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H.G. Wells said more than 100 years ago"statistical thinking will one day be as necessary for efficient citizenship as the ability to read." H.G. Wells wrote TIME MACHINE and WAR OF THE WORLDS
Three reasons to study statistics
1. Being informed
To be an informed consumer of such reports, you must be able to
a. Extract information from charts and graphs
b. Follow numerical arguments
c. Know the basics of how data should be gathered, summarized, and analyzed to draw statistical conclusions
2. Understand and making decisions
To make informed decisions, you must be able to do the following:
a. Decide if you have enough information or need more
b. If necessary, collect more information in a reasonable and thoughtful way
c. Summarize available data in a useful and informative manner
d. Analyze the data
e. Draw conclusions, make decisions, and assess the risk of an incorrect decision
3. Evaluating Decisions that Affect Your Life
Help understand the validity and appropriateness of processes and decisions that affect your life
Statistics is the scientific discipline that provides methods to help us make sense of data.
Data collections of observations such as measurements, genders, survey responses
Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.
A population is the complete collection of all individuals (scores, people, measurements, etc.) to be studied.
A census is the collection of data from every member of the population.
A sample is a subcollection (subset) of members selected from a population.
Example: sample2.3 million respondents in the Literary Digest Poll
Populationentire collection of all adults eligible to vote
It is extremely important to obtain sample data that are representative of the population from which the data are drawn. Sample data must be collected in an appropriate way usually through a random selection. If it is not corrected in an appropriate way, the data is of no use to us.
12 Statistical Thinking
Consider these factors when conducting a statistical analysis of data or analyzing statistical data from another's research.
1. Context of the data
2. Source of the data
3. Sampling method
4. Conclusions
5. Practical implications
13 Types of Data
A goal of statistics is to make inferences, or generalizations, about a population
Parametera numerical measurement describing some characteristic of a population
Statistica numerical measurement describing some characteristic of a sample
Example: percent of Democrats or Republicans in the United States Senate is a parameter
57% of the 2.3 million polled in 1936 for the Literary Digest is a statistic
Quantitative or numerical data consist of numbers representing counts and measurementsweight, height, amount of money in checking account
Categorical or qualitative or attribute data consists of names or labels that are not numbers representing counts or measurementseye color, gender, church affiliation
Quantitative data is divided into discrete and continuous data
Discrete data is data that can be countednumber of bedrooms in a house
Continuous data is data that is measuredheight, weight
Data can be classified by levels of measurements. The levels of measurements help us to decide which statistical procedure to use.
Levels of Measurements
1. Nominaldata that consists of names, labels, or categories only; the data cannot be arranged in an order; political party, gender, social security number, area code
2. Ordinalcan be arranged in some order, cannot do differences on the data or the differences do not make sensegradesA,B,C, D, F or good, better, best
3. Intervalcan be arranged in some order and the difference between any two values is meaningful; there is not a natural zero starting pointnone of the quantity is presenttemperature
4. Ratiothere is a natural zero starting point and ratios are meaningfuldistances, cost
14 Critical Thinking
Key Conceptfocus on the meaning of the information obtained by studying data
Ways statistical conclusions can be flawed.
1. Use of bad graphs
2. Bad sample
Voluntary response sampledo not use voluntary response sample data to make conclusions about a population
Internet polls, telephone call in polls, mail in polls
3. Saying something caused something elsecorrelation does not imply causation
4. Using reported results instead of actual measurements
5. Using too small of a sample
6. Citing misleading or unclear percentages
7. Using loaded questions
8. Order of questions
9. Nonresponse
10. Missing data
11. Selfinterest study
12. Precise numbers
13. Deliberate Distortions
15 Collecting Sample Data
The method used to collect sample data influences the quality of our statistical analysis.
Observational studywe observe and measure specific characteristics, but we do not attempt to modify the subjects being studiedexample: Gallup poll; you cannot draw cause and effect conclusions from an observational study. The goal of an observational study is usually to draw conclusions about the corresponding population or about differences between two or more populations.
