Fall 2014 Project 3 BIO4835
BIOSTATISTICS
BIO 4835
Dr. Osborne
Project 3: Collection and analysis of data
Name ______
Due December 15, 2014
Introduction. The purpose of this project is to obtain and analyze bivariate data that you will collect. The project is a team project although each member of the team is required to submit a separate report on their own data. Each member of the team individually collects a sample of 60 items. Your sample will be the heights and weights of 30 men and the heights and weights of 30 women. Each student will collect the 60 data points.
Data and analysis. Each member of your research team records the height and weight of their 30 men and their 30 women but they keep the samples separate from the other members of the team. Each member of the team collects the 60 measurements which constitutes their sample. You will not need anyone’s data except for the ANOVA section. For your own sample of 60 heights and weights, you will prepare each of the following:--
1. basic statistical analysis on the heights: including the sample mean, median, mode, standard deviation, range, quartiles, skewness, kurtosis. One set for the men, the other for the women
2. histogram of the heights of each set, men and women
3. frequency polygon of the heights of each set, men and women
4. box plot of the heights of each set, men and women
5. x-y scatter plot based on heights and weights
6. confidence intervals for population parameters based on the sample statistics of each set of heights
7. hypothesis test for population mean of the heights of each set, men and women
8. ANOVA on the multiple samples to find results about the population of the heights. This is the only place where you need the heights from the other members of your group of each set, men and women
9. regression and correlation analysis including calculations of the regression equation based on the heights and weights taken as (x-y) pairs, correlation coefficient (r), coefficient of determination (r2) of each set, men and women
Report. Each member of the group writes a separate report on their own data using the following template. This will include the following parts.
an abstract which summarizes the results of the report
a description of the methods used to obtain the data and to perform the analysis
results of the analysis on the individual data sample
conclusions based on the results of the project
The report must be written correctly using proper standard format for papers in the Biological Sciences. Length is not a factor. Brevity is generally stressed, especially in situations where you have to pay by the page to get it into print. However, all of the required calculations, tables, graphs and results have to be in the paper and must be explained well enough to make them understandable. Write answers using Microsoft Word. Graphs can be done on the graph papers provided, or you can do them using Microsoft Excel and insert them into the document in place of the graph papers.
A. Abstract: Write an abstract of the report in this space.
B. Methods Describe how your data were collected and analyzed in the space below. List your data in the tables on the next two pages.
C. Results
1. (a) Data and Basic Statistical Analysis: Data from 30 Men
Data Table: Heights and Weights of 30 Men
Person Number / Height (x)(in) / Weight (y)
(lbs) / Person Number / Height (x)
(in) / Weight (y)
(lbs)
1 / 16
2 / 17
3 / 18
4 / 19
5 / 20
6 / 21
7 / 22
8 / 23
9 / 24
10 / 25
11 / 26
12 / 27
13 / 28
14 / 29
15 / 30
Basic Statistical Analysis: Data from 30 Men
Using your values for heights from the data table above, find the following basis statistics for your sample. Use Microsoft Excel. Either enter the data in the table below, or erase the table and replace it with the table provided by Microsoft Excel.
Sample mean / Quartiles / ----Median / First
Mode / Second
Standard Deviation / Third
Range / Fourth
Min / Skewness
Max / Kurtosis
Count
1. (b) Data and Basic Statistical Analysis: Data from 30 Women
Data Table: Heights and Weights of 30 Women
Person Number / Height (x)(in) / Weight (y)
(lbs) / Person Number / Height (x)
(in) / Weight (y)
(lbs)
1 / 16
2 / 17
3 / 18
4 / 19
5 / 20
6 / 21
7 / 22
8 / 23
9 / 24
10 / 25
11 / 26
12 / 27
13 / 28
14 / 29
15 / 30
Basic Statistical Analysis: Data from 30 Women
Using your values for heights from the data table above, find the following basis statistics for your sample. Use Microsoft Excel. Either enter the data in the table below, or erase it and replace it with the table provided by Microsoft Excel.
