Inferential Statistics

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Chapter 1 : Introduction

Learning goals
❖ What is meant by Statistics
❖ What is meant by Descriptive Statistics and Inferential Statistics ❖ Difference between Parameter & Statistic
❖ Types of Statistical Inferences

What is meant by Statistics ?
Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

Types of Statistics
Descriptive Statistics :
• Methods of organizing, summarizing, and presenting data in an informative way. Inferential Statistics:
• A decision, estimate, prediction, or generalization about a population, based on a sample.

Population versus Sample
• A population is a collection of all possible individuals, objects, or measurements of interest. • A sample is a portion, or part, of the population of interest

Parameter and Statistic
• A measure found from the entire population is called a population parameter or simply a parameter. (such as µ, σ, σ²) • A measure found from analysing sample data is called a sample statistic or simply a statistic (such as x¯, s¯, s²)

Types of Statistical Inferences
It refers to the process of selecting and using a sample statistic to draw inference about a population parameter Two types of inferences :
• Estimation : To use the ‘statistics’ obtained from the sample (such as sample mean & sample variance) as the ‘estimate’ of the unknown ‘parameter’ of the population (such as population mean and variance) • Tests of significance and hypotheses : To test hypothesis about the population

Chapter 2 : Sampling Process

Learning objectives
• Why Sample the Population ?
• What is sampling process ?
• What are sampling methods ?

Why Sample the Population?
• The physical impossibility of checking all items in the population. • The high cost of studying all the items in a population . • The sample results are usually adequate.
• Contacting the whole population would often be time-consuming. • The destructive nature of certain tests.

What is sampling process ?
• In order that the statistical inference be valid, samples must be chosen so as to be a true representative of the population i.e. there should be a proper sampling or sample selection process

• 7 steps
1. Define the population
2. Identify the sampling frame
3. Specify the sampling unit
4. Specify the sampling method
5. Determine the sample size
6. Specify the sampling plan
7. Select the sample

Probability sampling
• Simple random sampling
• Systematic random sampling
• Cluster sampling
• Stratified sampling
• Double sampling

Simple Random Sample
• A sample formulated so that each item or person in the population has the same chance of being included. • When the population is homogeneous
– N slips - shuffle - n to be drawn at random
– Random number tables (no in any row or column or diagonal selected at random)

Non probability sampling
• Convenience sampling
• Judgment sampling
• Quota sampling
• Snowball sampling

Determine the sample size
• The larger is the sample size, the lower is the likely error in generalizing to the population, but then amount of time and money invested in collecting, checking & analyzing the data will be more. The choice of sample size will be governed by the compromise between these two.

Sampling error
• The sampling error is the difference between a sample statistic and its corresponding population parameter.

Chapter 3 : Sampling distribution

Learning objectives
❖ What is sampling distribution
❖ Standard error of statistic
❖ Sampling distribution of sample mean
❖ When population has non-normal distribution
o Central limit theorem
❖ When population has normal distribution

What is sampling distribution
❖ It is a probability...
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