# Statistical Sciences 2035 Lecture Notes - Random Number Table, Systematic Sampling, Ordinal Data

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Published on 1 Dec 2011

Department

Statistical Sciences

Course

Statistical Sciences 2035

Professor

Populations and Samples (section 1.1)

What is a population?

•It is a set of all units that you are interested in studying

•Units = people OR objects OR events

Examples

All undergraduates at UWO are about 26000.

All consumers who bought a cell phone last year.

Patients waiting in line for a family doctor.

You are usually interested in studying a certain characteristic of the population

•Any particular characteristic is called a variable

Examples

Height, weight, ago, textbook expenses

Cellphone age distribution, monthly usage, brand, satisfaction level

Two Types of Variables

1. Quantitative Variable

•This is a variable that is assigned a meaningful numerical value

E.G. Height, weight, income, waiting time

The types of quantitative variables:

i. Interval: The distances between points are fixed and meaningful.

ii. Ratio: When a variable has a meaningful zero and equal distances between points,.

2. Qualitative (Categorical) Variable

•This is a variable where the characteristic can assign to different categories

E.G. Brand of cellphone, monthly usage (high, medium, low), satisfaction level

i. A nominative variable is used for categorizing only and has no meaningful order.

ii. An ordinal variable is ranked in order that have more meaning than at the nominative level.

The levels of measurement in order from the simplest level of measurement to the most complex:

NOIR

NominativeOrdinalIntervalRatio

If we examine every unit of the population (for the variable of interest), we say we are conducting a census of

the population

•As you can imagine, many populations are too large to study

•It would be too time consuming OR too costly to conduct a census

Thus, it makes more sense to select and analyze a subset (or portion) of the population

This subset is called a sample

Once you have selected a sample from the population you wish to study, you will want to begin your analysis of

the data by first describing the sample data:

•Graph the sample data

•Calculate some numbers that summarize the data

Two Main Types of Analysis

1. Descriptive analysis

a) Population is known

b) Take a sample from the population

c) Using probability to assume how the sample should behave

2. Statistical inference

a) Population is unknown

b) Take a sample from the population.

c) Use the sample’s characteristics to infer (conclude) about the population

Sampling From A Population (section 1.2)

In order to be able to draw valid conclusions about a population, your sample needs to be taken in such a way

that it is representative of the population from which it is drawn

The best way to achieve this is by taking a random sample

Definition

A random sample (r.s.) is a sample of data that is selected so that each unit in the population is equally likely to

be chosen

You can sample with OR without replacement

With Replacement

After sampling a unit, you record the value of your variable, then return the unit back to the population (and

thus is can conceivably be chosen again on a succeeding selection)

Without Replacement

We do not place the unit chosen back into the population (this way, it can not be chosen again)

If the population is large (which it is in most situations), sampling without replacement will still give you a

“random” sample.

•Thus, most of the time, random sampling will be done without replacement

How Do You Select a Random Sample?

1. In theory, you would give every unit in your population a number

•Put the numbers in a “hat” or “bowl”

•Mix the numbers up

•Pull numbers out of the hat or bowl (mixing them up after each selection)

2. Use a random number table OR a computer program that has a random number generator

•Again, the units of the population need to be numbered (this creates a list that is called a frame)

•A random number table is a table of random numbers from 0 to 9, one after the other, row by row

•You can start anywhere in the table and move in any direction