Elementary Statistics and Computer Application

Sampling Error

Sampling Error

• From sample data, the statistic is computed and the parameter is estimated through the statistic. The difference between the parameter and the statistic is known as the sampling error.

Test of Significance

• Based on the sampling error the sampling distributions are derived. The observed results are then compared with the expected results on the basis of sampling distribution. If the difference between the observed and expected results is more than specified quantity of the standard error of the statistic, it is said to be significant at a specified probability level. The process up to this stage is known as test of significance.

Decision Errors

• By performing a test we make a decision on the hypothesis by accepting or rejecting the null hypothesis Ho. In the process we may make a correct decision on Ho or commit one of two kinds of error.
• We may reject Ho based on sample data when in fact it is true. This error in decisions is known as Type I error.
• We may accept Ho based on sample data when in fact it is not true. It is known as Type II error.
• Accept H_o Reject Ho
• Ho is true Correct Decision Type I error
• Ho is false Type II error Correct Decision
• The relationship between type I & type II errors is that if one increases the other will decrease.
• The probability of type I error is denoted by α. The probability of type II error is denoted by β. The correct decision of rejecting the null hypothesis when it is false is known as the power of the test. The probability of the power is given by 1-β.