1 Statistical concepts Module 1, Session 2

2 Objectives From this session participants will be able to: Define statistics Enter simple datasets once the data entry form is set up Recognise the type of each variable in a dataset Know some ways to summarise data of each main type Explain how statistical investigations deal with variability Differentiate between descriptive and inferential statistics

3 Activities 1. This introduction 2. Entry of the data from the CAST survey 3. Discussion/presentation on statistical concepts 1. Using the data entered 2. And other case studies 4. The statistical glossary 1. For when you need to remind yourself about terminology

4 What is statistics - 1? From RSS webpage: 1. Statistics changes numbers into information. 2. Statistics is the art and science of deciding: what are the appropriate data to collect, deciding how to collect them efficiently and then using them to give information, answer questions, draw inferences and make decisions.

5 What is statistics - 2? 3. Statistics is making decisions when there is uncertainty. We have to make decisions all the time, in everyday life, and as part of our jobs. Statistics helps us make better decisions. 4. Statistics is NOT just collecting a lot of numbers It is collecting numbers for a purpose

6 What is statistics - 3? From Wikipedia: 5. Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation and presentation of data. 6. Statistics are used for making informed decisions and misused for other reasons in all areas of business and government

7 What is statistics - 4? From the book “Statistics: A guide to the unknown”: 7. Statistics is the science of learning from data. Question 1 in the practical sheet From these 7 definitions – in the practical sheet either chose the one you think is most appropriate or make your own a) A one – line definition b) A longer definition

8 Data checking and entry – Question 2 What can we learn from the data you collected? Work in pairs or small groups First check the data from the CAST survey Check each others, not your own Is it legible? Can it be entered into the computer? Is the response to the open-ended question clear? Can the text be simplified? If there are many points, ask the respondent to state which are the most important 2 or 3. Brief notes (as a report) to be made to establish the data are ready for entry

9 Data entry into Excel Just type the number. The label is automatic

10 Data entry and checking – Question 3 The data are now entered This can be a class exercise on a single computer Data is entered by someone else for each respondent (never by themselves) Then it must be checked read it out check by reading back Put the record number from the Excel form on your original sheet or add your names as another field in the Excel sheet Why might it be better to just have a number?

11 Data entry and checking You should now have completed question 3 On the practical sheet How long to you estimate For 1000 records to be entered?

12 Once the data are entered Remember: “Statistics is the science of learning from data.” To learn as much as possible we must have confidence in the data so they must be entered and checked well This is what we have done in the groups Now the data are ready for the analysis Before that, look at some other data sets Look for the common points That apply to all the sets and look for differences

13 Types of data - 1 The analysis depends on the type of data What are the types in the CAST qusetionnaire? For questions 1 to 6 Your answer was one of 5 categories e.g. 1: Strongly agree, 2: Agree, … 5: Strongly disagree These categories have an ordering from strongly agree to strongly disagree This type of data are called categorical or factor or qualitative With the ordering, they are sometimes called ordered categorical data

14 Types of data - 2 The last question in the survey was a sentence or two that was written This is also an example of qualitative data It is an open-ended response These data can be reported and reporting the sentences can be very useful So it is good if they are entered as they stand To summarise perhaps the responses can be coded?

15 Coding open-ended questions – Question 4 This is question 4 in the practical sheet Looking at the responses in your groups Could you code them? What different codes would you have? How would you enter the codes? Might you lose anything by coding For a quick analysis Could you enter the complete texts And analyse the other columns And then code later? What might you lose by coding?

16 Coding and entering open- ended data Discuss the suggestions for the codes. If some points are made by many students then prepare a summary, how many as a frequency and as a percentage With the small number of responses there is no need to enter them into the computer But discuss how it could be done It is an example of a multiple response question because respondents may give no points or more than one point If you ask for the most important observation then it becomes a single qualitative response

17 Other data sets Zambia rainfall data Tanzania agriculture survey Look for the layout of the data is it the same as for the simple CAST survey? Look for the types of data Which are the qualitative variables? are they ordered? Which are the quantitative variables? which of them are discrete? and which are continuous? have any been coded to become qualitative?

18 Annual climatic data from Zambia

19 Survey data from Tanzania - 1

20 Survey data from Tanzania - 2

21 Discussion- Question 5 The layout of the data Was always the same! In a rectangle Each row is a record There are as many records (rows of data) as there were respondents, or students, or units Each column is a variable Variables can be qualitative or they can be quantitative Discuss which type they are For each data sets complete the tables in the practical sheet, question 5

22 Qualitative variables They are categorical They may be nominal, (which implies there is no ordering) Give some examples from the Tanzania survey They may be ordered – as in the CAST survey Give an ordered example from the Tanzania survey

