Introduction to Statistics ECO 3401 - B. Potter Introduction to Statistics

Definitions Statistics Data Population Census Sample ECO 3401 - B. Potter Definitions Statistics Data Population Census Sample Inferential Statistics

Definitions Statistics ECO 3401 - B. Potter Definitions Statistics The science of the collection, organization, and interpretation of numerical data. The analysis of population characteristics by inference from sampling.

Definitions Statistics Data ECO 3401 - B. Potter Definitions Statistics Data collections of observations (measurements, survey responses, etc.)

Definitions Statistics Data Population ECO 3401 - B. Potter Definitions Statistics Data Population The complete collection of all individuals to be studied.

Definitions Statistics Data Population Census ECO 3401 - B. Potter Definitions Statistics Data Population Census The collection of data from every member of the population.

Definitions Statistics Data Population Census Sample ECO 3401 - B. Potter Definitions Statistics Data Population Census Sample A subset of the population

Definitions Statistics Data Population Census Sample ECO 3401 - B. Potter Definitions Statistics Data Population Census Sample Inferential Statistics Mathematical methods used to infer the properties of a population from the analysis of the properties of a sample drawn from it.

Types of Data Parameter Statistic Quantitative data ECO 3401 - B. Potter Types of Data Parameter Statistic Quantitative data Categorical (qualitative) data Discrete data Continuous data

Types of Data Parameter ECO 3401 - B. Potter Types of Data Parameter Numerical measurement describing a characteristic of a population.

Types of Data Parameter Statistic ECO 3401 - B. Potter Types of Data Parameter Statistic Numerical measurement describing a characteristic of a sample.

Types of Data Parameter Statistic Quantitative data ECO 3401 - B. Potter Types of Data Parameter Statistic Quantitative data numbers representing counts or measurements. The number of students who are in-state residents. The weights of students at UCF.

Types of Data Parameter Statistic Quantitative data ECO 3401 - B. Potter Types of Data Parameter Statistic Quantitative data Categorical (qualitative) data Names or labels (representing categories). Can be numerical Gender Jersey numbers

Types of Data Parameter Statistic Quantitative data ECO 3401 - B. Potter Types of Data Parameter Statistic Quantitative data Categorical (qualitative) data Discrete data The number of possible values is either a finite number, or a “countable” number (0, 1, 2,…) The number of students enrolled in ECO 3401 (0 – 350) The number of students enrolled at UCF.

Types of Data Parameter Statistic Quantitative data ECO 3401 - B. Potter Types of Data Parameter Statistic Quantitative data Categorical (qualitative) data Discrete data Continuous data Within an interval there are an infinite number of possible values. The distance a student travels between home and school

4 Levels of Measurement Nominal Ordinal Interval Ratio ECO 3401 - B. Potter 4 Levels of Measurement Nominal Ordinal Interval Ratio

4 Levels of Measurement Nominal ECO 3401 - B. Potter 4 Levels of Measurement Nominal Data that consist of names, labels, or categories only Cannot be arranged in an ordering scheme (such as low to high) Ex.: Survey responses (yes, no, undecided)

4 Levels of Measurement Nominal Ordinal ECO 3401 - B. Potter 4 Levels of Measurement Nominal Ordinal Data that can be arranged in some order. Differences between data values either cannot be determined or are meaningless Ex.: BCS college football rankings.

4 Levels of Measurement Nominal Ordinal Interval ECO 3401 - B. Potter 4 Levels of Measurement Nominal Ordinal Interval Data that can be arranged in some order. Difference between any two values is meaningful. No natural zero starting point, where zero means the absence of any quantity. Ex.: Temperature.

4 Levels of Measurement Nominal Ordinal Interval Ratio ECO 3401 - B. Potter 4 Levels of Measurement Nominal Ordinal Interval Ratio Data that can be arranged in some order. Difference between any two values is meaningful. There is a natural zero starting point, where zero means the absence of any quantity. Ex.: The number of points earned on a test.

