- Sample size should be neither too small nor too large, but rather an optimal size that adequately represents the population. It can be calculated using factors like availability of funds, time, nature of study, and sampling technique. - There are two main approaches to determining sample size: one based on precision and confidence level using formulas, and one based on Bayesian statistics. Effect size indicates how meaningful a relationship or group difference is, and can be small, medium, or large. It is calculated in various ways depending on the statistical test.

1. Presented by
Sarithra K
I-M.Sc Psychology
SAMPLE AND EFFECT SIZE

2. SAMPLE SIZE
What should be the size of the sample?”
• If the sample size is too small it may not serve to achieve the objectives
and if it is too large, we may incur huge cost and waste resources
• As a general rule the sample must be an optimum size.
• Technically, the sample size should be large enough to give a
confidence interval of desired width and as such the size of the sample
must be chosen by some logical process before sample is taken from
the universe.
• Size of the sample should be determined by a researcher keeping in
view the following points.

3. Nature of universe: Universe may be either homogenous or
heterogenous in nature. If the items of the universe are homogenous, a
small sample can serve the purpose. But if the items are heteogenous, a
large sample would be required. Technically, this can be termed as the
dispersion factor.
Number of classes proposed: If many class-groups are to be formed, a
large sample would be required because a small sample might not be
able to give a reasonable number of items in each class-group.
Nature of study: If items are to be intensively and continuously studied,
the sample should be small. For a general survey the size of the sample
should be large, but a small sample is considered appropriate in
technical surveys.

4. Type of sampling: Sampling technique plays an important part in
determining the size of the sample.
Availability of finance: Size of the sample depends upon the amount of
money available for the study purposes. This factor should be kept in
view while determining the size of sample for larger samples result
increasing the cost of sampling estimates.
Other considerations: Nature of units, size of the population, size of
questionnaire, availability of trained investigators, the conditions under
which the sample is being conducted, the time available for completion
of the study are a few other considerations to which a researcher must
pay attention while selecting the size of the sample.

5. There are two alternative approaches for determining the size of the
sample.
1. Approach based on precison rate and confidence level.
This approach is capable of giving a mathematical solution, and as such
is a frequently used technique of determining ‘n’. The limitation of this
technique is that it does not analyse the cost of gathering information
compared to the expected value of information.
B bbnnb Where, n- size of sample
z2- z-score for confidence level
σ2- standard deviation of population
e2- accepted error

6. 2. Approach based on bayesian statistics.
• This approach of detennining n'utilises Bayesian statistics and
as such is known as Bayesian approach. The procedure for
finding the optimal value of 'n' or the size of sample under this
approach.
• This approach is theoretically optimal, but it is seldom used
because of the difficulty involved in measuring the value of
information.

7. EFFECT SIZE
• Effect size tells you how meaningful the relationship between
variables or the difference between groups.
• According to Cohen’s criteria effect size can be categorized into
small, medium and large.
• Small effect sizes mean the difference is unimportant; medium
effect sizes means the difference is somewhat important large effect
sizes mean the difference is important.
• Effect size can be calculated in various ways. The American
Psychological Association (APA) Publication Manual lists 13
different effect size estimates that are commonly used. Now, we see
a couple of common approaches.

8. • Cohen's d is a common effect size calculation that looks at the difference
between the means of two groups and takes into account the variability, using
the pooled sample standard deviation.
Where, M1- mean of group 1
M2- mean of group 2 .
SDpooled- Single standard deviation to represent
all groups
• The above method is commonly used with a t test, but if you are investigating a
relationship between variables. You may calculate a correlation coefficient such
as pearson’s correlation coefficient. The correlation coefficient r tells you the
strength of the relationship between your variables.

9. • A related effect size calculation that is commonly used in analysis of
variance (ANOVA) is eta-squared. eta-squared is a calculation of
the proportion of the total variability of the dependent variable that
is accounted for by the independent variable. So, in an ANOVA, it is
calculated by dividing the treatment sum of squares by the total sum
of squares. It indicates the strength of the effect of the independent
variable on the dependent variable.
Where, SStreatment- Sum of squares
Cc ccccccvcvvvvv SStotal- Total no. of squares

10. Cramer’s v, which is suitable for the chi-square
test for independence.
Cohen’s w for chi-square goodness of fit.

12. Lets do with an example
A large study compared two weight loss methods with 13,000
participants in a control intervention group and 13,000 participants in an
experimental intervention group. The control group used scientifically
backed methods for weight loss, while the experimental group used a
new app-based method.
After six months, the mean weight loss (kg) for the experimental
intervention group (M = 10.6, SD = 6.7) was marginally higher than the
mean weight loss for the control intervention group (M = 10.5, SD = 6.8).
To calculate Cohen’s d for the weight loss study, you take the means of
both groups and the standard deviation of the control intervention
group.

13. M1- 10.6
M2- 10.5
SD- 6.8
d = 0.015
With a Cohen’s d of 0.015, there’s limited to no practical significance of
the finding that the experimental intervention was more successful than
the control intervention.

14. SUMMARY
• Sample size is neither too small nor large. It should be in optimum size.
Sample should represent our population. Sample size can be calculated in
various ways such as availability of money, time availability to complete
our study, nature of the study and sampling technique also plays an
important role to determine our sample size.
• There are some approaches that can determine our sample size such as
approach based on precision rate and confidence leveland Bayesian
statistics. By using formula we can calculate our sample size.
• Effect size tells about the how important the relationship between two
variables or difference between the group. Effect size can be categorized
into small, medium and large. It have some values.

15. • According to those values we can interpret whether the effect size is
large means it is important, if it is small means unimportant and it
is medium means somewhat important. Based on the effect size we
come to know that whether we can use for real world or not.
• Effect size can be calculated into various ways. If you want to know
the difference between two group mean we can use Cohen’s d
formula. If you want you know the relationship between variable
means you can use Pearson correlation coefficient. If you want to
test the ANOVA means you can use eta squared. If you want to test
the chi square means you can use Cohen’s w and Cramer’s v formula.
By substituting appropriate values we can get our effect size.

16. MCQ
1. Effect size can be categorized into ________ types
a) Two b) Three c) Four d) Nine
2. Choose the formula which is used to calculate the difference between
the means of two group_______
a) Cohen’s w b) Cohen’s d c) Cohen’s kappa d) Cramer’s v
3. What is ‘n’ denotes _______
a) Size of population b) Size of sample c) Sample mean
d) Standard deviation

17. 4. What should be the sample size_______
a) Small b) Optimum c) Large d) neither small nor large
5. Which formula is used to calculate the effect size of
ANOVA________
a) r² b) d c) n2 d) η2
5 MARK:
Write about sample size and any one of its approaches?
10 MARK:
Write a detailed note on effect size?

18. VIDEO PRESENTATION

19. REFERENCES
Evans, A. N&Rooney,B.J.(2008).Methods in psychological
research . Sage publications.
Kothari,C.R.,&Garg,G. (2019).Research methodology methods
and techniques(4th ed.).New age international publishers.
(Original work published 1985).
Bhandari, P. (2023, June 22). What is Effect Size and Why Does It
Matter? (Examples). Scribbr. Retrieved August 12, 2023, from
https://www.scribbr.com/statistics/effect-size/

20. THANK YOU