Graphing 1
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Biometry, Graphing 1
1
Biometry
Graphing 1
Text: Sections 2.1, 2.2, 2.5
Objectives
o
Introduction to Biometry lab
o
Classes of Data; Roles of Different Variables
o
Introduction to JMP software o
Creating Basic Graphs (“charts”) in JMP o
Interpreting Graphs and Creating Figures
Classes of Data
Categorical data
: the groups or categories for the data; often employed in making a frequency table or bar chart as the independent variable.
Discrete numerical data
: a single value, or group of possible values, that the data can take on, and defines a group or category; often employed in making a frequency table or histogram.
Continuous numerical data
: an interval of values on the real axis that defines or describes a group; often employed in making a frequency table or histogram. When plotting this data as a frequency table or histogram, the data is treated as discrete by “binning” the data into groups
.
Tips for making Figures
●
Think about which type of graph would best display your data. Often, one type of graph is clearer to interpret than others.
●
The independent variable goes on the x-axis; the dependent variable goes on the y-axis.
(The independent variable is that variable that we/you hypothesize is causing the other (or dependent) variable to behave the way that it is behaving).
●
Make sure to display variation
in your data, not just the raw data or means. Standard deviation or standard error bars are one good way to do this.
●
Be sure that the axes are labeled properly and clearly!
●
Be sure to add a descriptive figure legend for each graph underneath it
. The graph combined with the legend, is a figure. ●
Double-check your figure once it’s done. Does it look like you expected it should, from the data? This final check will help you catch a lot of errors. Don’t just make a graph and consider it done: always ask yourself if it looks right!
Biometry, Graphing 1
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●
Note that the graphs below are not properly formatted figures. Make sure you using the formatting guide (below, after part B) for your final figure formatting.
Tips and terminology on interpreting distributions of numerical variables
When interpreting a numerical distribution (dotplot or histogram) for one variable, look for the overall pattern
and striking deviations
from that pattern (from Moore & McCabe’s Introduction to the Practice of Statistics
, Freeman):
Overall pattern:
center:
the class, or value of the data with roughly half of data on each side (in the class where you reach 50%), and/or
the class or value where the data balances (visually). These correspond to the locations of the median and/or mean.
variability: the range of the data, from the minimum to the maximum (but without the outliers). tail
: portion of a distribution far from the mode(s), where relative frequencies are low.
shape: see Figure 2.21 below for examples of these shapes
roughly symmetric = the right and left halves of the distribution are nearly mirror images of one another. One important type: bell-shaped (“bell curve”)
skewed right
= right tail is stretched out (also positively skewed
)
skewed left
= left tail is stretched out (also negatively skewed
)
mode
: a peak or high-point in the distribution (or modes
). When plotted, data can be unimodal
, bimodal
or multimodal
.
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Striking
deviations from the overall pattern:
outliers:
data points whose values are much higher or lower than the rest of the data set. Always check your data and graphs for outliers. In order to qualify as an outlier, there should be at least one or two
classes/bars (in a histogram) between the remaining data and the outlier(s). gaps
:
are there any gaps (empty classes/bars) in the middle of the data? Gaps that make an outlier an outlier are not considered in this case.
Types of graphs ( “charts” in JMP), examples, and when to use each type
●
bar chart
: can be used to display categorical data
. The categories are plotted on the x-
axis. Data are usually displayed as frequencies (counts) or relative frequencies (%), on the y-axis.
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Figure 1: Bar graph of the relative frequency and cause of manatee deaths for Florida in 2008.
Biometry, Graphing 1
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Figure 2: Comparative bar graph of the number of federally threatened (blue) and endangered (red) species in the United States as of 2010.
