chapter 2 - collection of data

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Tuesday 6th January 2009 Objectives: ·To learn and know the different types of data: quantitative qualitative continuous discrete categorical ranking interval scale ratio scale bivariate scale primary secondary data from experiments and surveys explanatory/response variables

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To obtain data we must observe or measure something. This something is known as a variable. e.g. shoe size, height and eye colour. QUANTITATIVE variables have numerical measurements QUALITATIVE variables have non-numerical measurements CONTINUOUS DISCRETE data are measured on a scale and can take any value on that scale data are concerned with a number of countable values e.g. height e.g. shoe size

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CATEGORICAL DATA e.g. highest cost is ranked 1, and so on e.g. the age of racehorses e.g. one unit of length along the scale might represent 10, two units represent 100, three units 1000, etc. e.g. the price of a car and the age of the car the heights and weights of a group of people According to the rules all racehorses become officially a year older on 1 January each year. Horses are known as 1 year olds, 2 year olds, but 3 year old horses could have real ages from 3 years to nearly 4 years.

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PRIMARY OR SECONDARY DATA Data that is collected by or for the person who is going to use it is called primary data Data that is not collected by or for the person who will use it is called secondary data e.g. if you collect the birth dates of your class by asking each student e.g. if you collect the birth dates by looking at the school records ADVANTAGES AND DISADVANTAGES

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Experiments and surveys Data can be collected using an experiment or a survey. In a statistical experiment, one of the variables will be controlled while its effect on the other variable is observed. The controlled variable is called the explanatory or independent variable. The effect being observed is called the response or dependent variable.

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Population & Sampling Learning Objectives: - To understand the difference between a population & a sample. - To understand the reason behind taking a random sample of a popluation. A population = everything / everybody that could possibly be involved in an investigation. If carrying out an investigation into the whole population, will need to collect/use census data. A sample is when you collect data about just part of the population, and use it to make conclusions about the whole population. If you take a sample, you always need to ensure it is free from bias. Wednesday 7th January 2009

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ADVANTAGES / DISADVANTAGES

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Randomness When taking a sample, you have to ensure that your sample is completely random, ie that every item in the population has an equal chance of being selected. Helps to avoid bias. Possible methods: 1. Use a table of random numbers. 2. Pick numbers / names out of a hat. 3. Use the random number generator on a calculator.

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Methods of Sampling Learning Objectives: - To understand the different methods of sampling that can be used, and the advantages / possible disadvantages of each. - Simple random sampling, Stratified sampling, Systematic sampling, Cluster sampling, Quota sampling, Convenience sampling, a combination of the above.

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Stratified sampling This is when the population is divided into strata / groups (by gender, age, earnings, etc), then a random sample is taken from each group, with the number from each group being in proportion to the relative size of their group. This method ensures a fair proportion of responses from each group is sampled. Example: A headteacher wants sample of 60 students. The proportion of the year groups is as follows:

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Quota Sampling Is most commonly used in market research. Instructions are given about the quota or number of each section of the population with certain characteristics (ie age) to be sampled. Is easy, but major disadvantage is the surveyor's decision re numbers could lead to bias. Once the NUMBER of people you wish to sample has been decided, you then need to consider the sampling method you will use.

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Method 1. Simple random sampling (discussed last lesson) - use a random number table, a random number generator on a scientific calculator / a computer, or pick names from a hat. Method 2. Systematic sampling - when items are chosen at regular intervals from an unordered list. So if 20 students wanted from a list of 100, will pick every 5th. The first one chosen will be picked using a random number (say 3), then pick the 3rd, 8th, 13th, etc. Is simple to use, used for very large populations, but not always truly representative. Method 3. Cluster sampling - the population is split into groups/clusters, the clusters to be sampled are then randomly chosen and every item in the group is looked at. Best to use lots of groups of small clusters - will be more representative. Method 4. Convenience sampling - when the most convenient sample is used, say the first 50 people in the register, coming out of a shop, etc. Very quick & easy, but can have loads of bias & will probably be unrepresentative.

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Monday 12th January 2009 Objectives: ·To know how to write appropriate questionnaires ·To recognise bad and good questionnaires

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A QUESTIONNAIRE IS A SET OF QUESTIONS DESIGNED TO OBTAIN DATA FROM A POPULATION Anyone who answers a questionnaire is called a respondent. Rule 1 - Questions must not be biased Rule 2 - Questions can give a choice of possible answers. There are are usually boxes to tick. Sometimes you can use groups for the boxes (CLOSED QUESTIONS) Rule 3 - Questions should not upset people Rule 4 - Questions should be clear Rule 5 - Questions should be relevant Rule 6 - Don't ask questions that allow people to give many different answers. (OPEN QUESTIONS) Rule 7 - Questions should be in a sensible order A pilot survey is a small scale replica of the survey or experiment that is to be carried out.

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EXPERIMENTAL DESIGN CAPTURE - RECAPTURE METHOD The capture-recapture method is used to estimate the size of a self-contained population. (Read through example p. 22) DATA LOGGING This is a mechanical or electronic method of collecting primary data. MATCHED PAIRS You use two groups to investigate the effect of a particular factor. You need to ensure that both groups to be tested have everything in common except the factor being tested or studied. Identical twins can be very important in these sorts of experiments.