Statistical and critical thinking
- 1. Statistical and Critical Thinking Key Concept: Analyzing sampling data relative to context, source and sampling methods Distinguishing between population and sample. Determining the difference between parameter and statistics. Understanding the difference between statistical significance and practical.
- 2. Key Language of Statistics Statistics is the study of procedures for collecting, describing, and drawing conclusions from information. Data Population Sample
- 3. Answers: Data: Collections of observations, such as measurements, genders, or survey responses A population is the entire collection of individuals about which information is sought. A sample is a subset of a population, containing the individuals that are observed.
- 4. Example: Residential Carbon Monoxide Detectors: Identify the population and sample. In the journal article “Residential Carbon Monoxide Detector Failure Rates in the United States”, it was stated that there are 38 million carbon monoxide detectors installed in the United States. When 30 of them were randomly selected and tested, it was found that 12 of them failed to provide an alarm in hazardous carbon monoxide conditions.
- 5. Example 2 Reported Versus Measured: In a survey of 1046 adults conducted by Bradley Corporation, subjects were asked how often they wash their hands when using a public restroom, and 70% of the respondents said “always.”
- 7. Prepare: 1. Context What do the data represent? What is the goal of the study? 2. Source of the data Are the data from a source with a special interest so that there is pressure to obtain results that are favorable to the source? 3. Sampling Method Were the data collect in way that is unbiased. Was the data collect to be biased?(Volunteer sampling)
- 8. Analyze: 1. Graph data 2. Explore the data. Are there any outliers. Summaries data How is the data distributed? Are there missing data? 3. Applying Statistical Methods Use technology to obtain results.
- 9. Conclude: Significance Do the results have statistical significance? Do the results have statistical significance?
- 10. Voluntary Response Sample Voluntary Response Sample or Self-Selected Sample is one in which the respondents themselves decide whether to be included. Examples • Internet polls, in which people online can decide whether to respond. • Mail-in polls, in which people can decide whether to reply • Telephone call-in polls, in which newspaper, radio, or television announcements ask that you voluntarily call a special number to register your opinion. By their very nature, all are seriously flawed because we should not make conclusions about a population on the basis of samples with a strong possibility of bias:
- 11. Statistical Significances Vs Practical Significances Statistical Significances: is achieve in a study when we get a result that is very unlikely to occur by chance. A common criterion is that we have statistical significance if the likelihood of an event occurring by chance is 5% or less. Practical Significance: It is possible that some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use or to be practical.
- 12. Example 3 Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of the Gender Aide method of gender selection used to increase the likelihood of a baby being born a girl, 2000 users of the method gave birth to 980 boys and 1020 girls. There is about a 19% chance of getting that many girls if the method had no effect.