Experimentwe apply some treatment and then proceed to observe its effects on the subjects; observe how a response variable behaves when the researcher manipulates one or more factors; the researcher manipulates something and measures the effect of the manipulation on some outcome of interest; exampleclinical trial
Types of sampling methods:
A simple random 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. Simple random sampling provides researchers with a sampling method that is objective and free of bias.
In a random sample members from the populations are selected in such a way that each individual member in the population has an equal chance of being selected. Random sampling requires very careful planning and execution. The goal of random sampling is to produce a sample that is likely to be representative of the population.
A probability sample involves selecting members from a population in such a way that each member of the population has a known (but not necessarily the same) chance of being chosen.
Systematic sampleselect some starting point and then select every kth element in the population; this method can be used when it is possible to view the population as a list; there needs to be no pattern in the population
Convenience samplingsimply use results that are easy to get; convenience sampling is not reliable
Stratified samplingsubdivide the population into at least 2 different, nonoverlapping subgroups (strata) so that subjects within the same subgroup share the same characteristics (such as gender or age bracket) then we choose a simple random sample from each subgroup; the advantage of stratified sampling is that it often allows us to make more accurate inferences about a population than does a simple random sample; often used to reduce the variation in results; uses homogeneous groups
Cluster samplinguses heterogeneous groups; divide the population into nonoverlapping subgroups called clusters; clusters are then randomly selected, and then all individuals in the selected clusters are included in the sample; cluster sampling can be faster and less expensive than random sampling
Multistage samplinguses some combination of the basic sampling methods
Part 2: Beyond the Basics of Collecting Data
Different types of observational studies:
Crosssectional studydata are observed, measured, and collected at one point in time
Retrospective studydata are collected from the past by going back in time
Prospective studydata are collected in the future from groups sharing common factors
Design of Experiments
Randomizationsubjects are assigned to different groups through a process of random selection. Random assignment of subjects to treatments or treatments to trials ensures that the experiment does not systematically favor one experimental condition over another. It reduces the likelihood that results will be affected by confounding or bias that often is present in observational studies. Randomized experiments are important because they often allow us to determine whether there is a causeandeffect relationship between two variables.
Replication is the repetition of an experiment on more than one subject. Replication is used effectively when we have enough subjects to recognize differences from different treatments.
Placebosomething identical to the treatment received by the treatment group except that it contains no active ingredients
Blinding is a technique in which the subject does not know whether he or she is receiving a treatment or a placebo. Blinding minimizes the placebo effect or takes account for it.
Double blind is a technique in which neither the participant nor the researcher taking the measurements knows who had the treatment.
Results of experiments are sometimes ruined because of confounding. Confounding occurs in an experiment when you are not able to distinguish among the effects of different factors.
ExamplePeople who attended church regularly had lower blood pressure than those who stayed home and watched the service on television. Confounding variable could be health issues.
Four Methods Used to Control Effects of Variables.
1. Completely Randomized Experimental Design
2. Randomized Block Designyou create groups (blocks) of subjects that are similar in the ways that might affect the outcome of the experiment and then make certain that all treatments are tried in each block. This controls known sources of variability.
3. Rigorously controlled designhold factors that are of not of interest in the current study but might affect the outcome constant
4. Matched pairs designcompare exactly two treatment groups by using subjects matched in pairs that have similar characteristics
Three important considerations in the design of experiments:
1 Use randomization to assign subjects to different groups.
2. Use replication by repeating the experiment on enough subjects so that effects of treatments or other factors can be clearly seen.
3. Control the effects of variables by using techniques as blinding and a completely randomized experimental design.
Sampling errorthe difference between a sample result and the true population result; such an error results from chance sample fluctuations.
A nonsampling error occurs when the sample data are incorrectly collected, recorded, or analyzed.
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