Collecting data and sampling - created from Mind Map

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Introduction

Charts, diagrams and histograms are an attempt to represent information in a way that is easy to understand. The information that is gathered is generally called data.

The branch of maths that deals with collecting, presenting and analysing data is called statistics.

Types of data

Data which can be counted or measured is called numerical data because the answer is a number. Numerical data can be either discrete or continuous.

Discrete data:

data which can take only certain individual values is called discrete data.

e.g. The number of goals scored by football teams on a Saturday.

The number of desks in the classrooms of the school.

Continuous data

is measured on some scale and can take any value on that scale.

e.g. The heights of students in your class.

The speeds of cars passing a certain point on a road.

The time taken to complete a 100-metre sprint.

N.B. A variable is something that is measured or observed.

Categorical data

Data which fits into a group or category is called categorical data.

e.g. Gender (male or female)

Country of birth (Romania, Ireland, France)

Univariate data

When one item of information is collected, for example, from each member of a group of people, the data is called univariate data.

e.g. colour of eyes.

Bivariate data

Data that contains two items of information such as the height and the weight of a person is generally called paired data or bivariate data.

e.g. hours of study per week and marks scored in an examination.

Colour of hair and gender is an example bivariate categorical data.

Te number of rooms in a house and the number of children in the house is an example of bivariate dicrete data.

Collecting data

Data is collected for a variety of reasons from a variety of sources.

Data can be collected by carrying out a survey, doing an experiment or by doing interviews and completing questionnaires. Before you collect data, you need to have a clear aim in mind. You then need to decide what sort of data to collect and the most suitable and efficient method of collecting it.

The data you collect can be divided in two broad categories, namely, primary data and secondary data.

Primary data

Data that is collected by an organisation or an individual who is going to use it is called primary data.

Primary data is generally obtained:

by using a questionnaire

by carrying out an experiment

by investigations

by making observations and recording the results.

Secondary data

Data which is already available or has been collected by somebody else for a different purpose is called secondary data.

Secondary data is obtained:

from the internet

from published statistics and databases

from tables and charts in newspapers and magazines.

The advantages and disadvantages of both types of data are given below.

Surveys

Surveys are particularly useful for data that is likely to be personal.

The main survey methods are:

Postal survey in which people are asked questions.

Personal interviews in which people are asked questions; this type of survey is very widely used in marked research.

Telephone surveys; here the interview is conducted by phone.

Observation, which involves monitoring behaviour or information.

Experiments

Experiments are particularly useful for collecting scientific data. Drug companies carry out experiments to check if a new drug has any benefits or side-effects.

When you carry out an experiment you can use a data capture sheet to record your results.

Questionnaires

A questionnaire is a set of questions designed to obtain data from individuals.

People who answer questionnaires are called respondents.

There are two ways in which the questions can be asked:

An interviewer asks the questions and fills in the questionnaire.

People are given a questionnaire and asked to fill in the responses.

When you are writing questions for a questionnaire, you must:

be clear what you want to find out and what data you need.

ask short, simple questions.

start with simple questions to encourage the person who is giving the responses.

provide response boxes where possible, i.e. Yes or No.

avoid leading questions such as

"Don't you agree that there is too much sport on television?"

"Do you think that professional footballers are overpaid?"

avoid personal questions such as those which involve name, exact age or weight.

Multiple-response questionnaire

A question has multiple answers to choose from.

Opinion scales

If you use an opinion scale, responses tend to cluster around the middle of the scale as often people do not want to appear extreme.

One way to avoid a middle cluster is to provide an even number of options so that there is no middle choice.

Avoiding bias

When you are collecting data, you need to make sure that your survey or experiment is fair and avoids bias. If bias exists, the data collected might be unrepresentative.

N.B. Words like sometimes, occasionally and often are subjective.

Avoid using leading questions like "Normal people enjoy swimming. Do you enjoy swimming?", as it may cause the result to be biased. The first sentence should not be there.

Whenever you undertake a survey or experiment it is sensible to do a pilot survey. A pilot survey is one that is carried out on a very small scale to make sure the design and methods of the survey are likely to produce the information required.

It should identify any problems with the wording of questions and likely answers.

Sampling

In statistics a population is everything or everybody that could possibly be involved in a particular investigation or study.

When a population is too large for a study, we collect data or information from some of the population only.

In statistics this group is called a sample. The purpose of a sample is to collect data from some of the population and use it to draw conclusions about the whole population.

The size of a sample is important. If the sample is too small, the results may not be very reliable. If the sample is too large, the data may take a long time to collect and analyse.

Bias

The sample you select for your study is very important. If the sample is not properly selected, the results may be biased. If bias exists, the results will be distorted and so will not be representative of the population as a whole.

Bias in a sample may arise from any of the following:

Choosing a sample which is not representative.

e.g. Cara is doing a survey on people's attitude towards gambling. If she stands outside a casino and questions people as they enter or leave, the results will be biased as these people are already involved in gambling.

Not identifying the correct population.

e.g. The school principal wants to find out about students' attitudes to school uniforms. She questions 10 Leaving Certificate students only. This may lead to biased results as the opinions of the younger students (from 1st year to 5th year) are not included.

Failure to respond to a survey.

many people do not fill in responses to questionnaires sent through the post. Those who do respond may not be representattive of the population being surveyed.

Dishonest answers to questions.

Simple random sample

One of the ways to avoid bias in a survey is to take a simple random sample (or more commonly called a random sample).

In a random sample every member of the population being considered has an equal chance of being selected. Random samples need to be carefully chosen.

Methods for choosing a simple random sample could involve giving each member of the population an number and then selecting the numbers for the sample in one of these ways:

putting the numbers into a hat and then selecting however many you need for the sample

using a random number table

using a random number generator on your calculator or computer.

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