Statistical analysis for large sample

Statistical tests for large sample size

1. STATISTICAL ANALYSIS FOR LARGE SAMPLE BY,NAVYA KINI H.

2. WHAT IS SAMPLE SIZE? A small part of a whole population is called sample. Sample  size determination is the act of choosing the number of observations or replicates to include in a statistical sample. Determination of sample size is very important in statistical analysis. Sample size varies from study to study, based on the complication of the topic.

3. WHY SAMPLE SIZE IS IMPORTANT? The major factor affecting the power of a study are the sample size A study should only be undertaken once there is a realistic chance that the study will yield useful information A study that has a sample size which is too small may produce inconclusive results and could also be considered unethical by exposing human subjects or lab animals to needless risk. A study that is too large will waste scarce resources and could expose more participants than necessary to any related risk. Thus an appropriate determination of the sample size used in a study is a crucial step in the design of a study.

4. What is large sample Test The tests based on large samples are called large sample tests. Here the tests are based on normal distribution because sampling distribution of large samples (n ≥ 30) approaches normal distribution

5. DIFFERENCE BETWEEN LARGE SAMPLE TEST AND SMALL SAMPLE TEST The test is based on sample size more than or equal to 30 is called large sample test For  large samples the sampling distributions of statistic are normal(Z test) The value of a statistic obtain from the sample can be taken as an estimate of the population parameter If the test is based on sample size below 30 is called as small sample test For small samples the sampling distributions are t, F and χ2 distribution. The value of a statistic obtain from the sample cannot be taken as an estimate of the population parameter

6. Z TEST STEP 1: Setting up of null hypothesis(H o ) STEP 2:Setting up of alternative hypothesis (H 1 ) It enables us to decide whether to use two tailed test or one tailed test (right or left ) tailed test STEP 3: Relavent statistic- Hypothetical value Standard error STEP 4: Depending on H1 and α , the critical table value k is chosen

7. Continued.. STEP 5:If the calculated value of the test statistic ( Z cal ) lies in acceptance region then Ho is accepted. Otherwise Ho is rejected (H1 is accepted) For two tailed test ,if –k < Z cal ≤ k then H o is accepted For left tailed test ,if Z cal ≥ -k ,then H o is accepted For right tailed test if Z cal ≤ k then H o is accepted α TABLE OF CRITICAL VALUES TWO TAILED TEST ONE TAILED TEST -K K Left (-k) Right (k) 5% -1.96 1.96 -1.65 1.65 1% -2.58 2.58 -2.33 2.33

8. TEST FOR POPULATION MEAN: Z = x̅ - µ σ  / √n Where x̅ is sample mean σ is population standard deviation µ is a given value of testing n is sample size

9. TEST FOR EQUALITY OF MEANS OF TWO POPULATION Where x̅ 1 and x̅ 2 are sample means σ 1 and σ 2 are population standard deviation n 1 and n 2 are sample size