Chapter 1: Sampling and Data
Chapter 1 Review
Chapter Review from 1.1
The mathematical theory of statistics is easier to learn when you know the language. This module presents important terms that will be used throughout the text.
Chapter Review from 1.2
Data are individual items of information that come from a population or sample. Data may be classified as qualitative, quantitative continuous, or quantitative discrete.
Because it is not practical to measure the entire population in a study, researchers use samples to represent the population. A random sample is a representative group from the population chosen by using a method that gives each individual in the population an equal chance of being included in the sample. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Convenience sampling is a nonrandom method of choosing a sample that often produces biased
data.
Samples that contain different individuals result in different data. This is true even when the samples are well-chosen and representative of the population. When properly selected, larger samples model the population more closely than smaller samples. There are many different potential problems that can affect the reliability of a sample. Statistical data needs to be critically analyzed, not simply accepted.
Chapter Review from 1.3
Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.
In addition to rounding your answers, you can measure your data using the following four levels of measurement.
- Nominal scale level: data that cannot be ordered nor can it be used in calculations
- Ordinal scale level: data that can be ordered; the differences cannot be measured
- Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
- Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.
When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.
Exercises
What type of measure scale is being used? Nominal, ordinal, interval or ratio.
- High school soccer players classified by their athletic ability: Superior, Average, Above average
- Baking temperatures for various main dishes: 350, 400, 325, 250, 300
- The colors of crayons in a 24-crayon box
- Social security numbers
- Incomes measured in dollars
- A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied
- Political outlook: extreme left, left-of-center, right-of-center, extreme right
- Time of day on an analog watch
- The distance in miles to the closest grocery store
- The dates 1066, 1492, 1644, 1947, and 1944
- The heights of 21–65 year-old women
- Common letter grades: A, B, C, D, and F
Solution
- ordinal
- interval
- nominal
- nominal
- ratio
- ordinal
- nominal
- interval
- ratio
- interval
- ratio
- ordinal
Chapter Review from 1.4
A poorly designed study will not produce reliable data. There are certain key components that must be
included in every experiment. To eliminate lurking variables, subjects must be assigned randomly to different treatment groups. One of the groups must act as a control group, demonstrating what happens when the active treatment is not applied. Participants in the control group receive a placebo treatment that looks exactly like the active treatments but cannot influence the response variable. To preserve the integrity of the placebo, both researchers and subjects may be blinded. When a study is designed properly, the only difference between treatment groups is the one imposed by the researcher. Therefore, when groups respond differently to different treatments, the difference must be due to the influence of the explanatory variable.
“An ethics problem arises when you are considering an action that benefits you or some cause you support, hurts or reduces benefits to others, and violates some rule.”4 Ethical violations in statistics are not always easy to spot. Professional associations and federal agencies post guidelines for proper conduct. It is important that you learn basic statistical procedures so that you can recognize proper data analysis.
Exercises
Design an experiment. Identify the explanatory and response variables. Describe the population being studied and the experimental units. Explain the treatments that will be used and how they will be assigned to the experimental units. Describe how blinding and placebos may be used to counter the power of suggestion.
Solution
Answers will vary.
Exercises
Discuss potential violations of the rule requiring informed consent.
- Inmates in a correctional facility are offered good behavior credit in return for participation in a study.
- A research study is designed to investigate a new children’s allergy medication.
- Participants in a study are told that the new medication being tested is highly promising, but they are not told that only a small portion of participants will receive the new medication. Others will receive placebo treatments and traditional treatments.
Solution
- Inmates may not feel comfortable refusing participation, or may feel obligated to take advantage of the promised benefits. They may not feel truly free to refuse participation.
- Parents can provide consent on behalf of their children, but children are not competent to provide consent for themselves.
- All risks and benefits must be clearly outlined. Study participants must be informed of relevant aspects of the study in order to give appropriate consent.