●
histogram
: ‘bar chart’ for quantitative data. Data are displayed as frequencies, relative frequencies or percent frequency distributions. For continuous data, data are divided into classes or intervals (usually equal in width), and are generally plotted on the horizontal
axis, with ether the endpoints or the midpoint of the class displayed. The classes are usually of the form [a,b), or closed on the left and open on the right. For discrete data
, the range of possible data values are generally shown on the horizontal axis, with the value displayed in the middle of the bar.
Figure 3: Histogram of the height of pygmy pine (
Lepidothamnus
laxifolius
)
at 20 years of age in New Jersey
.
Biometry, Graphing 1
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●
pie chart
:
an alternative display to the bar chart for categorical data
. Data are displayed as relative frequencies (the distribution of the percent or proportion of data found in each category, out of 100).
Figure 4:
Side-by-side pie chart of electricity generation by fuel type in the United States for 1990 and 2009. Coal = Red, Nuclear = Blue, Natural Gas = Yellow, Petroleum = Orange, and Renewable Energy = Green.
●
segmented bar chart
:
an alternative display to the bar and pie charts for categorical data
. This type of graph is particularly useful for comparing the same variable from two separate populations or samples
. Data are treated as in the bar chart description. Data from each class of one population or sample are “stacked” within the appropriate bar on the x-axis. Data are displayed as relative frequencies (the distribution of the percent or proportion of data found in each class or category) on the y-axis. (Note that JMP variously
refers to this type of graph as a mosaic plot
or a stacked bar chart
.)
Figure 5:
Stacked bar graph of power generation (kWh) by fuel type in the United States for 1990 and 2009. Coal = Red, Nuclear = Blue, Natural Gas = Yellow,
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Petroleum = Orange, and Renewable Energy
= Green.
Figure 6:
Mosaic plot of electricity generation by fuel type in the United States for 1990 and 2009. Coal = Red, Nuclear = Blue, Natural Gas
= Yellow, Petroleum = Orange, and Renewable
Energy = Green.
Biometry, Graphing 1
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Formatting Figures in the Biometry Course
The example charts above are not properly formatted for the biometry course and do not include a written figure legend. You will need a written figure legend, it should be sequentially numbered, and appear underneath the figure. The first line of the figure legend is the title of the figure and should identify the type of plot being display as well as what the content of the figure is. Additional lines after the figure identify any additional information that the reader needs to understand in order to read the figure. Be sure to add/format the axis-labels. DO NOT
include a graphical legend or “key”. Writing out the graphical legend or key in your
own words help you connect the process of making a figure to the act of interpreting the
figure. In other contexts (outside of this course) graphical keys/legends might be appropriate. This is an example of how a bar chart should look in the biometry course, including the figure legend:
Figure 1: Bar graph of the bubble-gum preferences for Rowan University Students. Students chose between Bubblicious (b), Another brand (o), Trident (t), and Winterfresh
(w) gum.
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Lab Exercise
Use the JMP website and instruction below to guide you through the following
exercises and help familiarize yourself with the use of this software. Use the “Survey” data
– posted on drive - in the exercises below.
Part 1
A.
Using Graph Builder, create the three different plots below using a single categorical variable. Make a space below to copy those figures into this assignment and write a figure legend for each figure (see instructions above). Do not use the Gender variable for this section. o
Bar chart Figure 1: Bar graph of favorite music. Students had to choose between c which country, hh which is hip hop, j which is jazz, o is other or r which is rock. o
Pie chart
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Figure 2: Pie chart of Favorite Music. Students had to choose between country colored in blue, hip hop colored in pink, jazz colored in green, other colored in purple or rock colored in orange.
o
Mosaic plot
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Figure 3
: Mosaic chart of favorite music. Students had to choose between country colored in blue, hip hop colored in pink, jazz colored in green, other colored in purple or rock colored in orange. Questions: 1.
Which graph from “A” do you think gives the clearest depiction of the variable you chose? Why?
