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Simple Random Sample

Recall that a simple random sample is a sample of n elements from a population of N in which each possible sample of size n has the same probability of selection, namely

The probability of any element being selected is equal to the ratio of the sample size to the population size

Example for a Population Mean

If n = 200 was selected from N = 1,000 and the sample mean was = 94.22 with a sample variance of = 445.21, the bound on the error of estimation, B, would be

Example for a Population Total

If n = 50 was selected from N = 750 and the sample mean was = 10.31 ( = 750(10.31) = 7,732.5) with a sample variance of = 2.25, the bound on the error of estimation, B, would be

Sample Size for Estimating Population Means

Often, the population variance, , is unknown

An approximate value of can be obtained by

Example for a Population Mean

If N = 1,000 and the estimated range is 100, the sample size necessary to estimate with B = 3 would be

and

Sample Size for Estimating Population Totals

If N = 1,000 and = 36.00, the sample size necessary to estimate the population total, , with B = 1,000 would be

then

Example for a Population Proportion

If n = 100 was selected from N = 300 and the sample proportion was = 0.15 the bound on the error of estimation, B, would be

Example for a Population Proportion

If N = 2,000 and the desired bound on the error of estimation, B, were 0.05, and no prior information is available to estimate , the necessary sample size would be

Issues to Consider

What survey mode(s) will be used to ask the questions?

Is the question being repeated from another survey, and/or will answers be compared to previously collected data?

Will respondents be willing and motivated to answer accurately?

What type of information is the question asking for?

Choosing Words and Forming Question

- Make sure the question applies to the respondent
- Make sure the question is technically accurate
- Ask one question at a time
- Use simple and familiar words
- Use specific and concrete words to specify the concepts clearly
- Use as few words as possible to pose the question
- Use complete sentences with simple sentence structures
- Make sure “yes” means yes and “no” means no
- Be sure the question specifies the response task

Visual Presentation of Survey Questions

Use darker and/or larger print for the question and lighter and/or smaller print for answer choices and answer spaces

Use spacing to create subgrouping within a question

Visually standardize all answer spaces or response options

Use visual design properties to emphasize elements that are important to the respondent and to deemphasize those that are not

Make sure words and visual elements that make up the question send consistent messages

Integrate special instructions into the question where they will be used rather than including them as freestanding entities

Separate optional or occasionally needed instructions from the question stem by font or symbol variation

Organize each question in a way that minimizes the need to reread portions in order to comprehend the response task

Choose line spacing, font, and text size to ensure the legibility of the text

Additional Considerations

- Abilities/aptitudes
- Knowledge or skill
- Attitudes
- General and enduring evaluation of a person, object, or concept
- Behaviors
- Actions and mannerisms
- Opinions/beliefs
- Subjective beliefs that occur as a result of emotion or interpretation of facts

Guttman Scaling

Individuals who endorse the first response should also endorse all others as they represent less extreme views

Midterm Examination

- The examination will consist of 50-75 multiple-choice items, scored as 0 or 1
- You will have 2½ hours to complete the examination
- You may use one page of notes (front and back) on 8½” X 11’’ paper
- You will be required to determine necessary sample sizes and calculate bounds on the error of estimation for means, totals, and proportions
- You may use a calculator or an Excel spreadsheet on a laptop computer
- You cannot use the internet or textbooks

Case Study Activity

- Write a focal question that addresses what proportion of foundations formally assess the effectiveness of their grant making activities
- Determine the motivational features that you would use to encourage high quantity and quality of responses, with particular attention to:
- How the perceived rewards for responding would be increased
- How the perceived costs of responding would be reduced
- How trust would be established so that people believe the rewards will outweigh the costs of responding
- Determine the necessary sample size to estimate the population proportion, p, of foundations (N = 888) to address your focal question with a bound on the error of estimation of B= 0.05 and B = 0.10

Case Study Activity

- Consider the guidelines for “choosing words and framing questions” and “visual presentation of survey questions”
- Are there any errors associated with the guidelines for choosing words and framing questions?
- Are there any errors associated with the guidelines of the visual presentation of survey questions?

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