King Abdulaziz University Building 90A, Office 26F34 Department of StatisticsFaculty of Science Dr. Ali. Algarni

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Dr. Ali. Algarni

Department of Statistics Faculty of Science

Building 90A, Office 26F34 King Abdulaziz University

Web page: ahalgarni.kau.edu.sa Email: [email protected]

@Algarni, 2023, STAT-110

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Orientation Session

Welcome to STAT-110

• Coordinator : Dr. Ali Algarni

• Book

“Elementary Statistics A step by step Approach” by Bluman. Customized edition for the Department of Statistics at King Abdulaziz University.

• Syllabus and MegaStat from (ahalgarni.kau.edu.sa)

• Slides for each chapter (ahalgarni.kau.edu.sa)

• White Board Lectures (Classrooms)

• Eight Homework Assignments (10 Marks) (BlackBoard)

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Chapter 1: The Nature of Probability and Statistics

Objectives:

• Understand the meaning of Statistics.

• Differentiate between descriptive statistics and inferential statistics.

• Identify types of variables, and understand the nominal and ordinal measurement levels for qualitative variable.

• Identify the four basic sampling techniques.

• Understand the difference between an observational study and an experimental study.

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Overview of Chapter 1

Sec # Topics Page(s)

Introduction 2

1 -1 Descriptive and Inferential Statistics 3 -4

1 -2 Variables and Types of Data 6 -8

1 -3 Data Collection and Sampling Techniques 11 -16

1 -4 Experimental Designs 18 -19

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Introduction

Statistics is the science of conducting studies to :

 collect,

 organize,

 summarize,

 analyze and

 draw conclusions

from data.

(COSAD)

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Variable & Data

• A variable is a characteristic or attribute that can assume different values.

Example:

Gender is a characteristic in your class with takes only one value i.e. male so gender with reference to your class only is a constant. But if we study the gender of customers visiting Hyper panda then it is considered as variable.

Height is a characteristic in your class with can take different values so height is a variable.

• Data are the values (measurements or observations) that variables under study can assume. A collection of data is called a dataset.

Example: Ages of three students are 18,19,20. The different values here will

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Population and Sample

• A population consists of all subjects (human or otherwise) that are studied

• A sample is a subset/part of the population.

Population Sample

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Branches of Statistics

Descriptive statistics (Present or past)

Inferential statistics

Future (can be, will be)

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Descriptive Statistics

Descriptive statistics consists of collection, organization, summarization, and

presentation of data (COSP

⁾

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Inferential Statistics

Inferential statistics definition has 3 parts:

1. Generalizing from samples to populations,

2. Performing estimations and hypothesis tests(usage of probability)

3. Determining relationships among variables, and

making predictions

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Part of Example 1-1 (page 4)

Determine whether descriptive of inferential statistics were used:

• Based on a survey of 9317 consumers, the average amount the consumers spent on Eid Holidays in 2017 was SR 5000.

• Scientists at the University of Oxford found that a good laugh significantly raises a person’s pain level tolerance.

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Part of Example 1-1 (page 4)

Determine whether descriptive or inferential statistics were used:

• Based on a survey of 9317 consumers, the average amount the consumers spent on Eid Holidays in 2017 was SR 5000.

(Descriptive statistics- average based on a sample)

• Scientists at the University of Oxford found that a good laugh significantly raises a person’s pain level tolerance.

(Inferential statistics- inference from a sample to a population)

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1 –2: Variables and Types of Data

Variable

Qualitative (categorical)

Levels of measurement

Nominal Ordinal

Quantitative (numerical values)

Discrete (countable)

Continuous (measurements)

Levels of measurement

interval ratio

We will not study Interval and Ratio levels

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Part of Example 1 –2 (Page 7)

• Classify each of the following variables as discrete or continuous:

a. The number of pages in a statistics book (Discrete) b. The weight of baggage on an airplane (Continuous) c. Distance from your house to King Abdulaziz

University (Continuous)

(Students can also share their personal examples as well)

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Part of Example 1 –4 (page 9)

• What level of measurement would be used for each variable?

a. Colors of football team shirts (Nominal)

b. Ratings of movies released this month (Ordinal) c. Rankings of Players (Ordinal)

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Examples Nominal Variables

Jeddah 21589 Jeddah 24212

Gender Eye Color Zip codes Blood Group

Religion Nationality

Car Numbers

Skin Color

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Examples Ordinal Variables

gradesا

Qualificationا

ranking of players

stages of disease

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Examples Discrete Variables

Number of students in a class

Number of rooms in a house Number of CDs rented

Number of litres of petrol in your car (suggest an answer)????

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Examples Continuous Variables

Heights Weights Temperature

Speed

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1-3:Data Collection and Sampling Techniques

Collection of Data

Census

(Complete enumeration) Sample Surveys

All persons included Some persons included

Surveys are the most common method of collecting data

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1 –3: Data Collection and Sampling Techniques Common Survey Methods are :

• Telephone surveys.

• Mailed (emailed) questionnaire surveys.

• Personal interview surveys.

• Surveying records.

• Direct observation of situations.

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Sampling Techniques

 Random Sampling

 Stratified Sampling – divide population into

“layers”

 Cluster Sampling– use intact groups

 Systematic Sampling – every k

^th

subject

How the sample is selected for survey?

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Random Sample

A random sample is a sample in which all members of the population have an equal chance to be selected.

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Systematic Sampling

• A systematic sample is a sample obtained by selecting every k^th member of the population where k is a counting number.

• Note: This type of sampling involves a random start and then proceeds with the selection process mentioned above.

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Stratified Sampling

• A stratified sample is a sample obtained by dividing the population into strata according to some characteristic relevant to the study.

Then subjects are randomly selected from each stratum.

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Cluster Sampling

• A cluster sample is obtained by dividing the population into clusters and then selecting one or more cluster and using all members in the cluster(s) as the members of the sample.

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Example 1 –5: Sampling Method(page 16)

• The subscribers to a magazine are numbered. Then a

sample of these people is selected using random numbers.

(Random Sampling)

• Every 10thbottle of Cola is selected, and the amount of liquid in the bottle is measured. The purpose is to see if the machines that fill the bottles are working properly.

(Systematic Sampling)

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Example 1 –5: Sampling Method(page 16)

State which sampling method was used.

a. A researcher divides a group of students according to gender. Then he randomly selects six students from each group to answer questions from survey.

(StratifiedSampling)

b. If all schools in Jeddah are divided into 4 groups on the basis of (North, East, West, South) regions. All teachers from a region are selected for interviews.

(Cluster Sampling)

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1 –4: Experimental Designs

• In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.

• In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

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Variables in Observational & Experimental studies

Studies usually include one or more independent variables and one dependent variable.

Independent Variable: is the one that is being manipulated by the researcher. Also called an Explanatory variable.

Dependent Variable: is the resultant variable. Also called an

Outcome variable.

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Practice Example for Observational and Experimental Studies.

• A teacher divides his students into two groups A and B. He adopts different teaching methodology for each group. For group A he only gives lectures on white board and for group B he also used overhead projector. After 4 months he compares the performance of both groups.

a. Is it observational or experimental study?

b. Which is the independent variable in the study?

c. Which is the dependent variable in the study?

d. Which variable can the teacher manipulate?