Presentation on theme: "Sampling and Basic Descriptive Statistics"— Presentation transcript:
1Sampling and Basic Descriptive Statistics Sampling and Basic Descriptive Statistics. Basic concepts and Techniques. Lecture 6 Leah Wild
2Overview Sampling In Quantitative Research Basic Descriptive Statistics And Graphical Representation Of DataQuantification, Variables And Levels Of Measurement
3Sampling In Quantitative Research Total PopulationRepresentative sampleProbability SamplingNon-Probability SamplingSample Size
4Total PopulationThe total collection of units, elements or individuals that you want to analyse.These can be countries, lab-rats, light bulbs, university students, banks, residents of a particular area, regional health authorities etc.The population for a study of infant health might be all children born in the U.K. in the 1980's.
5SampleA sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the larger group.Using example for study of infant health the sample might be all babies born on 7th May in any of the years.samples selected because the population is too large to study in its entirety.Important that the researcher carefully and completely defines the population, including a description of the members to be included
6Representative sample A sample whose characteristics correspond to, or reflect, those of the original population or reference populationTo ensure representativeness, the sample may be either completely random or stratified depending upon the conceptualized population and the sampling objective (i.e., upon the decision to be made).A thorny issue in the social sciences- is it possible to achieve?
7Probability Sampling A probability provides a quantitative description of the likely occurrence of a particular event.A probability sampling method is any method of sampling that uses some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen (Clark 2002: 37).
8Most Common Types of Probability Sampling Simple Random SamplingStratified Random SamplingSystematic Random SamplingCluster Or Multistage Sampling
9Simple Random Sampling where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen randomly and each member of the population has an equal chance of being included in the sample.Every possible sample of a given size has the same chance of selection; that is, each member of the population is equally likely to be chosen at any stage in the sampling process. (Easton & Mc Coll 2004).A lottery draw is a good example of simple random sampling. A sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.
10Stratified Random Sampling Often factors which divide up the population into sub-populations (groups / strata)measurement of interest may vary among the different sub-populations.This has to be accounted for when we select a sample from the population to ensure our sample is representative of the population.This is achieved by stratified sampling.A stratified sample is obtained by taking samples from each stratum or sub-group of a population.Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from these (Easton and Mc Coll 2004).
11Systematic Random Sampling Systematic sampling, sometimes called interval sampling, means that there is a gap, or interval, between each selection.Often used in industry, where an item is selected for testing from a production line (say, every fifteen minutes) to ensure that machines and equipment are working to specification.Alternatively, the manufacturer might decide to select every 20th item on a production line to test for defects and quality. This technique requires the first item to be selected at random as a starting point for testing and, thereafter, every 20th item is chosen. used when questioning people in surveys eg market researcher selecting every 10th person who enters a particular store, after selecting a person at random as a starting point;interviewing occupants of every 5th house in a street, after selecting a house at random as a starting point. If researcher wants to select a fixed size sample. In this case, it is first necessary to know the whole population size from which the sample is being selected. The appropriate sampling interval, I, is then calculated by dividing population size, N, by required sample size, n, as follows:If a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10,000, the sampling interval would be:I = N/n = 10,000/500 =20
12Cluster Or Multistage Sampling Cluster sampling is a sampling technique where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected. All observations in the selected clusters are included in the sample.every element should have a specified (equal) chance of being selected into the final sample.typically used when the researcher cannot get a complete list of the members of a population they wish to study but can get a complete list of groups or 'clusters' of the populationCheap, easy economical method of data collection.
13Non-Probability Sampling Main TypesConvenience/ opportunity/accidental sampling.Purposive/ judgemental samplingQuota samplingSnowball sampling
14Convenience/ opportunity/accidental sampling. volunteer samplesSometimes access through contacts or gatekeepers‘easy to reach’ population.
15Purposive/ judgemental sampling Involves selecting a group of people because they have particular traits that the researcher wants to studye.g. consumers of a particular product or service in some types of market researchMy own questionnaire research on ‘New-Age’ Travellers.
16Quota sampling widely used in opinion polls and market research. Interviewers given a quota of subjects of specified type to attempt to recruit.eg. an interviewer might be told to go out and select 20 male smokers and 20 female smokers so that they could interview them about their health and smoking behaviours .
17Snowball sampling Involves two main steps. Identify a few key individualsAsk these individuals to volunteer to distribute the questionnaire to people who know and fit the traits of the desired sample (e.g. my research on Travellers)
18Sample SizeIn general, the larger the sample size (selected with the use of probability techniques) the better. The more heterogeneous a population is on a variety of characteristics (e.g. race, age, sexual orientation, religion) then a larger sample is needed to reflect that diversity. (Papadopoulos 2003)Response rates vary on the type of surveys (e.g. mail surveys, telephone surveys). Response rates under 60 or 70 per cent may compromise the integrity of the random sample. (ibid)
19Basic Descriptive Statistics And Graphical Representation Of Data Can be divided into two typesDescriptive.InferentialSome authors suggest a third type ‘Associative’ (Downey 1975)
20Descriptive Statistics Statistics which describe attributes of a sample or population.includes measures of central tendency statistics (e.g., mean, median, mode), frequencies, percentages. minimum, maximum, and range for a data set, variance etc.organise and summarise a set of data
21Inferential Statistics Used to make inferences or judgments about a larger population based on the data collected from a small sample drawn from the population.Eg Exit polling used during US elections to determine how the population of voters votedA key component of inferential statistics is the calculation of statistical significance of a research finding.used to determine whether changes in a dependent variable are caused by an independent variable (Clark 2004)(HOMEWORK- WHAT ARE SOME OF THE PROBLEMS ASSOCIATED WITH THESE KIND OF STATISTICS?
