Course:MBASubject: Quantitative

Technique Unit :5

Population: a set which includes all measurements of interest to the researcher(The collection of all responses, measurements, or counts that are of interest)Sample:A subset of the population

Get information about large populations Less costs Less field time More accuracy i.e. Can Do A Better Job of

Data Collection When it’s impossible to study the whole

population

Target Population: The population to be studied/ to which the

investigator wants to generalize his results

Sampling Unit: smallest unit from which sample can be

selectedSampling frame List of all the sampling units from which

sample is drawnSampling schemeMethod of selecting sampling units from

sampling frame

Non-probability samples

Probability samples

Convenience samples (ease of access)sample is selected from elements of a

population that are easily accessible Snowball sampling (friend of friend….etc.) Purposive sampling (judgemental)

You chose who you think should be in the study

Quota sample

Probability of being chosen is unknownCheaper- but unable to generalisepotential for bias

Random sampling• Each subject has a known probability of

being selected Allows application of statistical

sampling theory to results to: • Generalise • Test hypotheses

Probability samples are the best

Ensure • Representativeness• Precision

Simple random sampling Systematic sampling Stratified sampling Multi-stage sampling Cluster sampling

Simple random sampling

6 8 4 2 5 7 9 5 4 1 2 5 6 3 2 1 4 05 8 2 0 3 2 1 5 4 7 8 5 9 6 2 0 2 4 3 6 2 3 3 3 2 5 4 7 8 9 1 2 0 3 2 59 8 5 2 6 3 0 1 7 4 2 4 5 0 3 6 8 6

Sampling fractionRatio between sample size and

population size

Systematic sampling

Systematic sampling

Cluster: a group of sampling units close to each other i.e. crowding together in the same area or neighborhood

Section 4

Section 5

Section 3

Section 2Section 1

Stratified sampling Multi-stage sampling

Systematic error (or bias) Inaccurate response (information bias)

Selection bias

Sampling error (random error)

Errors in sample

The probability of finding a difference with our sample compared to population, and there really isn’t one….

Known as the α (or “type 1 error”)

Usually set at 5% (or 0.05)

The probability of not finding a difference that actually exists between our sample compared to the population…

Known as the β (or “type 2 error”)

Power is (1- β) and is usually 80%

Sample size

Quantitative Qualitative

2D

2σ2Zn

2

22

21

D)xFσ(σn

2

2

Dπ)π(1Zn

2DF )P-(1 P 2n

Problem 1A study is to be performed to

determine a certain parameter in a community. From a previous study a sd of 46 was obtained.

If a sample error of up to 4 is to be accepted. How many subjects should be included in this study at 99% level of confidence?

881~3.88024

246 x 22.58n

2D

2σ2Zn

A study is to be done to determine effect of 2 drugs (A and B) on blood glucose level. From previous studies using those drugs, Sd of BGL of 8 and 12 g/dl were obtained respectively.

A significant level of 95% and a power of 90% is required to detect a mean difference between the two groups of 3 g/dl. How many subjects should be include in each group?

groupeachin

243~6.2423

)x10.512(8n 2

22

2

22

21

D)xFσ(σn

It was desired to estimate proportion of anaemic children in a certain preparatory school. In a similar study at another school a proportion of 30 % was detected.

Compute the minimal sample size required at a confidence limit of 95% and accepting a difference of up to 4% of the true population.

505~21.504(0.04)

0.3)0.3(1 x 1.96n 2

2

2

2

Dπ)π(1Zn

In previous studies, percentage of hypertensives among Diabetics was 70% and among non diabetics was 40% in a certain community.

A researcher wants to perform a comparative study for hypertension among diabetics and non-diabetics at a confidence limit 95% and power 80%, What is the minimal sample to be taken from each group with 4% accepted difference of true value?

2.24130.04

x7.80.55) -(1 0.55 x 2n 2

2DF )P-(1 P 2n

PrecisionCost

Fundamentals of Statistics by SC Guta Publisher Sultan Chand               

Quantitative Techniques in management by N.D. Vohra Publisher: Tata Mcgraw hill