Sample mean / Quartiles / ----Median / First
Mode / Second
Standard Deviation / Third
Range / Fourth
Min / Skewness
Max / Kurtosis
Count
2. (a) Histogram of the Heights of 30 Men
In the space below, draw a histogram of the heights based on your data sample. Use class intervals (bins) of two inches (58-59, 60-61, 62-63, etc.) as needed. Use the graph provided or create it using Microsoft Excel and paste it where the graph is.
2. (b) Histogram of the Heights of 30 Women
In the space below, draw a histogram of the heights based on your data sample. Use class intervals (bins) of two inches (58-59, 60-61, 62-63, etc.) as needed. Use the graph provided or create it using Microsoft Excel and paste it where the graph is.
3. (a) Frequency Polygon of the Heights of 30 Men
In the space below, draw a frequency polygon of the heights based on your data sample. Use class intervals (bins) of two inches (58-59, 60-61, 62-63, etc.) as needed. Use the graph provided or create it using Microsoft Excel and paste it where the graph is.
3. (b) Frequency Polygon of the Heights of 30 Women
In the space below, draw a frequency polygon of the heights based on your data sample. Use class intervals (bins) of two inches (58-59, 60-61, 62-63, etc.) as needed. Use the graph provided or create it using Microsoft Excel and paste it where the graph is.
4. (a) Box Plot of the Heights of 30 Men
In the space below, draw a box plot of the heights.
4. (b) Box Plot of the Heights of 30 Women
In the space below, draw a box plot of the heights.
5. (a) x-y Scatter Plot of the Heights of 30 Men
In the space below, draw an x-y scatter plot of the weights against the heights. Use the graph provided or create it using Microsoft Excel and past it where the graph is.
5. (b) x-y Scatter Plot of the Heights of 30 Women
In the space below, draw an x-y scatter plot of the weights against the heights. Use the graph provided or create it using Microsoft Excel and past it where the graph is.
6. (a) Confidence Interval for Mean Height of 30 Men
Assume that the population mean height for males in the United States is 70 inches. Create a confidence interval for your sample of men with a = .05.
6. (b) Confidence Interval for Mean Height of 30 Women
Assume that the population mean height for females in the United States is 65 inches. Create a confidence interval for your sample of women with a = .05.
7. (a) Hypothesis Test of the Mean Height of 30 Men
The population mean height for males in the United States is 70 inches. Can you conclude that the mean height of your sample of men is not 70 inches?
7. (b) Hypothesis Test of the Mean Height of 30 Women
The population mean height for females in the United States is 65 inches. Can you conclude that the mean height of your sample of women is not 65 inches?
8. Regression and Correlation Analysis
The methodology of these calculations begins with a table of values in the form of (x,y) pairs. The example in lecture dealt with breathing data from goldfish where x was the temperature of the water and y was the breathing rate. The calculations are done in four steps.
1. .First, the data were placed into two lists of the TI-83 calculator. The x values were in L1 and their corresponding y values were in L2.
2. From TI-83 calculations, this table containing values for calculations was prepared.
3. The slope (b) was calculated using appropriate data from the table. This regression equation will be in the form: y = a + bx.
4. The y-intercept (a) was calculated.
Result: Regression equation was: y = 4.54x – 1.57
(a) Regression and Correlation Analysis of Data for Men.
We begin with your tables of heights and weights back in Part C, Section 1. Note that the data are in the form of (x,y) pairs as (height, weight) for each person sampled. You have one table of (x,y) pairs for men and another table of (x,y) pairs for women.
Begin by using the TI-83. Place your list of Heights into list L1. Then place their corresponding Weights into list L2. With the two lists, you can complete the data table below for the terms needed for the calculations.
Data item for calculation / Symbol / From TI-83 Calc / Value for menMean of x values / 1-Var Stats L1
Sum of x values / Sx / 1-Var Stats L1
Sum of x values squared / (Sx)2 / Square Sx value
Sum of squared x values / Sx2 / 1-Var Stats L1
Mean of y values / 1-Var Stats L2
Sum of y values / Sy / 1-Var Stats L2
Sum of y values squared / (Sy)2 / Square Sy value
Sum of squared y values / Sy2 / 1-Var Stats L2
Number of ordered pairs / n / 1-Var Stats L2
Sum of xy products / Sxy / L1*l2àL3
1-Var Stats L3
Regression Equation Calculation
Using the terms in the table, calculate the regression equation for your data of men.
