Sampling and sampling distributions

What is a sample? Why study it?

SAMPLING- the method of gathering

information about a population by taking a representative of the population called sample

Can the data gathered from the sample be used to make

inferences about the population?

Statistically speaking, yes.

However, every sample has a different statistic. And this

statistic is also considered a random variable because the data vary from one sample to

another.

SAMPLING AND SAMPLING DISTRIBUTIONS

SAMPLING SAMPLING DISTRIBUTION OF STATISTIC

STATISTICS

PARAMETERS

NORMAL DISTRIBUTION

t DISTRIBUTION

SIMPLE RANDOM

SAMPLINGSYSTEMATICSAMPLINGSTRATIFIEDSAMPLINGCLUSTER

SAMPLING

is used to formulate

is done to generate

to approximate

may follow

is done using the methods

SAMPLING METHODS

1. Simple Random Sampling2. Systematic Random

Sampling3. Stratified Sampling4. Cluster Sampling

SIMPLE RANDOM SAMPLING

- involves selecting a sample size n from a population of size N so that all elements of the

population have equal chances of being part of the sample.

• lotteries• tables of random numbers• automatic random number

generator

SYSTEMATIC RANDOM SAMPLING

- involves using a random start to determine the first element

of the sample and the selection of the rest of the sample is

done systematically, i.e., every kth interval, where k = N/n.

STRATIFIEDSAMPLING

- involves dividing the population into groups called

STRATA according to some chosen classification category

such as age, gender, geographic location, and so on. Subsample from each stratum are selected by simple random

sampling.

CLUSTERSAMPLING

- the elements of the population are divided into groups called CLUSTERS.

Clusters are naturally occurring like barangays, cities, or

municipalities. Samples are obtained from each cluster by

SRS.

SLOVIN’S FORMULA- Used to calculate the sample

size n given the population size N and a margin of error e.

Slovin's formula is used when nothing about the

behavior of a population is known at all.

EXERCISESDetermine the sampling

method to be used in each scenario.

EXERCISESDetermine the sampling

method to be used in each scenario.

1. From a list containing the names of 500 members of an alumni association, a sample size of 50 is obtained by including every 10th person in the list in the sample.

2. The students in a given school are classified according to grade level. Twenty students from each group will be randomly chosen to participate in a study involving students’ study habits.

3. All the students who belong to ten chosen sections in a certain school will participate in a study designed to improve students’ critical thinking skills.

4. A researcher is interested in studying the effects of diet on the attention span of third-grade students in a large city. There are 1,500 third-graders attending the elementary schools in the city. The researcher selects 150 of these third-graders, 30 each in five different schools, as a sample for study.

5. An administrator in a large urban high school is interested in student opinions on a new counseling program in the district. There are six high schools and some 14,000 students in the district. From a master list of all students enrolled in the district schools, the administrator selects a sample of 1,400 students (350 from each of the four grades, 9–12) to whom he plans to mail a questionnaire asking their opinion of the program.

6. The principal of an elementary school wants to investigate the effectiveness of a new U.S. history textbook used by some of the teachers in the district. Out of a total of 22 teachers who are using the text, she selects a sample of 6. She plans to compare the achievement of the students in these teachers’ classes with those of another 6 teachers who are not using the text.

ACTIVITY

Using the members of your class as the population, use AGE as the quantitative variable of interest and obtain a sample size of 10 using the four sampling techniques. Calculate the sample mean age (statistics) of your data and compare it with the population mean (parameter). Do this by triads in a one whole piece of paper.

QUESTION: Which of the four sampling techniques produced statistics which is closest to the population parameters? farthest? What does this imply?