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Quantitative Data

Quantitative Data. Numerical Summaries. Objective. To utilize summary statistics to evaluate and compare distributions of quantitative data. Trident Commercial.

cameron-cote
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Quantitative Data

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  1. Quantitative Data Numerical Summaries

  2. Objective To utilize summary statistics to evaluate and compare distributions of quantitative data

  3. Trident Commercial What does this mean? First it appeals to the idea that dentist know a thing or two about teeth. However, do we truly know what 4 out of 5 means? Was there a pole of thousands of dentists and this was the resulting proportion? Was there only 5 dentists? How were they selected? Did the advertisers keep surveying until 4 out of 5 in a group recommended Trident? Were thousands asked any only 5 responded to the survey? Also, how do dentists generalize this conclusion? Did they take the time to run a comparative experiment where some patients chewed Trident for 6 months and the others didn’t? Is this the dentist’s opinion? This is not relevant data, even though it is dress up to be such

  4. Shape

  5. Measures of Center • Numerical descriptions of distributions begin with a measure of its “center”. If you could summarize the data with one number, what would this typical number be? Mean: The “average” value of a dataset. Median: Q2 or M The “middle” value of a dataset. Arrange observations in order min to max Locate the middle observation, average if needed.

  6. Mean vs. Median • The mean and the median are the most common measures of center. If a distribution is perfectly symmetric, the mean and the median are the same. • The mean is not resistant to outliers. • You must decide which number is the most appropriate description of the center... MeanMedian Applet

  7. Measures of Spread Variability is the key to Statistics. Without variability, there would be no need for the subject. When describing data, never rely on center alone. Measures of Spread: • Range - {rarely used...why?} • Quartiles - InterQuartile Range {IQR=Q3-Q1} • Variance and Standard Deviation {var and sx} Like Measures of Center, you must choose the most appropriate measure of spread.

  8. Standard Deviation Another common measure of spread is the Standard Deviation: a measure of the “average” deviation of all observations from the mean. To calculate Standard Deviation: • Calculate the mean. • Determine each observation’s deviation (x - xbar). • “Average” the squared-deviations by dividing the total squared deviation by (n-1). • This quantity is the Variance. • Square root the result to determine the Standard Deviation.

  9. Standard Deviation Variance: Standard Deviation: • Example 1.16 (p.85): Metabolic Rates

  10. Standard Deviation Metabolic Rates: mean=1600 What does this value, s, mean?

  11. Linear Transformations Variables can be measured in different units (feet vs meters, pounds vs kilograms, etc) When converting units, the measures of center and spread will change. Linear Transformations (xnew=a+bx) do not change the shape of a distribution. • Multiplying each observation by b multiplies both the measure of center and spread by b. • Adding a to each observation adds a to the measure of center, but does not affect spread.

  12. Summary Data Analysis is the art of describing data in context using graphs and numerical summaries. The purpose is to describe the most important features of a dataset.

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