Sample size

Sample size

is the number of observations in a sample (Evans et al., 2000),

Standard error

sampling distribution of sample means,

Sample size

is an estimation of the number of subjects required to detect an association of a given effect size and variability,

Type I

False positive

Type II

False negative

Miaoulis and Michener

(1976) argued that for research sample size calculation three critical components need to consider for the appropriateness they are required:

Level of precision, Level of confidence or risk, Degree of variability in attributes to be measured.

three critical components

statistical precision*

defined as the closeness between the calculated value and relevant population value*

Statistical precision

It is normally estimated by standard error in two ways: descriptively and inferentially

Descriptively

Precision can be estimate using standard error that is the difference between sample estimate and population parameters.

Inferentially

Standard error is commonly used in estimating the significance difference between or among parameter estimate

Confidence / risk level

the degree to which an assumption or number is likely to be true. • It is a statistical measure of the number of times out of 100 that results can be expected to be within a specified range

Degree of variability

is the distribution of attributes in the population

heterogeneous population

larger sample size is required for given precision

homogenous population

small sample size is sufficient to meet given precision level

Cochran (1963), Gupta and Kapoor (1970) and Israel et al. (1992)

They proposed four methods to determine the sample size for the research:

census method

the entire population as the sample: this method is suitable only when the population size is very small otherwise cost associated with this method is more. This method is very suitable for medical because of its accurate preciseness.

census method

This method is very suitable for medical because of its accurate preciseness.

Replicate a Sample size

If the researcher doing research in same field or domain and literature are available, replicate the sample size of similar studies.

Replicate a Sample size

The disadvantage of this method is the same error will carry forward from the previous research what we consider for sample size determination

APPLYING FORMULAS

Using formulas for a different combination of levels of precision, confidence and variability researcher can determine the sample size.

APPLYING FORMULAS

this method, the researcher can customize the sample size based on the precision and type of the research

Power analysis

Recent developments suggest that researchers should determine sample size through_____?

Power analysis

determines the minimum sample size by taking into account the part of a model with the largest number of predictorsIt requires information related to power, effect size, and significance level to calculate the minimum required sample size

Power analysis

It requires information related to power, effect size, and significance level to calculate the minimum required sample size

Power analysis

is a “statistic’s ability to correctly reject the null hypothesis when it is false”

(1-β error probability)

Signs of Power?

80 percent or more

A value of _________ or more represents an adequate level of power in social science research

Effect size

measures the magnitude of the effect that individual independent variables actually have on the dependent variableTo estimate sample size, it is necessary to know the extent of the effect in order to achieve statistical power of 80 percent or greater.

Effect size

To estimate sample size, it is necessary to know the extent of the effect in order to achieve statistical power of 80 percent or greater.

Effect size

As a general guideline, Cohen (1988) suggested that the values of 0.02, 0.15, and 0.35 be interpreted as small, medium, and large effects respectively.

0.02, 0.15, and 0.35

As a general guideline, Cohen (1988) suggested that the values of ____, _____, and, ______ be interpreted as small, medium, and large effects respectively.

Level of Significance

relates to the probability of rejecting the null hypothesis.

Level of significance*

(ὰ)?*

0.05 (5%)

social and behavioral science research, significance is generally accepted at?

0.01 (1%)

In medical research, significance is generally accept at?

preliminary survey

When 𝝈 is unknown, it is common practice to conduct a ___________ to determine 𝒔 and use it as an estimate of 𝝈. • Or use results from previous studies to obtain an estimate of 𝝈.

Estimating mean or ave

The sample size required to estimate population mean, 𝜇 , to with a level of confidence with specified margin of error given by

𝑛 ≥ (𝑍𝜎 / 𝑒)²

where 𝑍 is the z-score corresponding to level of confidence, and 𝑒 is the level of precision

Estimate mean /ave

When using this approach, the size of the sample should be at least 30

Estimating proportion (infinite population)

The sample size required to obtain a confidence interval for 𝑝 with specified margin of error, 𝑒, is given by

𝑛 ≥ (𝑍 / 𝑒)² 𝑝𝑞

where 𝑍 is the z-score corresponding to level of confidence, and 𝑒 is the level of precision, 𝑝 is the population proportion, and 𝑞 is 1 − 𝑝.

Yamane’s formula

(simplified form of proportions for finite population) is used to calculate the sample size 𝑛 given the population size and error.

𝑛 ≥ 𝑁 / 1 + 𝑁𝑒 2

where: 𝑁 is the total population, and 𝑒 is the level

Infinite population correction

The conservative formula using the strong law of large number:

𝑛 = 1 / 4 (𝑍 / 𝑒) ²

Finite population correction

If the population is small then the sample size can be reduced slightly:

n= n0 / 1+ n0−1 / N