The clarity of the bar graph in depicting the variable "fav music" is further enhanced by its clear labeled x and y axes. The x-axis typically represents the different categories of favorite music, while the y-axis indicates the frequency of respondents favoring each category. This explicit labeling provides viewers with a precise understanding of the data and facilitates easy interpretation. In contrast, pie charts and mosaic plots may lack the straightforward labeling found in bar graphs,
making it more challenging for individuals to accurately comprehend and compare the distribution of preferences for different music genres. The combination of clear labeling and simplicity in the bar graph makes
it a superior choice for conveying information about the variable "fav music."
2.
Describe the main features of the variable/distribution. What does the graph tell you (i.e. interpret the data)?
The graph tells us that most people chose the ‘other’ category which means that they preferred something other than the choices provided. After the other the most preferred category is rock, then it's hop hop, then country and the least preferred kind of music is jazz. B.
Using either the same variable as in A, or another categorical variable we have not yet used in class or lab, create two separate groups based on gender, and make the following graphs:
o
Two comparative bar charts
(Hint: One variable should be in “X” and the other should be in “Overlay” in graph builder)
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Figure 4: Comparative bar charts of Favorite Music (blue) and gender (red). Students had to choose between c which country, hh which is hip hop, j which is jazz, o is other or r which is rock.
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Figure 5: Comparative bar graphs of gender versus favorite music. Students had to choose between country colored in blue, hip hop colored in pink, jazz colored in green, other colored in purple or rock colored in orange.
o
Two SETS
of pie charts
(one set by gender, one set by your other categorical variable. Hint: use the “X” and “Group X” areas in Graph Builder to make these plots)
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Figure 6: Side-by-side pie chart of Favorite Music by Gender (F for Female and M for Male). Students had to choose between country colored in blue, hip hop colored in pink,
jazz colored in green, other colored in purple or rock colored in orange.
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Figure 7: This pie chart illustrates the breakdown of different music types showcased by gender. Each slice represents a specific genre, and the size of each slice corresponds to the proportion of that genre within the respective gender category (Male is Blue and Female is Red).
o
Two comparative segmented
bar charts
(Hint: the setup here is the same as in the normal comparative bar charts, but you “stack” the bars)
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Figure 8:
Comparative segmented bar chart of gender vs. favorite music. Students had to choose between c which country, hh which is hip hop, j which is jazz, o is other or r which is rock and the graph was segmented into males which is red and blue which is female.
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Figure 9: Comparative segmented graph of gender versus favorite music. Students had to choose between country colored in blue, hip hop colored in pink, jazz colored in green, other colored in purple or rock colored in orange.
Questions: 3.
Which graph from part “B” do you think is best for comparing the genders?
Why?
Figure 4 is the best for comparing genders because it has two different
bars for each gender for each kind of music. Each of the bars can be read exactly due to the availability of a labeled x and y axis. Therefore, we can be precise as to how each gender likes each kind of music making Figure 4 the best for comparing genders. 4.
Describe the main features of the data/distributions. What does the graph tell you (i.e. interpret the data)?
The bar chart allows easy comparison of favorite music between genders with clear labels. The pie chart shows the proportion of each music type within genders but may be less straightforward to compare.
The mosaic chart depicts the joint distribution of gender and favorite
Biometry, Graphing 1
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music, offering insights into their relationship but introducing complexity. Examples of two comparative bar charts
with the same data arranged differently:
Examples of segmented bar charts
made from the comparative bar charts above:
Part 2
C.
Make a histogram using the foot length data (in cm) in the Survey Data file.
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Figure 10:
Histogram of the foot length data (in centimeter). Question: 5.
What does the histogram from “C” tell you? Interpret the data, including making comments on the shape of the distribution (see tips above for guidance).
Histogram from “C” indicates that most of the people have a foot length between 20 cm to 32 cm. The outliers in the histogram are present after 42 cm. The graph is skewed to the right (positive skew) indicating that most of the data is clumped together to the left of the graph. D.
