False rejection of a true null hypothesis is due to?
Ans. is 'b' i.e., Type I error Statistical errors Statistical errors are used to describe possible errors made in statistical decision. Before reading about the types of error you must know null hypothesis because these tests are related to null hypothesis. Null hypothesis says - Any kind of difference or significance you see in a set of data is due to chance and not significant that means there is no variation (difference) exists between variables. Null hypothesis testing (e.g., in Chisquare test) is used to make a decision about whether : - i) The data contradict the null hypothesis - That means there is true difference (which is significant) between variables and it is not due to chance. Or ii) The data approve the null hypothesis There is no difference between variables and the difference you see is due to chance. Now see types of error :? There are two basic type of statistical errors : ? Type I error Type II error Type I error It is also known as an error of first kind or a-error or false positive. This type of error rejects null hypothesis when it is true - False rejection of null hypothesis. That means in real there is no difference (as null hypothesis says) but we observe a difference (by rejecting the null hypotesis due to error). In very simple words "we observe a difference when it is not true" - false positive. One of the simplest example of this would be if a test shows that a women is pregnant when in reality she is not, i.e., she is false positive for pregnancy. Probability of type-I error is given by 'P-value' (probability of declaring a significant difference when actually it is not present). Significance (a) level is the maximum tolerable probability of type I error. Significance (a) level is fixed in advance and calculation of P value (probability of type I error) can be less than, equal to or greater than the significance (a) level. If the probability of type I error (P -value) is less than significance (a) level, the results are declared statistically significant. Therefore, to declare the results statistical significant, type I error (a-level) should be kept to minimum . Type I error is more serious that type II error. Type II error It is also known as an error or second kind or A-error or false negative. This type of error accept/fail to reject the null hypothesis when it is false False acceptance of null hypothesis. That means we fail to observe a difference when in truth there is one - False negative. An example of this would be if a test shows that a woman is not pregnant when in reality she is i.e., she is false negative.
Type II error
Type I error
Beta error
Error of second kind