Chapter 3 - Chapter 3 Descriptive Analysis and Presentation...

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Chapter 3 Descriptive Analysis and Presentation of Bivariate Data
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Boating and Manatees
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Florida Manatees Large, slow moving mammals that live in Florida waterways Controversy between environmentalists and boat operators Manatee deaths continue despite creation of refuges and slow-speed zones
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Recent data show similar trend in # of boats and in # of manatee deaths Pleasure Boats 68 68 67 70 71 73 76 81 83 84 0 10 20 30 40 50 60 70 80 90 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Year # pleasure boats regist Florida (x 10,000) Manatee Deaths 53 38 35 49 42 60 54 67 82 78 0 10 20 30 40 50 60 70 80 90 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Year # Deaths in Fl Is there a relationship between # boats and # deaths?
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Use statistics to think about… Best way to show relationship between boat number and manatee deaths Describing statistical relationship between these 2 variables
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Bivariate Data Occurs when 2 variables are measured on same experimental unit Data come in pairs (1 pair/experimental unit) Assumes each pair of observations was collected independently and without bias Example: measure age and number of hours sleep per night on the same person Then collect same info on many people
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Bivariate Variables can be: 2 Qualitative variables Ex: Gender and Major of College Students 1 Qualitative and 1 Quantitative Ex: Gender and Height 2 Quantitative variables Ex: Height and Shoe Size Let’s go through an example of each
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TV Radio NP Male 280 175 305 Female 115 275 170 2 Qualitative Variables: data often shown as contingency table or bar graph Example : survey to investigate preferences for television, radio, or newspaper for national news, and gender. 0 5 10 15 20 25 TV Radio NP Male Female Percentages Based on Grand Total Percent
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1 Quantitative and 1 Qualitative Variables: random sample of households from three different parts of the country for June electric bill. Data Set: region vs. electric bill Bar Chart showing means or Box and Whisker are both good ways to this type of display data
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Northeast Midwest West 20 30 40 50 60 70 Electric Bill ($) The Monthly Electric Bill Your turn: what do arrows indicate? Region in US
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Manatee Example Year Boats Deaths 1991 68 53 1992 68 38 1993 67 35 1994 70 49 1995 71 42 1996 73 60 1997 76 54 1998 81 67 One pair of observations for 1 year 2 Quantitative Variables Assumes data for each year is independent 2 Quantitative Variables
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Observed Pairs often graphed using a Scatter Plot 0 10 20 30 40 50 60 70 80 90 60 65 70 75 80 85 90 # Boats (*10,000) Manatee Deaths 2 Quantitative Variables
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Scatterplot Is there a pattern? What is the pattern? Does the Scatterplot show this pattern better than the side by side plots I showed you at the beginning? How can we interpret this pattern? 2 Quantitative Variables
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Linear Correlation A correlation exists between 2 variables when one of them is related to the other in a linear manner Linear Correlation Analysis measures the direction and strength of the linear relationship between 2 quantitative variables Described by Linear Correlation Coefficient ‘ r 2 Quantitative Variables - Correlation
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Chapter 3 - Chapter 3 Descriptive Analysis and Presentation...

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