Chapter 1 Statistical and Critical Thinking
Chapter 1
Statistical and Critical Thinking
Vocabulary:
Population – The complete collection of all measurements or data that are being considered.
Sample – A sub-collection of members selected from the population.
1) Concepts:
Context of the data – What do the data mean?
What is the goal of the study?
Source of the data – Were the data from a source with a special interest?
Sampling Method – Were the data collected in a way that is unbiased?
Statistical significance vs. Practical significance – Statistical significance is achieved in a study when we get a result that is very unlikely to occur by chance.
2) What is statistical thinking and what does it mean to you? – Answers may vary
Types of Data
Parameter – A numerical measurement describing some characteristic of a population.
Statistic – A numerical measurement describing some characteristic of a sample.
Quantitative (numerical) data – Consists of numbers representing counts or measurements.
Discrete Data – When the number of possible values is either a finite number or a countable number.
Ex. Number of cars through a drive thru
Continuous Data – Infinitely many possible values.
Ex Height and weight
Qualitative (categorical) Data – Consists of names or labels.
Levels of Measurement:
Nominal – Names, labels, or categories. Cannot be arranged in any order.
Ex. Yes/No
Ordinal – Can be arranged in order. Differences between data values are meaningless.
Ex. Course grades
Interval – Can be arranged in order. Differences between data values are meaningful.
Ex. Temp., years
Ratio – Interval level of measurement with 0 as a starting point.
Ex. Height
Voluntary response survey – Self-selected sample.(Not good!)
Correlation and causation – Correlation does not imply causality
Ex. Ice cream sales and shark attacks, horsepower and fuel efficiency
Watch out for…
Percentages – Often misleading. Ex. Lose 300% of total weight
Survey Questions – Issues
Loaded or incorrectly worded
Order
Non-response
Self-Interest Study – Source with a special interest? Ex. American Dental Association doing a survey to see if flossing is effective.
Collecting Sample Data
Observational Study – Observing and measuring specific characteristics without attempting to modify the subjects being studied.
Experiment – Apply some treatment and then observe its effects on the subjects. Subjects = experimental units
Simple Random Sample – A sample of n subjects is selected in such a way that every possible sample of the same size, n, has the same chance of being chosen.
Random Sample – Members of the population are selected in such a way that each individual member in the population has an equal chance of being selected.
Sampling Techniques:
Systematic Sampling – Select some starting point and then select every kth element in the population.
Convenience Sampling – Use results that are easy to get. (Bad)
Stratified Sampling – Subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum).
Cluster Sampling – Divide the population into sections (or clusters). Then randomly select some of those clusters. Now choose all members from the selected clusters.
Confounding – Occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors.
Sampling Error – The difference between a sample result and the true population result. Such an error results from chance sample fluctuations.
Non-Sampling Error – Sample data incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective measuring instrument, or by copying the data incorrectly).