Variables, sampling, and sample size

Overview  Variables  Types of variables  Sampling  Types of samples  Why specific sampling methods are used

Variable  Anything which varies and can be measured  Variables differ according to definition  Categories __________  Continuous _________  Can you think of any examples ?  Specifically, variables represent persons or objects that can be manipulated, controlled, or merely measured for the sake of research.  Variation: How much a variable varies. Those with little variation are called constants.

Independent Variable  Independent: influences the dependent variable  more or less controlled.  researchers manipulate these variables  Often there are many in a given study.

Dependent variable  not controlled or manipulated, but are measured  These vary in relation to the independent variables, and while results can be predicted, the data is always measured.  There can be any number of dependent variables, but usually there is one to isolate reason for variation.

Independent V. Dependent  Intentionally manipulated  Controlled  Vary at known rate  Cause  Intentionally left alone  Measured  Vary at unknown rate  Effect

Measurement of variables  Nominal (qualitative, category or categorical variable)  Two or more named categories  Dichotomous – friend/anyone else  Multinominal – more than two

Quantitative variables  Numbers or values are assigned to each person or case represent increasing levels of variables  Social class – lower =1, middle = 2, upper = 3  Higher values = higher social class

Example Students of different ages were given the same jigsaw puzzle to put together. They were timed to see how long it took to complete the puzzle.

What was the independent variable?  Ages of the students  Different ages were tested by the scientist

What was the dependent variable?  The time taken to put the puzzle together  The time was observed and measured by the scientist

What was a controlled variable? Same puzzle  All of the participants were tested with the same puzzle.  It would not have been a fair test if some had an easy 30 piece puzzle and some had a harder 500 piece puzzle.

Universalism Is human behaviour the same ? For all people For all cultures For all societies Can Psychologists really make generalisations about human behaviour

Representative and Convenience samples How big should our sample be How should we pick our sample If done effectively both help psychologists to generalise their findings

How and Why Do Samples Work?  Sample a small collection of units taken from a larger collection.  Population a larger collection of units from which a sample is taken.  Random sample a sample drawn in which a random process is used to select units from a population  These are best to get an accurate representation of the population  But are difficult to conduct.

How and Why Do Samples Work?

Four Types Of Non-Random Samples  Convenience sampling (opportunistic)  Participants are picked due to availability  Does not include the whole population as potential participants  Stopping shoppers (not a true random sample!)  Quota sample  Pre-set categories that are characteristics of the population (gender / age) e.g st years (10 male – 10 female)

Four Types Of Non-Random Samples

 Purposive (Judgmental) sampling Researcher picks subjectively and tries to include a range between extremes.  Snowball (network) sampling Based on connections in a pre-existing network i.e. contact a few vegetarians, then ask if they know other vegetarians Four Types Of Non-Random Samples

Coming to Conclusions about Large Populations  Sampling element a case or unit of analysis of the population that can be selected for a sample.  Universe the broad group to whom you wish to generalize your theoretical results.  Population a collection of elements from which you draw a sample.

Coming to Conclusions about Large Populations  Target population the specific population that you used.  Sampling frame a specific list of sampling elements in the target population.  Population parameter any characteristic of the entire population that you estimate from a sample.

Coming to Conclusions about Large Populations  Sampling ratio the ratio of the sample size to the size of the target population.

 Why Use a Random Sample?  Representation.  mathematical or mechanical.  Allow calculation of probability of outcomes with great precision.  sampling ratio the ratio of the sample size to the size of the target population.  Sampling error the degree to which a sample deviates from a population. Coming to Conclusions about Large Populations

 Types of Random Samples  Simple Random Samples random number table or computer  Sampling distribution A plot of many random samples, with a sample characteristic across the bottom and the number of samples indicated along the side.

Coming to Conclusions about Large Populations  Types of Random Samples  Systematic Sampling  7000/100= 70 (every 70 th student on the list)  Rnd(70)= any number between 1-70  Every 70 th student after that

Coming to Conclusions about Large Populations  Types of Random Samples  Stratified Sampling  a type of random sampling in which a random sample is draw from multiple sampling frames, each for a part of the population.

Coming to Conclusions about Large Populations

 Types of Random Samples  Cluster (multi-stage) sampling a multi-stage sampling method, in which clusters are randomly sampled, then a random sample of elements is taken from sampled clusters. e.g.3 schools picked, 33 pupils randomly selected from each (cluster again – year groups)

Coming to Conclusions about Large Populations

Three Specialized Sampling Techniques  Random Digit Dialing Computer based random sampling of telephone numbers.  Within Household Samples Random sampling from within households.  Sampling Hidden Populations  Hidden Population A group that is very difficult to locate and may not want to be found, and therefore, are difficult to sample.

Inferences from A Sample to A Population  How to Reduce Sampling Errors  the larger the sample size, the smaller the sampling error.  the greater the homogeneity (or the less the diversity), the smaller its sampling error.  How Large Should My Sample Be?  the smaller the population, the bigger the sampling ratio must be for an accurate sample.  as populations increase to over 250,000, sample size no longer needs to increase.