Lab 7 biometry done
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Rowan College, Burlington County *
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280
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Mathematics
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Apr 3, 2024
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MTH 280 Lab 7 – Common probability distributions in biology 1 Text: Sections 2.2, 3.4, 3.6, 3.7, Chapter 4 Objectives & topics o
Collecting and plotting data from different distributions common in biology o
Familiarizing yourself the kinds of variables likely to have each type of distribution How to fit probability distributions to data, and test the fit, in JMP A) Plot the data set you want to analyze by making a histogram of the data. For clarity and ease of interpretation you should:
Turn the graph to a horizontal orientation (“Stack”)
Turn off the “outlier box plot” by unchecking it under the red triangle at the top of the histogram
Turn off the Quantiles by unchecking them under “Display Options”
Add in the “count axis” in the “Histogram options” B) Click on the red triangle at the top of the histogram and scroll down to “Continuous Fit” or “Discrete Fit” depending upon the type of data you have. Select the type of distribution you want to fit in the menu that opens up. (If you are trying to create a binomial distribution, see the note on the supplemental sheet) C) Click on the red triangle next to the name of the fitted distribution and select “Goodness of Fit”. This tests the null hypothesis (H
o
) that the data come from this particular distribution, giving you a test statistic (names vary depending upon the test) and the p- value associated with the test statistic. Remember, we are using
=0.25 here. A low p- value (p<0.25) rejects this null hypothesis, indicating that the data do NOT fit this distribution. If p > 0.25, then you cannot reject the null hypothesis and you can conclude you have evidence that the data are consistent with the distribution. Lab exercise (what to do and hand in): Use the posted data “BabyBoom.jmp” to evaluate the following probability distributions. This will require some data manipulation, so follow the lab closely through each step. Instructions on fitting continuous and discrete probability distributions to datasets are found at the end of this lab For each dataset (A-D) answer the questions in a word document.
MTH 280 Lab 7 – Common probability distributions in biology 2 Dataset 1: Number of girls born for every 2 babies born
Using the “BabyBoom.jmp” file, calculate the number of girls born for every two babies born in this dataset. Go in order of the births, using the table below to calculate whether there were 0, 1, or 2 girls born for every two babies. Pair of babies born # girls born Pair of babies born # girls born Babies 1 and 2 2 Babies 23 and 24 2 Babies 3 and 4 0 Babies 25 and 26 1 Babies 5 and 6 1 Babies 27 and 28 0 Babies 7 and 8 1 Babies 29 and 30 1 Babies 9 and 10 0 Babies 31 and 32 1 Babies 11 and 12 0 Babies 33 and 34 0 Babies 13 and 14 2 Babies 35 and 36 0 Babies 15 and 16 1 Babies 37 and 38 1 Babies 17 and 18 1 Babies 39 and 40 0 Babies 19 and 20 0 Babies 41 and 42 1 Babies 21 and 22 1 Babies 43 and 44 2
Create two new rows in the JMP file, and enter these data. Make sure the data are the appropriate format (i.e. “numerical” or “character”, etc.)
Fit a probability distribution to these data. Look at the type of data these are and the descriptions earlier in this lab about types of probability distributions.
Submit the answers to the following in the word document for Dataset A: 1A – Identify the appropriate distribution for these data, and make a clear argument for your choice. The best fit was binomial distribution, represent the distribution when data are combined from two different distributions. 1B - Fit the distribution to the data and draw your conclusion. Include JMP output showing the distributions, with all graph axes completely labeled. Figure 1 - number of girls born for every two babies born. 1C - Report the test statistic, p-value, and make a statement interpreting the result using α=0.25
MTH 280 Lab 7 – Common probability distributions in biology 3 to determine if you can reject the null hypothesis. (If you can – binomial and multimodal do not provide goodness of fit options) binomial do not provide goodness of fit options 1D - Propose two biological variables that could fit the distribution, meeting all assumptions. Do not use variables discussed by the instructor in class, or addressed in this lab. (You may work in groups and use the same examples as your group members) Age for example Old and Yung in a class. Color of eyes as dark or light color eyes
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MTH 280 Lab 7 – Common probability distributions in biology 4 Dataset 2: Number of babies born each hour in the 24-hour period
Using the “BabyBoom.jmp” file, calculate the number of babies born every hour for the 24-hour period. Remember, each hour ends at 59 minutes after the hour, as shown in the data table below. Hour # babies born Hour # babies born Hour # babies born 0:00 to 0:59 1 8:00 to 8:59 2 16:00 to 16:59 2 1:00 to 1:59 3 9:00 to 9:59 1 17:00 to 17:59 1 2:00 to 2:59 1 10:00 to 10:59 3 18:00 to 18:59 3 3:00 to 3:59 0 11:00 to 11:59 1 19:00 to 19:59 4 4:00 to 4:59 4 12:00 to 12:59 2 20:00 to 20:59 3 5:00 to 5:59 0 13:00 to 13:59 1 21:00 to 21:59 2 6:00 to 6:59 0 14:00 to 14:59 4 22:00 to 22:59 2 7:00 to 7:59 2 15:00 to 15:59 1 23:00 to 23:59 1
Create two new rows in the JMP file, and enter these data. Make sure the data are the appropriate format (i.e. “numerical” or “character”, etc.)
