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

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Published on 1 Dec 2011
School
Western University
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
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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
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