ECO 3401 - B. Potter Deceptive Statistics “There are three kinds of lies: Lies, damned lies, and statistics.” - Benjamin Disraeli “Some people use statistics as a drunken man uses lampposts – for support rather than illumination” – Historian Andrew Lange “There are two kinds of statistics, the kind you look up, and the kind you make up.” – Rex Stout

Deceptive Statistics Two common sources Evil intent ECO 3401 - B. Potter Deceptive Statistics Two common sources Evil intent Unintentional errors

ECO 3401 - B. Potter

Deceptive Statistics Common deceptive methods Misuse of graphs ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Misuse of graphs Bad samples Correlation/Causation Reported results Small samples Loaded questions Order of questions

Deceptive Statistics Common deceptive methods Misuse of graphs ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Misuse of graphs To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape. READ labels and units on the axes!

Deceptive Statistics Common deceptive methods Misuse of graphs ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Misuse of graphs Pictographs Exaggerate the difference by increasing each dimension in proportion to the actual amounts

Deceptive Statistics Common deceptive methods Bad samples ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Bad samples Voluntary response samples Internet surveys valid conclusions can be made only about the specific group of people who agree to participate and not about the population.

Deceptive Statistics Common deceptive methods Correlation/Causation ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Correlation/Causation Concluding that one variable causes the other variable when in fact the variables are linked Two variables may seemed linked, smoking and pulse rate, this relationship is called correlation. Cannot conclude the one causes the other.

Deceptive Statistics Common deceptive methods Reported results ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods How tall are you? Reported results When collecting data from people, it’s better to take measurements yourself instead of asking subjects to report results. I’m 6’ 4” tall

Deceptive Statistics Common deceptive methods Small samples ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Small samples Conclusions should not be based on samples that are too small. Children Out of School in America (Children’s Defense Fund, 1974): Among secondary school students suspended in Los Angeles County, 67% were suspended at least 3 times. Sample size: 3

Deceptive Statistics Common deceptive methods Loaded questions ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Loaded questions Survey questions can be “loaded” or intentionally worded to elicit a desired response. In a recent study using two different randomly selected groups: Question Agree Too little money is being spent on welfare. Too little money is being spent on assistance to the poor.

Deceptive Statistics Common deceptive methods Loaded questions ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Loaded questions Survey questions can be “loaded” or intentionally worded to elicit a desired response. In a recent study using two different randomly selected groups: Question Agree Too little money is being spent on welfare. 19% Too little money is being spent on assistance to the poor. 63%

Deceptive Statistics Common deceptive methods Order of questions ECO 3401 - B. Potter Deceptive Statistics Common deceptive methods Order of questions Questions are unintentionally loaded by such factors as the order of the items being considered. Does traffic contribute more or less to air pollution than industry? Results: 45% said traffic, 27% said industry Does industry contribute more or less to air pollution than traffic ? Results: 57% said industry, 24% said traffic

Collecting Sample Data ECO 3401 - B. Potter Collecting Sample Data Observational Study Experiment Random Sample Simple Random Sample Other Sampling methods…

Collecting Sample Data ECO 3401 - B. Potter Collecting Sample Data Observational Study Observing and measuring specific characteristics without attempting to modify the subjects being studied.

Collecting Sample Data ECO 3401 - B. Potter Collecting Sample Data Observational Study Experiment Apply some treatment and then observe its effects on the subjects

Collecting Sample Data ECO 3401 - B. Potter Collecting Sample Data Observational Study Experiment Random Sample members from the population are selected in such a way that each individual member in the population has an equal chance of being selected

Collecting Sample Data ECO 3401 - B. Potter Collecting Sample Data Observational Study Experiment Random Sample Simple Random Sample selected in such a way that every possible sample of the same size n has the same chance of being chosen Other Sampling methods…

Systematic Sampling Select some starting point and then ECO 3401 - B. Potter Systematic Sampling Select some starting point and then select every kth element in the population

use results that are easy to get ECO 3401 - B. Potter Convenience Sampling use results that are easy to get

subdivide the population into at ECO 3401 - B. Potter 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)

divide the population area into sections ECO 3401 - B. Potter Cluster Sampling divide the population area into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

End of Intro to Statistics ECO 3401 - B. Potter End of Intro to Statistics