Sampling Techniques in Statistics: A Comprehensive Guide - Prof. Amri, Summaries of Statistics

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Chapter 1: Sampling

Lassad El Moubarki. Tunis Business School

October 3, 2022

Outline I

(^1) The questionnaire Definition Responses quantification Creating an online questionnaire by google (^2) Generalities about Sampling Sampling vs census Why sample? (^3) Probability sampling techniques Simple random sampling (SRS) Systematic sampling Sampling with probability proportional to the units size Stratified random sampling Cluster sampling Multistage sampling (^4) Non-probability methods

The questionnaire Definition

The questionnaire

A questionnaire is a research instrument consisting of a series of questions for the purpose of gathering information from respondents. Advantages They are cheap, do not require as much effort as for verbal surveys. Have standardized answers that make it simple to analyse. Disadvantages Standardized answers may frustrate users. Questionnaires are also sharply limited by the fact that respondents must be able to read the questions and respond to them. Thus, for some demographic groups conducting a survey by questionnaire may not be concrete.

The questionnaire Responses quantification

Types of responses

One of the more difficult skills in data analysis is deciding which statistical models and tests to use in a particular situation. The statistical model is often dependent on the type of the variable. Statistical variables can be classified as follow. Categorical (Qualitative) Categorical nominal. Example: Are you married? Categorical ordinal. Example: What is the mention of your baccalaureate? Quantitative (Numerical) Continuous: Responses are numbers that can be broken into finer and finer units. The set of possible numbers is large. Example: What is your height? Discrete: The set of possible numbers is finite. Example: How many child do you have?

The questionnaire Creating an online questionnaire by google

Rensis Likert Scale

A Likert scale is a psychometric scale commonly involved in research that employs questionnaires. It is widely used in marketing area. When responding to a Likert item, respondents specify their level of agreement or disagreement on a symmetric agree-disagree scale for a series of statements. Thus, the range captures the intensity of their feelings for a given item. A scale can be created as the simple sum or average of questionnaire responses over the set of individuals items (questions). In so doing, Likert scaling assumes distances between each choice (answer option) are equal. To give possibility for neutral answer, the number of choices must be odd.

The questionnaire Creating an online questionnaire by google

Example: Website user survey (source Wikipedia)

Generalities about Sampling Sampling vs census

Sampling vs census

Generalities about Sampling Why sample?

Why sample?

We need to sample when the census is unachievable or difficult to perform. Often, the census is: Expensive. Time consuming. Technically difficult to perform.

Generalities about Sampling Why sample?

0 500 1000 1500 2000

convergence en fonction de n

n

les estimations de p

Generalities about Sampling Why sample?

Probability vs non-probability sampling

Probability sampling is a sampling methods, wherein, all the subjects of the population get an opportunity to be in the sample. Non-probability sampling is a method of sampling wherein, it is not known if a given individual will be in the sample or not. In practice, we use the non-probability sampling methods when we do not have the list of all contacts or identifiers of population subjects (The frame).

Probability sampling techniques Simple random sampling (SRS)

Notations

Let: X : variable of interest N: population size n: sample size f : sampling rate X (^) n: the mean of the SRS sample Sn: standard error of X gotten from the SRS sample μ: the expected value of X Remark: When the variable of interest is binary of type yes or no (0 or 1) the problem will be an estimation of a proportion ˆp. In such case S n^2 = ˆp(1 − pˆ).

Probability sampling techniques Simple random sampling (SRS)

Confidence interval of an SRS sample

Confidence interval of level 1 − α of the SRS sample mean:

IC 1 −α(μ) = [X (^) n ± Z 1 −α/ 2 Sn

√ √^1 −f n ]^ without replacement IC 1 −α(μ) = [X (^) n ± Z 1 −α/ 2 √Snn ] with replacement IC 1 −α(μ) = [X (^) n ± ]

: prediction accuracy

Probability sampling techniques Simple random sampling (SRS)

Exercise 1

We wish to asses the monthly expenses of students at a university of 3, students. It is therefore decided to construct a sample of 200 students using the simple random sampling method. A computer randomly chooses 200 student names from a list of 3,000 names. These people will form the sample that represents the population. If Sn = 70 dinars and Xn = 110 dinars, find out the 95% (α = 5%) confidence interval of the mean. (knowing that Z 0. 975 = 1.96)

Probability sampling techniques Simple random sampling (SRS)

Solution for exercise 1

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