Descriptive Statistics

Outline of lecture

Purpose of descriptive statistics

Describing categorical variables

Frequency analysis

Describing continuous variables

Summary statistics

Measures of central tendency, variability and normality

Normal distribution

Relevant SPSS commands:

Descriptives, Compare means, Histograms, Explore

Next lab session

lbic.navitas.com

navitas.com

Objectives for today

Understand the importance of exploring the characteristics of your data before conducting the final analyses

Appreciate why categorical and continuous data require different kinds of descriptive analysis Identify and define key measures of:

Central tendency, Variability, Normality

Explore these data characteristics using various SPSS commands (next lab session) lbic.navitas.com navitas.com

Population and Sample

Population

A group of people: e.g. all students at Brunel, all employees in

Company A, all customers

A set of objects: e.g. all cars produced by Company A in 2012

Census

When data is gathered from the whole population

Sample

Subset of the population

Constraints

Time

Money

Availability of researchers lbic.navitas.com 4

navitas.com

Why do descriptive statistics?

What do we need to do before we run statistical tests that will provide conclusive answers to our research questions?

We need to get to know our data better

A summary or overview

lbic.navitas.com

What do descriptive statistics allow us to do?

Describe the general characteristics of the sample from which the data was collected (sample/group sizes, mean age etc.)

Check variables for violations in the assumptions underlying the statistical tests you intend navitas.com to use

Categorical variables

Examples of categorical variables?

Gender, nationality, marital status, grade, education level

Level of measurement?

Nominal and ordinal

It is usually valuable to know how many cases belong to each group as defined by your categorical variables

How many cases are there in each category group?

Most statistical tests require

roughly equal numbers of cases in each group at least 10 cases (but more = better) in all groups

...in order to produce reliable results lbic.navitas.com navitas.com

Categorical variables

Example research questions:

“Is the Product easy to use, attractive, etc?”, “Is website A better than website B?”, “Does working from home decrease productivity”, “Does stress increase customer defection?”

What was the relative proportion of males and females in your sample?

Demographic information is normally reported in the method section of your report

For e.g. If this is not 50/50 then is the sample representative of the population of interest?

You may need to collect more data

If the sample does not reflect the demographic structure of the target population

Or is otherwise unbalanced or group sizes are too small for analysis lbic.navitas.com

navitas.com

Categorical variables

In SPSS to obtain descriptive statistics for categorical variables, select:

Analyse > Descriptive

Statistics > Frequencies

Examining the frequency

table for the Gender category variable.

Comparing the groups may be

problematic in this case. Why?

lbic.navitas.com

navitas.com

Categorical variables

Frequency tables may also be sufficient to fully answer simple questions

e.g. Running a count on responses to a question:

“Which is your favourite social media platform?”

Could also provide a rank order of popularity

But no test of statistical ‘significance’

(simplistic) example: in a sample of 200, 99 males and

101 females said they use Twitter.

So, can we conclude that females use Twitter more than males? We’ll look at significance testing next session lbic.navitas.com navitas.com

Continuous variables

Continuous variables are scale level measures

e.g. Age, weight, height, time, test scores,…