Warm up• A survey was given to a class to see if students
at the college were excited about taking statistics.
• The results are graphed below. Notice 20 people said no and 10 people said yes.
• According to the graph the number who said no is how many times the number who said yes?
• 20 is only twice as many as 10. What is wrong with this picture?
Yes No
Answers
• The graph on the previous slide had a NONZERO START. A nonzero start can deceive the viewer.
0
5
10
15
20
25
1 2
Series1
The accurate graph
• “There are three kinds of lies. Lies, damn lies, and statistics.”
• Author unknown
• One intention of this course is to teach students to think more critically and deeply about information presented to them instead of blindly accepting it.
Definitions
• Statistics is the science of planning studies and experiments, carrying them out and interpreting the results.
Objective
The objective of doing statistics is to use sample data as a basis for drawing a conclusion about the whole population.
Forming a hypothesis
• A hypothesis in a statistical study is a claim that the study or is trying to show or support.
• This can also be called the goal of the study.
Data is information gathered such as collections of observations, measurements, genders, or survey responses.
Definition
Definition-Population versus Sample
Population –Population – “ “The entire set”The entire set” A population is the complete A population is the complete
collection or all the data that are collection or all the data that are being considered.being considered.
Sample – “A part of that set”
A sample is a subset of members selected from a population.
A sampling method is a way of collecting sample data.
Statistical significance
• The results of a study have statistical significance if they are unlikely to occur by chance.
Practical significance
• The results of a study have practical significance if they are useful.
Example
In a test of the Atkins weight loss program, 40 subjects had a mean weight loss of 4.6 pounds after one year.
The results are statistically significant. It is unlikely that if the diet were ineffective the participants would have these results.
Example - continued
The results are not practically significant since losing 4.6 pounds in one year does not seem very worthwhile.
This shows that results can be statistically significant while failing to be practically significant.
Sound / Flawed sampling methods
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Samples that are too small.
• A method that is not flawed is called SOUND.
• The following are more examples of flawed sampling methods.
Source of data
• If data are collected from a source with a special interest the data may be biased
Voluntary Response Samples
• A voluntary response sample (also called a convenience sample) is a sample in which the respondents chose whether or not to respond
Correlation and causation
• Correlation between two variables occurs when the two variables seem to be associated with one another. Causation between two variables occurs when the values of one variable are directly causing the values of the other
• Remember that CORRELATION IS NOT NECESSARILY CAUSATION.
Percentage problems
• The word percent means out of 100 • To take a percent means to divide by 100 or to
multiply by 1/100 • To convert from a decimal to a percent we move
the decimal 2 places to the right and put a percent sign.
• To convert from a percent to a decimal we move the decimal 2 places to the left and remove the percent sign.
Example 1
• You've been hired to research recognition of the Nike brand name and you must conduct a telephone survey of 1,500 customers in the United States. What is wrong with using telephone directories to take a sample?
Answer Example 1
• Telephone directories only contain listed numbers and those unlisted would not be represented in the survey.
• In addition sometimes numbers appear more than once for example under the husband's name and the wife's name.
Which flaw did we see?
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Potential Bias• Samples that are too small.• Correlation is not causation
Example 2
• A report sponsored by the Florida Citrus Commission concluded that cholesterol levels can be lowered by eating citrus products. Why might the conclusion be suspect?
Answer Example 2
• Studies sponsored by groups with the desire to show a particular results are sometimes biased towards that result. Such bias is not necessarily intentional.
Which flaw did we see?
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Potential Bias• Samples that are too small.• Correlation is not causation
Example 3
• Glamour magazine published this survey result: “79% of those who responded to our August survey say that they believe America has become too lawsuit happy.” The survey question was published in the magazine and readers could respond by mail fax or email. How valid is the 79% result?
Answer Example 3
• The statement 79% of those who responded is correct. Applying that figure to the entire population would not be correct because those who responded are not necessarily representative of the entire population or even of the readers of the magazine. Those who subscribe to Glamour are probably more likely to be affluent and female. The subscribers who chose to respond are probably those with strong feelings on the issue.
Which flaw did we see?
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Potential Bias• Samples that are too small.• Correlation is not causation
Example 4
• In a study on college campus crimes committed by students high on alcohol or drugs, a mail survey of 1875 students was conducted. A USA Today article noted, 8% of the students responding anonymously say they have committed a campus crime and 62% of that group say they did so under the influence of alcohol or drugs. Assuming that the number of students responding anonymously is 1875, how many students actually committed a campus crime while under the influence of alcohol or drugs?
Answer Example 4
• The number that committed a crime is .08 times 1875 = 150
• The number that say they did so under the influence of alcohol or drugs is .62 times 150 = 93.
Example 5
• the Newport Chronicle claims that pregnant mothers can increase their chances of having healthy babies by eating lobsters. The claim is based on a study showing that babies born to Lobster eating mothers have fewer health problems then babies born to mothers who don't eat lobsters. What is wrong with this claim?
Answer Example 5
• That healthier babies are born to mothers who eat lobsters doesn't mean that eating lobsters caused the babies to be healthier. Mothers who eat lobster are probably more affluent in the general population and would tend to eat better, be more knowledgeable about proper prenatal care, have better health care, etc.
Which flaw did we see?
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Potential Bias• Samples that are too small.• Correlation is not causation
Example 6
• According to a nationwide survey of 250 hiring professionals Scuffed shoes was the most common reason for a male job seekers failure to make a good first impression. Newspapers carried the statement based on a poll commissioned by Kiwi brands, producers of shoe polish. Comment on why the results of the survey might be questionable.
Answer Example 6
• Since the poll was sponsored by a shoe polish company, the questions (especially if they were multiple choice and not open ended) may have been designed to encourage and or suggest responses relating specifically to the appearance of shoes.
Which flaw did we see?
Flawed sampling method• Voluntary response sample • Non-response • Missing data • Precise numbers • Potential Bias• Samples that are too small.• Correlation is not causation