Calculate Correlation Coefficient and Coefficient of Correlation
Calculate the correlation coefficient and coefficient of correlation for your data of men.
(a) Regression and Correlation Analysis of Data for Women.
We begin with your tables of heights and weights back in Part C, Section 1. Note that the data are in the form of (x,y) pairs as (height, weight) for each person sampled. You have one table of (x,y) pairs for men and another table of (x,y) pairs for women.
Begin by using the TI-83. Place your list of Heights into list L1. Then place their corresponding Weights into list L2. With the two lists, you can complete the data table below for the terms needed for the calculations.
Data item for calculation / Symbol / From TI-83 Calc / Value for womenMean of x values / 1-Var Stats L1
Sum of x values / Sx / 1-Var Stats L1
Sum of x values squared / (Sx)2 / Square Sx value
Sum of squared x values / Sx2 / 1-Var Stats L1
Mean of y values / 1-Var Stats L2
Sum of y values / Sy / 1-Var Stats L2
Sum of y values squared / (Sy)2 / Square Sy value
Sum of squared y values / Sy2 / 1-Var Stats L2
Number of ordered pairs / n / 1-Var Stats L2
Sum of xy products / Sxy / L1*l2àL3
1-Var Stats L3
Regression Equation Calculation
Using the terms in the table, calculate the regression equation for your data of women.
Calculate Correlation Coefficient and Coefficient of Correlation
Calculate the correlation coefficient and coefficient of correlation for your data of women.
9; ANOVA
(a) ANOVA for Data of Men.
Complete the ANOVA Data Table using data of the heights from your research team members. Write your name on line one and each other student’s name on the lines in the subsequent column headings.
Data Table for men.
/ 1. ______/ 2. ______/ 3. ______/ 4. ______/ 5. ______/ 6. ______/Sx
Sx2
N
Determine values for degrees of freedom and write them in the df column of the ANOVA table.
A. Calculate the Correction Factor. Write it here. ______
Calculate the necessary values required for ANOVA and write each result in its correct cell of the ANOVA Table.
B. Calculate Sum of Squares Total
C. Calculate Sum of Squares Group
D. Calculate Sum of Squares Error
E. Calculate Mean Squares Group
F. Calculate Mean Squares Error
G. Calculate Variance Ratio
ANOVA Table. Calculations for men.
Source / Df / SS / MS / V.R. /Total
Group
Error
9; ANOVA
(b) ANOVA for Data of women.
Complete the ANOVA Data Table using data of the heights from your research team members. Write your name on line one and each other student’s name on the lines in the subsequent column headings.
Data Table for women.
/ 1. ______/ 2. ______/ 3. ______/ 4. ______/ 5. ______/ 6. ______/Sx
Sx2
N
Determine values for degrees of freedom and write them in the df column of the ANOVA table.
A. Calculate the Correction Factor. Write it here. ______
Calculate the necessary values required for ANOVA and write each result in its correct cell of the ANOVA Table.
B. Calculate Sum of Squares Total
C. Calculate Sum of Squares Group
D. Calculate Sum of Squares Error
E. Calculate Mean Squares Group
F. Calculate Mean Squares Error
G. Calculate Variance Ratio
ANOVA Table for women.
Source / Df / SS / MS / V.R. /Total
Group
Error
D. Write conclusions based on the result of the project.
1. Describe and compare the histograms, frequency polygons and box plots for the data for the heights of men and women.
2. Describe and compare the scatter plots for the heights and weights of the data of men and women.
3. Describe and compare the results of the confidence intervals and hypothesis tests for the data of men and women.
4. Describe and compare the regression and correlation analysis for the data of men and women.
5. Describe and compare the ANOVA calculations for the data of men and women.
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