22Quantification, Variables And Levels Of Measurement Rowntree (2000) distinguishes between category variables and quantity variables.Category variables can be nominal or ordinal.Quantity variables can be discrete or continuous.
23Examples: Nominal Data Type of BicycleMountain bike, road bike, chopper, folding,BMX.EthnicityWhite British, Afro-Caribbean, Asian, Chinese, other, etc. (note problems with these categories).Smoking statussmoker, non-smoker
24Ordinal Data A type of categorical data in which order is important. Class of degree-1st class, 2:1, 2:2, 3rd class, failDegree of illness- none, mild, moderate, acute, chronic.Opinion of students about stats classes-Very unhappy, unhappy, neutral, happy, ecstatic!
25Discrete Data Continuous Data Only certain values are possible (there are gaps between the possible values). Implies counting.Continuous DataTheoretically, with a fine enough measuring device. Implies counting.
26Relationships between Variables. (Source. Rowntree 2000: 33) QuantityCategoryContinuous(measuring)Discrete(counting)OrdinalNominalOrderedcategoriesRanks.
27Quantification, Variables And Levels Of Measurement Fielding and Gilbert (2000: 15) distinguish between four levels of measurement.NominalOrdinal.IntervalRatio.
28Interval and ratio variables According to Fielding & Gilbert (2000) these are often used interchangeably, and incorrectly by social scientists.(pg15)Interval, ordered categories, no inherent concept of zero (Clark 2004), we can calculate meaningful distance between categories, few real examples of interval variables in social sciences. (Fielding & Gilbert 2000:15)Ratio. A meaningful zero amount (eg income), possible to calculate ratios so also has the interval property (eg someone earning £20,000 earns twice as much as someone who earns £10,000).(ibid)Difference between interval and ratio usually not important for statistical analysis (ibid).
29Interval variables- Examples Fahrenheit temperature scale- Zero is arbitrary- 40 Degrees is not twice as hot as 20 degrees.IQ tests. No such thing as Zero IQ IQ not twice as intelligent as 60.Question- Can we assume that attitudinal data represents real, quantifiable measured categories? (ie. That ‘very happy’ is twice as happy as plain ‘happy’ or that ‘Very unhappy’ means no happiness at all). Statisticians not in agreement on this.
30Ratio variables-Examples Can be discrete or continuous data.The distance between any two adjacent units of measurement (intervals) is the same and there is a meaningful zero point (Papadopoulos 2001)Income- someone earning £20,000 earns twice as much as someone who earns £10,000.HeightUnemployment rate- measured as the number of jobseekers as a percentage of the labour force (ibid).
31IMPORTANT! SEE ‘TYPES OF DATA REVISION SLIDES’ ON MY WEBSITE FOR EXTRA INFORMATION ON TYPES OF DATA
32Frequencies and Distributions Frequency-A frequency is the number of times a value is observed in a distribution or the number of times a particular event occurs.Distribution-When the observed values are arranged in order they are called a rank order distribution or an array. Distributions demonstrate how the frequencies of observations are distributed across a range of values.
33Example Look at the distribution below: This distribution shows the recorded ages of patients receiving treatment for heart disease in the Stroud district. There are 50 observed values. We can easily see how often each value occurs. What is the frequency of the following values, 79; 81; 94? What is the range of this distribution?(r = h – l ). What is the mode? What is the median? From this distribution we can also tell that most of the values tend to cluster around the middle of the range.62646566687071727374757677787980818283858687888990929496
34Two elements to a distribution Scale with a number of values -(Usually arrange the scores from the highest to lowest).Corresponding observations- Tally up the scores, convert them into frequencies.
35Types of Distribution Frequency distribution Class Intervals Relative (Proportional or percentage distributions)Cumulative distributions.
36Frequency Distributions Shows number of cases having each of the attributes of a particular variable. Divided into two typesUngrouped distribution-scores not collapsed into categories, each score represented as a separate valuesGrouped distribution. Scores collapsed into categories so that several scores are presented together as a group. Groups usually referred to as a class interval.
37Relative (proportional or percentage) distributions The proportion of cases in the whole distribution observed at each score or value.
38Cumulative distribution. The number of cases up to and including the scale value. Can appear in grouped or ungrouped format.Cumulative relative distribution for any particular value is the the total up to, and including, that value