Sampling in Research Suter, Chapter 8

Questions about sampling Sample size – do I have enough participants? Is it the right kind of sample? Is it representative?

Questions about sampling Sample size – do I have enough participants? Is it the right kind of sample? Is it representative?

Describing Data Central Tendency –A characteristic of a distribution of scores that describes where scores tend to center. Often referred to as an average, the most common one being the mean (sum of scores divided by the number of scores) Dispersion –A characteristic of a distribution of scores that describes the spread or scatter of scores around the central tendency –Common measure of dispersion is the standard deviation ▫The higher the standard deviation, the greater the spread of scores around the mean

The Normal Curve Normal Curve – Bell Curve – Normal Distribution of Scores

Basic Descriptive Statistics Describing Central Tendencies of a Sample Mean Median Mode Describing the Variation of Scores Range Standard Deviation

Example of the Mode, Median and Mean in a Distribution Mode = 62 Median 64.5 Mean = 66.7 Range = 93 (98 -5) St Dev = 17.1

Calculation of the Standard Deviation of a Distribution √ Raw ScoreMeanX – X(X – X) Variance (SD 2 ) = Σ(X – X) 2 n = 364 a Standard deviation (SD) = Σ(X – X) 2 n

Percentiles Standardized test scores often accompanied by percentiles. Percentiles are a comparison with the whole group – a norming function – normalizing Related to the normal curve in terms of comparing one person’s score with another – using standard deviations.

Probabilities Under the Normal Curve (Figure 10.13)

Percentages Under the Normal Curve (Figure 10.11)

Examples of Standard Scores (Figure 10.15)

Effect Size An index of a treatment effect expressed as a standardized difference between two means (mean difference divided by the standard deviation of a comparison group’s mean). It is often expressed as a percentile shift, or “boost” from a baseline at the 50th percentile. (Treatment Mean - Control Mean) d = _____________________________ Standard Deviation of Control

Overlapping Distributions Revealing an Effect Size of 0.5.

Overlapping Distributions Revealing a Large Effect Size

Rules of Thumb Older –Minimum per group size of 30 Newer –For strong evidence ▫“Rough rule of thumb” of 150 participants in each group –For entire schools or classrooms ▫Rigorous evidence is schools or classroom in each group –The dropout rate should not exceed 25%

Sample Size and Precision in Scientific Surveys Most scientific, national surveys use about 1,000 or so respondents in their sample Produces a “margin of error” around 3%, in other words, a boundary within which a value from the entire population would most likely fall

Questions about sampling Sample size – do I have enough participants? Is it the right kind of sample? Is it representative?

Population Target population – desired population Accessible population – feasible/practical population Target population: All 4 th graders Accessible population : 4 th graders at St Peter’s

Sample Subset of a Population Individuals in the Sample are the participants in the study Population (in the green) A person Sample (in the small circle)

Choosing the sample Random –Every person in the population has an equal chance of being selected –Best way to achieve “representative sample” –Difficulty is truly achieving a random sample

Simple Random Sample Sampling or selection is done by simply randomly selecting one member of the population, then another, then another, etc… Until the desired sample size is achieved Simple example: 100 people in the population, put their names in hat, and draw 20.

Simple Random Sample More likely methods: –Use computers –Use table of random numbers and a list

Stratified Random Sampling Every person still has an equal chance of being selected Select the sample based upon one or more characteristics – strata Determine the stratum or strata Determine their proportions Select persons from the strata to create a sample that is consistent with the strata proportions

Stratified Random Sampling Strata are gender and race –In Population, 60% women, 70% white –Thus you have four groups White women – 42% Minority Women - 18% White men – 28% Minority men – 12% –Want 200 sample size. Select: 84 White women from all the white women in the population 36 Minority women from all the minority women in the pop 56 White men from all the white men in the pop 24 Minority men from all the minority men in the pop Another example next slide:

Middle school students 7th, 8th, 9th –Population th graders 1500/3700 = 41% th graders 1200/3700 = 32% th graders 1000/3700 = 27% 100 students –41 are 7 th graders –32 are 8 th graders –27 are 9 th graders Helps creates representation, but is more work Stratified Random Sampling

Cluster Sample Still Random – every person in population has equal chance of being chosen But you are sample groups (clusters) of people rather than individuals Examples: 8 elementary schools in Quincy –Randomly select 2 3 sections of Ed Psych –Randomly select 1 Simpler than simple random sample but risk an non-representative sample

Two – Stage Random Sampling Combination of cluster and simple Conduct a cluster sampling Randomly select participants from the selected clusters 8 elementary schools, cluster sampling of 3 of the schools, then randomly select 30 students from school

Non-random Sampling Purposive Convenience Solicited (volunteers)

Questions about sampling Sample size – do I have enough participants? Is it the right kind of sample? Does my sample size provide me with enough information? Is it representative?

External Validity The degree to which research results can be generalized beyond the sample and conditions that yielded the findings Population generalization –The extent to which research findings extend beyond the sample of research participants that provided data Ecological generalization –The extent to which research findings extend beyond the setting which produced sampled data

Representation Is the sample representative of the population? The terms for this are: –Generalization –External Validity Example: –Results from 4 th graders in Adams Generalize to all 4 th graders in Quincy? Generalize to all 4 th graders in Illinois? Ecological Generalizabilty – next slide

Ecological Generalizabilty Degree to which the results of the study can generalize to other situations or conditions. 4 th graders = 3 rd graders? Live skits = video? Urban = rural?

Random is best The use of random sampling is strongest method to provide external validity or generalization. True Random sampling is often not possible Replication becomes more important

One summary QuantitativeQualitativeAction RandomPurposive Sample size important Not concerned with sample size External Validity is a concern External Validity can be a concern Not concerned with external validity StatisticsNo statisticsMaybe

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