Interferential statistics

1. Sampling Distribution, Standard
Error and Sample Size
Shital Bhandary
Assistant Professor
DCHS, PAHS-SOM

2. Review Preview
• Sampling distribution of means
• Standard Error of Mean
• Sample size and standard error

3. Objectives-1
Explain the concept of standard error:
– Describe a sampling distribution of means
– Define the standard error of the mean
– Discuss the use of the standard error of the mean
in relation to a sampling distribution of means.
– Identify other situations in which standard errors
are used

4. Sampling distribution of means
• Statistics uses samples to make inferences
about the population
• And It is always better to make inferences
using many sample (than taking a simple
sample) from the population under study (?)
• If many sample are taken then each sample
will have a mean (same or different)
• The distribution of such means is known as
“sampling distribution of means”

5. Mean, Variance and Standard
Deviation of Sampling Distribution

6. Central Limit Theory: Revisited
• It states that:
Given a population with a finite mean μ and a finite
non-zero variance σ2, the sampling distribution of
the mean approaches a normal distribution with a
mean of μ and a variance of σ2/N as N, the sample
size, increases.
• In other words, regardless of the shape of the
parent population, the sampling distribution
of the mean approaches a normal distribution
as N increases.

7. Sampling distribution w.r.t. sample size

8. Quick think!
• Why CLT is important?
– We need to take multiple samples to make our
sampling distribution normal
– We need increase our sample size to at least 30 -
50 samples to get a normally distributed data (for
a variable under study)

9. Why normal distribution is important?
• Normal distribution is most widely studied
and used “continuous probability distribution”
• It is the basis of many “parametric” statistical
tests: t-test, ANOVA, correlation, regression
etc.

10. N.B.
• We use the “standard error” along with the
“standard score” to calculate the minimum
sample size required for the study
• The “standard error” provides the theoretical lieu
for NOT taking multiple samples as it is actually
derived from the sampling distribution of means
• Yet, this minimum sample size is usually fulfilled
by taking multiple samples (e.g. clusters, stratas)
whenever possible

11. Quick Think!
• Can other statistic like proportion, median,
quartiles, skewness etc. can have standard
error?
• If yes, how can we interpret them?

12. Objectives-2
Describe how sample size affects standard error
– Identify the formula for the standard error of the
mean and use it to find the sample size
– Illustrate the relationship between sample size
and standard error
– Calculate sample size using proportions
– Discuss various methods used to calculate sample
size in medicine and health research (integrating
with the epidemiology, demography and other
disciplines)

13. Standard Error and Sample Size
• Two most commonly used sample size
determination are based on:
– Mean
– Proportion
• Both of them use standard error (why?)
• Both show that as N increase standard error
decreases and vice-versa (why?)

14. Review 1
• Sample size calculation using mean
• Key variable: Age at first marriage = 17.5 years
• Representative Population: Nepal
• Assumptions:
– age at first marriage follow a normal distribution
with larger sample size
– Level of significance = 5% = 0.05
– Margin of error = 1 – 5%
• Minimum sample size = ?

15. Review 2
• Sample size calculation using proportion
• Key variable: Childhood Overweight Prevalence =
4.5 %
• Representative Population: Nepal
• Assumptions:
– Childhood overweight prevalence follow a normal
distribution with larger sample size
– Level of significance = 1 – 5%
– Margin of error = 1 – 5%
• Minimum sample size = ?

16. N.B.
• We will come back to the concept of minimum
sample size many times
• Because we need to analyze the data in terms of
not only a single sample but also multiple
samples (and single variable with multiple
categories!)
• In multivariate analysis like regression analysis, it
is essential to know how many sample should
each variable MUST have during the modelling

17. Thank you!