Survey Research&

Understanding Statistics

Central Tendency

Measures of Central Tendency

Central Tendency

Average (Mean) Median Mode

1

1

n

ii

N

ii

XX

n

X

N

Mean (Arithmetic Mean)

• Mean (arithmetic mean) of data values– Sample mean

1 1 2

n

ii n

XX X X

Xn n

Sample Size

Mean

• The most common measure of central tendency

• Affected by extreme values (outliers)

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Mean = 5 Mean = 6

Median

• Robust measure of central tendency• Not affected by extreme values

• Median is the “middle” number

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Median = 5 Median = 5

Mode• A measure of central tendency• Value that occurs most often• Not affected by extreme values• Used for either numerical or categorical data• There may may be no mode• There may be several modes

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mode = 9

0 1 2 3 4 5 6

No Mode

Survey Research

What is a Survey?

• Researchers are often interested in the opinions of a large group of people about a particular topic or issue.

• There are three major characteristics that most surveys possess:

1) Information is collected from a group of people in order to describe some aspect of the population

2) Information is collected by asking questions of the members of the selected group

3) Information is collected from a sample rather than from every member of the population

Question

• What are common problems with survey research?

Why Are Surveys Conducted?

• The purpose of surveys is to describe the characteristics of a population.

• Researchers find out how the members of a population distribute themselves on one or more variables.

• A selected sample is surveyed and the description of the population is inferred from what is found out about the sample.

• In descriptive surveys, researchers are not as concerned about why the observed distribution exists as with what the distribution is.

Types of Surveys

• There are two types of surveys:1) Cross-sectional survey

– Collects information from a sample that has been drawn from a predetermined population

– Information is collected at just one point in time, even though it could take days to gather all the data

– A census is when the entire population is surveyed

2) Longitudinal survey– Information is collected at different points in time in order to

study changes over time– Three types are employed:

1) Trend study2) Cohort Study3) Panel Study

Survey Research and Correlational Research

• Techniques of Correlational Research can be tied in with Survey Research.

• Researchers could look at the relationship of responses to one question (survey) to another, or of a score based on one set of questions to another set.

• The use of calculating correlation coefficients or contingency tables could be determined and implemented.

Steps in Survey Research

• The following steps are used in conjunction with performing proper surveys in research:– Defining the problem– Identifying the target population (unit of analysis)– Choosing the mode of data collection

• Direct administration

• Mail surveys

• Telephone surveys

• Personal interviews

Example of an Ideal vs. an Actual Telephone Sample for a Specific

Question

Steps in Survey Research(cont.)

• The following steps are used in conjunction with performing proper surveys in research:– Selecting the sample– Preparing the instrument (questionnaire)

• Closed-ended questions• Open-ended questions• Pre-testing the questionnaire• Format• Cover letter

– Training interviewers

Example of Contingency Questions

Non-response

• In almost all surveys, some members of the sample will not respond.

• Item non-response is due to unclear or questionable forms of wording.

• Non-response is a serious problem in many surveys.• A variety of techniques are employed to reduce this

problem (e.g., rewards or incentive for completing the surveys).

Data Analysis in Survey Research

• After researchers receive the completed questionnaires, the task of summarizing the results remains.

• The total size of the sample and total percentage of returns should be reported.

• The percentage of the total sample responding for each item should be reported.

• The percentage of respondents who chose each alternative for each question should be given.

Variability

Shapes of Distributions

• Normal distribution

• Positive Skew– Or right skewed

• Negative Skew– Or left skewed

How is this variable distributed?

87654321

score

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Fre

qu

ency

Mean = 4.3Std. Dev. = 1.494N = 10

How is this variable distributed?

7.006.005.004.003.002.001.000.00

right

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Fre

qu

ency

Mean = 2.80Std. Dev. = 1.75119N = 10

How is this variable distributed?

8.007.006.005.004.003.002.00

left

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Fre

qu

en

cy

Mean = 5.40Std. Dev. = 1.42984N = 10

Standard Deviation

• Considered the most useful index of variability.• It is a single number that represents the spread of a

distribution.• If a distribution is normal, then the mean plus or minus 3

SD will encompass about 99% of all scores in the distribution.

Comparing Standard Deviations

Mean = 15.5 S = 3.338 11 12 13 14 15 16 17 18 19 20 21

11 12 13 14 15 16 17 18 19 20 21

Data B

Data A

Mean = 15.5 S = .9258

11 12 13 14 15 16 17 18 19 20 21

Mean = 15.5 S = 4.57

Data C

Facts about the Normal Distribution

• 50% of all the observations fall on each side of the mean.

• 68% of scores fall within 1 SD of the mean in a normal distribution.

• 27% of the observations fall between 1 and 2 SD from the mean.

• 99.7% of all scores fall within 3 SD of the mean. • This is often referred to as the 68-95-99.7 rule

Fifty Percent of All Scores in a Normal Curve Fall on Each Side of the Mean

Probabilities Under the Normal Curve

The Importance of Converging Evidence

• The connectivity principle– New theory in science must make contact with

established facts.– Beware of violations of connectivity.

• Converging evidence– Single studies have flaws

• Together the flaws should wash out.– When might this not be true?

Meta-Analysis

• A meta-analysis is a statistical procedure when the researcher averages the results of a group of selected studies to get an overall index of outcome or relationship.

Experimental vs. Nonexperimental

• Experiments– Treatment is administered

• Students divided into two groups; one group receives new reading materials the other uses the traditional materials.

• Cancer patients are divided into two groups; one group receives a new drug the other receives the current treatment of choice.

• Nonexperiments – No manipulation of treatment present

• Individuals given a survey asking about television viewing habits.

• Classrooms observed to see if teacher’s expectations affect student performance.

Correlational

• Study Relationships – SAT and Achievement– Income and achievement– Age and Cholesterol level

Causal-Comparative Studies.

• Causal-comparative (a.k.a. ex post facto)– Two characteristics

• Observe and describe a current condition• Look to the past, or demographic characteristics,

to identify a cause.

Survey Research

• Used to describe – Attitudes– Opinions– Beliefs– Behaviors

• Usually include large numbers