable difference (in mean and initial expected value) and the standard error (characteristic of the random variations, standard deviation of the sampling distribution of means, sx ), need to be compared

→ Characterizes whether the data stand for rejecting or accepting the null hypothesis, thus it is the measure of the “strength” of the data (evidences).

→ By analogy of the judicial example, the goal of the prosecution is to increase t, and that of the defense is to decrease it.)

Question 11

What is DEGREE OF FREEDOM?

Answer 11

the number of independent members or sample elements.

→ Evidently, every element cannot be independent if there is a relationship between them.

→ By subtracting the number of related elements from the total sample size we obtain the degree of freedom, that is, the number of independently chosen elements.

Question 12

The calculated t_s value should be __ in principleif thereis no change, no deviation, no difference or no correlation

Answer 12

zero

Question 13

What is type I error?

Answer 13

The error of rejecting a null hypothesis when it is really true

→ The probability of the type I error is called the probability level of the statistical decision ( p-value), or, rarely, it is called the level of error.

Question 14

What is type II error?

Answer 14

if a false null hypothesis (about which we do not really know whether it is false) is accepted.

Question 15

General formula for 2 sample t-test

Answer 15