Using the data below (which come from your textbook), make another histogram. You will need to enter these data into JMP in one column.
Total annual protein production (lbs.) for 28 two-year old Holstein cows
425
481
477
434
410
397
438
545
528
496
502
529
500
465
539
408
513
496
477
445
546
471
495
445
565
499
508
426
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Figure 11: Bar graph of the total annual production in lbs. for 28 two-year old Holstein cows. Question: 6.
What does the histogram from “D” tell you? Interpret the data, including making comments on the shape of the distribution (see tips above for guidance).
The histogram from “D” tells us that 475 lbs. to 500 lbs. of protein is produced by the most number of cows. Additionally, extreme levels (minimum and maximum) of protein are produced by the least amount of cows. E
. Enter the data shown in the table below (from exercise 2.2.9, pages 39-40 in your textbook) into two columns in JMP: one column will list the variable “Length, in microns”, and the other column will list the variable “Frequency”, or “Number of Individuals” (your choice).
Frequency distribution of trypanosome parasite lengths in the blood of a rat
Length
(
μ
m)
Frequency (# individuals)
Length
(
μ
m)
(continued)
Frequency (# individuals)
(continued)
15
1
27
36
Biometry, Graphing 1
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16
3
28
41
17
21
29
48
18
27
30
28
19
23
31
43
20
15
32
27
21
10
33
23
22
15
34
10
23
19
35
4
24
21
36
5
25
34
37
1
26
44
38
1
Figure 12: Histogram for Length in microns and Frequency of number of individuals. F
. In two new spreadsheet columns, list the same data from ”E” in only 6 categories (combine every 4 length classes, in numerical order). To do this, you will have to add up the number of individuals in each set of 4 length classes to calculate the “Frequency” or “Number of Individuals” for each new length class. The final format should look like this:
Size Category
Frequency
1
52
2
63
3
118
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4
153
5
103
6
11
Data showcases size category and its frequency
G. Create 2 separate histograms using the data in “E” and “F”. Depending on what version of JMP you have, you may need to change the “length” and “size category” variables to nominal prior to plotting. “Frequency” should be in the “freq” box for both figures. The plot in “E” should have 24 bins and the plot in “F” should have 6 bins. E. Figure 13: Histogram for Length in microns and Frequency of number of individuals.
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F. Figure 14: Histogram for size category and frequency of number of individuals. Questions: 7.
What does each histogram tell you? Interpret the data.
Each histogram indicates the length in microns and size category in relation to the frequency of the number of individuals. Histogram in figure 13 has more of a central tendency. The two peaks indicate bimodal data. While the data shown in figure 14 shows a skew to the left indicating the majority of data points are concentrated on the right side of the histogram.
8.
How did changing the width of each class (length, in this case) change your interpretation of the data?
Changing the width of each class in a histogram, which represents the range of values for a set of data, can affect how we perceive and understand the information. If we make the classes narrower, the histogram becomes more detailed, allowing us to see smaller variations in the data and making it more sensitive to outliers. On the
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other hand, if we make the classes wider, the histogram looks smoother, providing a general overview of the data but potentially losing some important details. The histogram from E shows measurements from a data set of multiple data points, whereas the histogram from F has a graph from a summarized data resulting in a histogram with significant drops on either side of the graph. Submission Details
●
Due in next week’s lab:
●
Review the course syllabus for information on completion and evaluation of lab assignments.
●
Your assignment should include all of the graphs/charts you were asked to make,
with figure legends, and correctly formatted as figures. You will also need to turn
in your answers to questions 1-8. ●
This assignment should be completed with your lab group.
Upload a final copy of your completed assignment to the link on Canvas. Adapted for JMP 16 F21 by NAR
Adapted for Remote F20 by NAR
Reformatted and edited F19 by NAR
Spring 14 – chd & dcw after tjo, cer, lms, nar; Added Figure Legends and altered assignment Ruhl 9/19/2014
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