DETERMINATION OF SAMPLE SIZE

A REVIEW OF STATISTICAL THEORY

BASIC CONCEPTS Descriptive statistics – Statistics used to

describe or summarize information about population or sample.

Inferential statistics – Statistics used to make inferences or judgment about population on the basis of sample.

BASIC CONCEPTS FREQUENCY DISTRIBUTION – A set of

data organized by summarizing the number of times a particular value of a variable occurs.

Amount (Rs.) fLess than 5000 50050001-10000 150010001-20000 70020001-30000 800Above 30000 600

BASIC CONCEPTS

Percentage distribution Probability distribution Proportion – The percentage of population

that successfully meet some criterion

CENTRAL TENDENCY MEAN – An important measure of central

tendency. Arithmetic average Mean = X / n = 311/4 =77.75

A B C D

Total

Marks 80 85 70 76 311

Name

CENTRAL TENDENCY MEDIAN – It is the mid-point of the distribution– the

value below which half of the values in a sample fall.

MODE– A measure of central tendency, the value

that occurs most often.

MEASURES OF DISPERSION RANGE – The distance between the

smallest and largest values of a frequency distribution. Range = L-S

STANDARD DEVIATION – A quantitative index of a distribution

spread or variability, the square root of the variance.

MEASURES OF DISPERSION Average deviation – A measure of

dispersion that is computed by calculating the deviation score of each observation value, summing up the deviation scores and dividing by the sample size.

Variance – A measure of variability or dispersion.

NORMAL DISTRIBUTION A symmetrical, bell-shaped distribution

that describes the expected probability distribution of many chance occurrences.

Z = X - µ / µ = hypothesized or expected value of mean

Population distribution & Sample distribution

Population distribution Sample distribution – A theoretical

probability distribution of all possible samples of a certain size drawn from a particular population.

Standard error of mean – The S.D of the sampling distribution of the mean.

SX = / n

CENTRAL LIMIT THEOREM The theory stating that as the sample size

increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

Confidence interval estimate – A specified range of numbers within which a population mean is expected to lie.

CONFIDENCE INTERVAL A percentage or decimal value that tells

how confident a researcher can be about being correct.It states the long run percentage of the time that a confidence interval will include the true population mean.

SAMPLE SIZE The factors determining the sample size

include – Variance / heterogeneity of the population Magnitude of acceptable error. Confidence level