14B

Arts and Humanities STEM Education Business
16 18 14 16
18 20 18 20
17.5 18.5 16 15.5
19 22 15.5 14
15 18 16.5 12
17.5 20.5 17 12
15.5 16.5 13 15
19.5 14 19 16.5
21 17 15 17.5
14 19 16 17
18 23 20 15
16.5 16 12 18
Source df Sum of Squares Mean Square F-Statistic P-value
Group 2 73.04 36.52 2.198 0.11
Error 250 4154.00 16.62
Total 252 4227.00
Fertilizer Level Height of Plant (inches)
Low 23.2, 20.9, 21.5, 25.3
Medium 24.6, 27.7, 22.5, 30.1
High 29.2, 30.2, 31.1, 33.6
Source Degrees of Freedom (df) Sum of Squares Mean Square F-Statistic
Group 1

(The number of groups minus 1)

 SSGroup
Error (The total number of data points minus the number of groups) SSError
Total  1

(The total number of data points minus 1)

 SSGroup + SSError
Source Degrees of Freedom (df)
Group
Error
Total
Source Degrees of Freedom (df) Sum of Squares Mean Square
Group 2 55.9134
Error 9 140.0108
Total 11 195.9242
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Make connections between the values presented in an ANOVA table. 1–3
Describe the shape of the F Distribution. 4
Describe how the P-value is represented on the F Distribution. 5
Describe how the F-statistic is used in hypothesis testing for a one-way ANOVA. 6
Use the P-value to make a conclusion about an ANOVA. 7, 8

Several people gathered around a table with papers, a computer, and other work materials. A box plot labeled “Hours of Sleep Per Night” on the horizontal axis and containing “Freshman,” “Sophomore,” “Junior,” and “Senior” on the vertical axis. For freshman, the line goes from approximately 5.8 to 9.9, with the box’s low end at approximately 7.2, the high end at approximately 8.5, and the middle line at approximately 7.9. For sophomore, the line goes from approximately 5.7 to 10.5, with the box’s low end at approximately 7.4, the high end at approximately 8.8, and the middle line at approximately 8.2. There is also a point at approximately 5. For junior, the line goes from approximately 6 to 10, with the box’s low end at approximately 7.5, the high end at approximately 8.3, and the middle line at approximately 7.9. For senior, the line goes from approximately 6.3 to 9.6, with the box’s low end at approximately 7.7, the high end at approximately 8.6, and the middle line at approximately 8. There is also a point at approximately 5 and another at approximately 5.8.

ANOVA Table:

Source df Sum of Squares Mean Square F Statistic P-value
Group 3 0.7708 0.2569 0.2736 0.8444
Error 249 233.8 0.939
Total 252 234.5708

A box plot labeled “Ramen Rating” on the x-axis, with “Cup,” “Pack,” and “Bowl” on the y-axis. For “Cup,” the low point is at approximately 2 and the high point is at approximately 5. The low end of the box is at approximately 3, the high end is at approximately 4, and the middle line is at approximately 3.8. There are points at approximately 0.5 and 1.5. For “Pack,” the low point is at approximately 3 and the high point is at approximately 5. The low end of the box is at approximately 3.5, the high end is at approximately 4.5, and the middle line is at approximately 4. For “Bowl,” the low point is at approximately 2.2 and the high point is at approximately 5. The low end of the box is at approximately 3.3, the high end is at approximately 4.8, and the middle line is at approximately 3.7. There are also points “y bar sub one” at approximately 3.4, “y bar sub two” at approximately 4.1, and “y bar sub three” at approximately 3.8.

ANOVA Table:

Source df Sum of Squares Mean Square F Statistic P-value
Group 2 5.466 2.734 3.2 0.0456
Error 87 74.34 0.8545
Total 89 79.808

A table and a box plot. The table is titled “Descriptive Statistics” and has the columns “Group,” “Sample Size,” “Mean,” “Standard Deviation,” and “Standard Error.” The first row reads “Drug 1,” 6, 204, 11.5, 4.70, the second row reads “Drug 2,” 6, 191, 12.5, 5.10, and the third row reads “Drug 3, 6, 176, 12.9, 5.28. Beneath this is a box plot labeled “Total Cholesterol (mg/dL)” on the horizontal axis. For Drug 1, the low point is at approximately 185 and the high point is at approximately 220. The low end of the box is at approximately 198, the high end is at approximately 209, and the middle line is at approximately 205. For Drug 2, the low point is at approximately 175 and the high point is at approximately 210. The low end of the box is at approximately 182, the high end is at approximately 196, and the middle line is at approximately 193. For Drug 3, the low point is at approximately 160 and the high end is at approximately 190. The low end of the box is at approximately 167, the high end is at approximately 188, and the middle line is at approximately 180. There are points on the horizontal axis “y bar sub 1” at approximately 204, “y bar sub 2” at approximately 191, and “y bar sub 3” at approximately 178. A table and a box plot. The table is titled “Descriptive Statistics” and has the columns “Group,” “Sample Size,” “Mean,” “Standard Deviation,” and “Standard Error.” The first row reads “Drug 1,” 5, 204, 1.58, 0.707, the second row reads “Drug 2,” 5, 191, 1.58, 0.707, and the third row reads “Drug 3, 5, 178, 1.58, 0.707. Beneath this is a box plot labeled “Total Cholesterol (mg/dL)” on the horizontal axis. For Drug 1, the low point is at approximately 202 and the high point is at approximately 206. The low end of the box is at approximately 203, the high end is at approximately 205, and the middle line is at approximately 204. For Drug 2, the low point is at approximately 188 and the high point is at approximately 193. The low end of the box is at approximately 190, the high end is at approximately 192, and the middle line is at approximately 191. For Drug 3, the low point is at approximately 176 and the high end is at approximately 180. The low end of the box is at approximately 177, the high end is at approximately 179, and the middle line is at approximately 178. There are points on the horizontal axis “y bar sub 1” at approximately 204, “y bar sub 2” at approximately 191, and “y bar sub 3” at approximately 178.

error sum of squares (SSError)
the total variation within the groups of interest.
group sum of squares (SSGroup)
the total variation between the groups of interest.
mean square
the sum of square values divided by the degrees of freedom associated with the respective source (i.e., Group or Error).