Question

1-Explain the empirical rule in your own words. How many standard deviations would it take for you to consider a value to be statistically different?

2- Explain the four different types of sampling and give an example of each.

Answer 1

1. The empirical rule states that for a normal distribution, nearly all of the data falls within three standard deviations (SDs) of the mean. It states that:

68% of data fall within 1 SD from the mean; 95% fall within 2 SDs and 99.7% fall within 3 SDs.

And by Convention, it would take about 2 standard deviations to consider a value to be statistically different. (Commonly used significance level )

2. The 4 main types of sampling are as follows:

(i)Simple random sampling.
Simple random sampling refers to any sampling method for which, each element of the population of size N has an equal chance of being included in a sample of size n. Here, all possible samples of n objects are equally likely to occur.

The commonly used method for drawing a simple random sample involves Lottery method where, each of the N population members is assigned a unique number. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n numbers. Population members having the selected numbers are included in the sample.

(Or)

Use a random number table for drawing large samples.

(ii)Stratified sampling

With stratified sampling, the population is divided into groups, based on certain characteristics. Then, within each group, a probability sample (often a simple random sample) is selected. In stratified sampling, the groups are called strata.

For example, in a survey, we divide the population into groups or strata, based on geography, age, gender etc. and then within each stratum, we might randomly select survey respondents.

(iii) Cluster sampling.

With cluster sampling, every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed. (unlike in stratified sampling, where we had drawn sample from every strata)

(iv) Systematic random sampling.

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.