23 Examples of analysis – Tanzania survey Question 6 There are 3223 records, but just take the 18 you can see in the figure Count the values for Q0123 – head of household There were 6 Females and 12 Males So 2/3 of the 18 households had a male head That’s about 70% but percentages are a bit misleading with so few numbers Now you give a similar summary for Q021 type of agricultural household And also Q3464 how often did the household have food problems

24 Add a simple chart A simple chart can also be sketched Here is one by Excel But a sketch can be “by hand” Excel will be used for these tasks from Session 3

25 Examples of analysis – CAST survey Question 7 Do a similar analysis of the CAST survey To make it quick each group could initially process just one question then report the results to the class Include a hand drawn chart Sketch a simple bar chart and include the numbers on the chart as shown earlier

26 Quantitative variables- Question 8 They may be discrete (whole numbers) Give examples from the climatic data And the Tanzania survey They may be (conceptually) continuous Give examples from the data sets Also they may be coded into (ordered) categories Give an example from the Tanzania survey

27 Examples of analysis – Tanzania survey An analysis of the 18 values in Q3462 The number of times meat was eaten last week minimum = 0 maximum = 5 adding the values: total = 31, so the mean = 31/18 about 1.7 times per week Note: the mean does not have to be an integer just because the individual values are whole numbers Repeat this analysis for Q3463 – times fish eaten last week and HHsize

28 Data analysis As the layout of the data is always the same Once you know how to analyse one data set You will have the principles to analyse them all And we have just done one analysis! You have seen that The appropriate analysis depends on the type of data So what are the principles of analysing (summarising) data of the different types?

29 The methods of analysis How many? are questions for qualitative variables for example the CAST survey, the Tanzania survey You used summaries Like counts, or proportions or percentages How large? How variable? are questions for quantitative variables for example the climatic data or the Tanzania survey We used summaries Like averages, extremes and measures of spread

30 A toolkit for analysis Different types of graph are also used Qualitative data “how many” Quantitative data how large how variable

31 Statistics and variation In the CAST survey - why not just ask one student? In the climatic data - why not just use one year? In the agriculture survey - why not just use one household? Because there is variation between the responses Remember this definition? “Statistics is making decisions when there is uncertainty.”

32 Variation is everywhere! In the book “Statistics a guide to the unknown” “Variation is everywhere. Individuals vary Repeated measurements on the same individual vary The science of statistics provides tools for dealing with variation” So statistics is concerned with making sense from data, when there is variation

33 Fighting the curse of variation To do good statistics you must tame variation fight the curse of variation You have 2 main strategies for overcoming variation 1. Take enough observations In the Tanzania survey there were 3223 households just from this one region 2. Measure characteristics that explain variation Variation itself is not necessarily the problem Variation you do not understand is the problem

34 An example: explaining variation Take the CAST survey Add a new record for an imaginary student Make it VERY DIFFERENT to the existing records So if most students were positive about CAST Then make this record very negative, etc You have added variation Now what could you (should you) have measured to explain this variation?

35 What you could have measured This little survey only asked about CAST It did not ask about you, e.g. male/female experience age computer access etc These measurements could help to understand the difference with this new student The Tanzania survey also asked about Education Possessions, etc Why – to be able to understand/explain variation

36 Analysis and variation together For statistical analysis you have: summarised columns of data i.e. summarised individual variables You did this for qualitative and quantitative variables To fight the curse of variation You take measurements So you add to the rows of data That helps you to explain the variation That’s statistics for you! You analyse the columns, i.e. the variables And you understand variability by looking at the rows

37 Types of statistics Wikepedia says roughly: Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modelled and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics.

38 Descriptive and inferential statistics We have just done descriptive statistics We will only do descriptive statistics in this module The sample in the Tanzania agricultural survey was 3223 households That’s just under 1% of the households in the region See the column called WT – with values like 137 So each observation “represents 137 households But with such a large sample The inferences for the whole region Will be quite precise So most of what we need now is descriptive tools In the later modules we add ideas of inferential statistics

39 Glossary of statistical terms Each subject becomes easier when you understand the terms A glossary is supplied Called the SSC Statistical Glossary It explains most of the terms For the 3 levels of this course So some terms may be new to you now An example is on the next slide You can print the glossary if you wish But it is good to look on-line Then all the terms in blue are links So you can easily move about in the document

40 Example from the glossary Descriptive statistics If you have a large set of data, then descriptive statistics provides graphical (e.g. boxplots) and numerical (e.g. summary tables, means, quartiles) ways to make sense of the data. The branch of statistics devoted to the exploration, summary and presentation of data is called descriptive statistics. If you need to do more than descriptive summaries and presentations it is to use the data to make inferences about some larger population. Inferential statistics is the branch of statistics devoted to making generalizations.

41 Learning objectives Can you now: Define statistics Enter simple datasets once the data entry form is set up Recognise the type of each variable in a dataset Know some ways to summarise data of each main type Explain how statistical investigations deal with variability Differentiate between descriptive and inferential statistics