SADC Course in Statistics

Tables and graphs for frequencies and summary statistics

Module I3 Sessions 10 to 12

Learning objectivesStudents should be able to:

• Produce multi-way tables • of counts and tables with the appropriate percentages

• Explain the criteria • that dictate how complex a table needs to be

• Produce tables for continuous variables• that include the appropriate summary statistics.

• Explain what the margins of a table are• and know when to include the margins in a table.

• “Drill-down” to examine the data• that have given rise to the elements of a table.

• Produce the charts • that correspond to a given table

Contents

• This presentation initially

• Review• Uses full demonstration “Describe data well”

• Practicals 1, 2 and 3:Counts and percentages• Practical 1 – on demonstration• Practical 2 – uses rice survey• Practical 3 – Survey on Principles of Official Statistics

• Presentation continued

• Practical 4: Summarising variates in tables

• Practical 5: Tables and graphs together• Using the Tanzania case study

Objectives from the rice survey

Simple objectives

Not so simple

objectives

Objectives for different types of variable

Factor, or category, or qualitative

variable

Two factors

Numeric or quantitative

variable

One numeric and one factor

Two numeric

Review and practicals 1 and 2

• Look at the demonstration• As a class or in pairs• Do practical 1 at the same time

• Then practical 2• Same ideas• Practice using Excel• Introduces a more complicated objectives (next slide)• To understand different percentages

• Then review these ideas

• Or continue with practical 3 first

Review of ideas

• Practical 1• Reminder of the steps in an analysis

• Practical 2• One-way and two-way tables• Which percentage is appropriate?

• Practical 3• Frequency tables in general• Tables with and without margins (“totals” in Excel)

How to describe data well• Look for oddities in the data

• and be prepared to adapt the summaries that you calculate

• Study the data as tables and graphs

• Use frequencies and percentages • to summarize categorical variables

• Use averages and measures of variability• to summarize numeric variables

• Identify any structure in the data• and use it in producing your summaries

Look at the data

The 2 types of variable are summarized in different ways

Simple summaries to meet simple objectives

Contents of these summaries

Summary of the yields

Does this summary

satisfy any of the

objectives?

In summary – for the simple objectives

Checking for oddities

What other suggestions

were made for coping with

outliers?

Answering more complicated objectives

AND explaining some of the variability

One-way and two-way tables

One way table – with 2 summary statistics

Two-way table

Margins of the table

The margins of a 2-way table are one-way tables

Percentages in tables

Consider carefully which percentage(s) are appropriate

Here “row” percentages compare types of country

Column percentages would compare where implemented

Sort of 2-way table?

Or one-way table with 9 summary statistics

This margin is meaningless – and should be hidden

Tables can be 3-way or higher

Excel gives all the totals

But is more limited in giving percentages

Practicals 4 and 5

• Practical 4• Rice survey again• Tables for numeric variables • As well as frequencies for factors

• Practical 5• Apply the ideas• To the data from Tanzania• Look at power used for lighting (factor)• At size of land holdings (numeric variate)• And at keeping indigenous chickens – both!

Tables that summarise variates as well

Objective: How do the yields relate to the variety grown?

More one-way tables: summary statistics

Also Lower s.d. for Variety than Village.

Why might that be important?

Summary statistics in 2-way tables

i.e. extends to objectives from those stated

How do the yields relate to fertilizer and variety?

Tanzania agriculture survey

• A huge survey of agriculture in Tanzania

• Involving about 1800 enumerators

• And a main questionnaire of 22 pages

• Given to 3223 households– In the district provided for analysis

• A technical report– Describes the process of data entry– And checking– Then there is the analysis – And reporting

Data for lighting

How large a table do you need?

Are these differences sufficiently large that you need this 2-way table?

If no, then the one-way presentation is simpler

If yes, then perhaps a one-way table/graph hides important information

One way table/graph

Objectives and many questions

• To help the extension service• Improve their service to households keeping chickens

• What proportion of households • keeps indigenous chickens?

• When they do, how many do they keep?

• Are these values roughly the same, • or do they differ by district?

• Do they differ by other factors, • in particular the sex of the household head • or the type of agriculture household (Q021).

Recap

• Now have the tools to process– Factors (categorical data)

• Using frequencies and percentages

– Variates (quantitative data)• Using means and medians• And quartiles, extremes, standard deviations• And proportions (risks), percentiles (return periods)

• You also know to use other measurements• to reduce the unexplained variation

• And the statistics can be presented • in tables and graphs

Good tables for Excel users – a guide

• A guide is provided• That summarises how to use tables in Excel• And can be used for reference

• It also introduces some additional topics

• where we need more than Excel• Other summaries in a table (e.g. medians)• Weights in tables• Multiple responses

• That are considered in the next sessions

Learning objectivesAre you now able to?:

• Produce multi-way tables • of counts and tables with the appropriate percentages

• Explain the criteria • that dictate how complex a table needs to be

• Produce tables for continuous variables• that include the appropriate summary statistics.

• Explain what the margins of a table are• and know when to include the margins in a table.

• “Drill-down” to examine the data• that have given rise to the elements of a table.

• Produce the charts • that correspond to a given table

In the next sessions we extend these analyses

To handle common problems that occur with many surveys