Fit a probability distribution to these data. Look at the type of data these are and the descriptions earlier in this lab about types of probability distributions.
Submit the answers to the following in the Word document for Dataset B: 2A – Identify the appropriate distribution for these data, and make a clear argument for your choice. The best fit was Poisson distribution, which represents the distribution of the number of individuals, events, counts, etc., in a given time/space/unit. 2B - Fit the distribution to the data and draw your conclusion. Include JMP output showing the distributions, with all graph axes completely labeled. Figure 2- Number of babies born each hour in the 24-hour period.
MTH 280 Lab 7 – Common probability distributions in biology 5 2C - Report the test statistic, p-value, and make a statement interpreting the result using α=0.25 to determine if you can reject the null hypothesis. (If you can – binomial and multimodal do not provide goodness of fit options). p-value 0.5802. We can not reject the null hypothesis 2D - Propose two biological variables that could fit the distribution, meeting all assumptions. Do not use variables discussed by the instructor in class, or addressed in this lab. (You may work in groups and use the same examples as your group members). How many times does it rain in the summer months. Another possibility is to measure the amount of potassium in the soil in a 5-inch pot monthly for a year.
MTH 280 Lab 7 – Common probability distributions in biology 6 Dataset 3
: Time between births (in minutes)
Using the “BabyBoom.jmp” file, use the variable “Time Between Births (Minutes)”.
Fit a probability distribution to these data. Look at the type of data these are and the descriptions earlier in this lab about types of probability distributions.
Submit the answers to the following in the word document for Dataset C: 3A – Identify the appropriate distribution for these data, and make a clear argument for your choice. The best fit was Exponential distribution, probability that the event will occur per unit time is constant. 2B - Fit the distribution to the data and draw your conclusion. Include JMP output showing the distributions, with all graph axes completely labeled. Figure 3- Time Between Births in Minutes 3C - Report the test statistic, p-value, and make a statement interpreting the result using α=0.25 to determine if you can reject the null hypothesis. (If you can – binomial and multimodal do not provide goodness of fit options) p-value 0.3500. We cannot reject the null hypothesis 3D - Propose two biological variables that could fit the distribution, meeting all assumptions. Do not use variables discussed by the instructor in class, or addressed in this lab. (You may work in groups and use the same examples as your group members) Population growth of bunnies during 5 years, distance a slime mold can reach in 1 hour. Dataset 4
: Birth weight of babies
Using the “BabyBoom.jmp” file, use the variable “Birth Weight (grams)”.
Fit a probability distribution to these data. Look at the type of data these are and the descriptions earlier in this lab about types of probability distributions.
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MTH 280 Lab 7 – Common probability distributions in biology 7
Submit the answers to the following in the word document for Dataset D: 4A – Identify the appropriate distribution for these data, and make a clear argument for your choice. The best fit was SHASH distribution, since the normal distribution is unimodal, symmetric and has a light to moderate tail weight.
4B - Fit the distribution to the data and draw your conclusion. Include JMP output showing the distributions, with all graph axes completely labeled. Figure 4 - Birth Weight in grams. 4C - Report the test statistic, p-value, and make a statement interpreting the result using α=0.25 to determine if you can reject the null hypothesis. (If you can – binomial and multimodal do not provide goodness of fit options) p-value 0.3500. We cannot reject the null hypothesis 4D - Propose two biological variables that could fit the distribution, meeting all assumptions. Do not use variables discussed by the instructor in class, or addressed in this lab. (You may work in groups and use the same examples as your group members) Heart disease in males of age 25 to 65. Age that infants start to walk.