Statistical tests for large sample size

1. STATISTICALANALYSIS 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(Ho)
STEP 2:Setting up of alternative hypothesis (H1)
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 (Zcal)
lies in acceptance region then Ho is accepted.
Otherwise Ho is rejected (H1 is accepted)
For two tailed test ,if –k < Zcal ≤ k then Ho is accepted
For left tailed test ,if Zcal ≥ -k ,then Ho is accepted
For right tailed test if Zcal ≤ k then Ho 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 x̅1 and x̅2 are sample means
σ1 and σ2 are population standard deviation
n1 and n2 are sample size