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QM Course Guide

Basic Concepts in Statistics

This video gives an introduction to some of the basic ideas you need to get started.

Descriptive and Inferential Statistics

 There are two major fields in statistics. QM starts with descriptive statistics then moves to inferential statistics.


Descriptive statistics

Inferential statistics

summarizes (describes) data

     from a sample

          using graphs and numbers

draws a conclusion (an inference)

     about a population

          based on data from a sample


  bar graphs


  mean and median

  standard deviation


  confidence intervals

  hypothesis tests

Populations and Samples

By collecting information from a representative sample, we can draw conclusions about a population.


  • the entire group of individuals we want information about
  • the complete set


  • the specific part of the group we get information from
  • a subset

Population parameter:

  • a number that describes a characteristic of a population
  • the number if fixed, but usually unknown

Sample statistic:

  • a number that describes the characteristic of a sample
  • we know what the number is, but it varies by sample

Variables, Types of Data, and Levels of Measurement

A variable’s level of measurement determines the type of graphs, measures of center and spread, and statistical tests that can be conducted.

An easy way to remember the levels of measurement is using the acronym N.O.I.R

Four levels of measurement


can only be grouped


can be measured





Categories with

no logical order

Categories with

a logical order

Zero is arbitrary

Zero actually means none

marital status

hair color


blood type

level of satisfaction (very low to very high)

education level (secondary to PhD)

temperature (F° or C°)

SAT scores


grade point average




cost of data plan

Sampling Methods and Techniques

Reliable data comes from a sample of individuals that accurately represents the population of interest.

Biased sampling methods (like convenience sampling or voluntary response sampling) may not produce a representative sample because some part of the population may be underrepresented or overrepresented.

To get unbiased samples, we choose a random sampling method, based on probability, that gives a representative, unbiased sample.

In this video we will be looking at the different methods of obtaining a sample.

adapted from: and

Sampling and non-sampling error

A sample statistic will never be a perfect representation of the population parameter—it is always an estimate.

There are two types of errors of possible errors: sampling and non-sampling.

We can measure sampling error by using the margin of error, or, how many points your sample statistic may differ from the true population parameter.

Errors when using a sample statistic to estimate a population parameter

Sampling errors

Non-sampling errors


how to reduce

possible causes

how to reduce

  • the fact that we only observe a part of the population
  • increase the sample size
  • use good sampling method
  • non-coverage
  • response error
  • non-response 
  • use all parts of population
  • construct clear questions
  • contact respondents multiple times 


This video summarizes why we use a probability sample and take a large sample to reduce sampling error.

Types of Statistical Studies

Experiments and observational studies are the main two types of statistical studies that social science researchers use.

In observational studies, we record the traits of individuals—we do not want to change their beliefs or behaviors. We want to describe a group or explore relationships between variables.

In experiments, we deliberately change a variable to see how it impacts other variables. We want to establish a cause-and-effect relationship.

Types of statistical studies

Observational studies



records characteristics of individuals with no intention of changing their beliefs or behaviors


intentionally manipulates one variable (the treatment) to see how it affects other variables

Good for:

describing populations

looking for association between variables

Good for:

establishing cause-and-effect relationships

There are three types of observational studies.




Case study


Gathers data from: a sample of a population

Gathers data from: every individual in a population

Gathers data from:

in-depth study of a few individuals


This video summarizes the main differences between an observational study and an experiment.


The objective of an experiment is to determine if the change in one variable (explanatory variable) causes change in another variable (response variable). This explanatory variable is called the treatment.

All other factors must be controlled so we know that the it is only the explanatory variable that is causing the change in the response variable.  So, we must eliminate any confounding, or lurking, variables that might also impact the response variable.

The placebo effect is another factor that can limit the effectiveness of a study. The placebo effect is when individuals believe that there they have experienced a change because they expected it by virtue of participating in the study.

To reduce the impact of confounding variables and the placebo effect, researchers do two things:

  • Create a control group, a group that does not receive the treatment and a treatment group that does
  • Randomly assign participants to the groups

In this video we will be talking about placebo effect, control groups and double-blind experiment.

Here is a diagram of a randomized, controlled experiment

An experiment is considered to be the “gold standard” in research, but many social research questions can only be answered using an observational study. How do you decide?

Measurement Errors

Measurement error is the difference between the observed (measured) value and the true value.

Two types of measurement error

Random error

Systematic error

Difference based on chance

Difference that is consistent

The measurement fluctuates: sometimes it’s higher than the true value and sometimes it’s lower.

The measurement is always higher or lower than the true value.

High precision: an instrument repeatedly produces the same measurement

High accuracy: the instrument represents what it purports to measure

For better precision:

take the average of repeated measures

For better accuracy:

improve measurement instrument

Precision vs accuracy

This video gives a clear example of the difference between accuracy and precision.

Other measurement errors in statistics

It’s important to recognize the types of measurement errors.

Measurement errors in statistics

Absolute error

Relative error

Percent error

Difference between the true value and the measured value

Size of the error relative to true value

Relative error shown as percentage

True value - measured value

Absolute error

  True value

Relative error  x 100

This video shows how to calculate absolute change and relative change using percentages.

Statistics Canada also has a useful guide to using percentages in statistics.

How to Evaluate the Trustworthiness of Statistical Studies

For tips on how to decide if a study is trustworthy, have a look at this webpage, Factors to Consider When Evaluating Statistics

For example:

Collection Methods & Completeness

  • How are the data collected? Count, measurement or estimation?
  • Even a reputable source and collection method can introduce bias. Crime data come from many sources, from victim reports to arrest records.
  • If a survey, what was the total population -- how does that compare to the size of the population it is supposed to represent?
  • If a survey, what methods used to select the population included, how was the total population sampled?
  • If a survey, what was the response rate?
  • What populations included? Excluded?