Paper Towel Efficiency
Teacher Notes
This lab can be utilized as an introductory exercise to the scientific method, as an
ecology activity, as a biochemistry-related exercise, and as a lab to reinforce statistical
analysis. In addition, it is quite suited for the physical sciences, stressing concepts of
measurement, repeatability, and inherent variation (error).
In this exercise, students are challenged to compare the water absorbing properties
of paper towel brands. Teachers can direct the activity procedure, though it might be
more revealing to allow students to design their own investigation. A standard procedure
is as follows:
1. Cut one paper towel sheet into 4 equivalent sections (this variation saves on cost).
2. Fold each section 3 times.
3. Mass the sections.
4. Immerse each section into a beaker of water for 10 seconds.
5. Remove and hold each section with forceps; allow to drain for 10 seconds.
6. Mass the wet sections.
7. For each section, calculate the change in mass, % change in mass, and cost
efficiency (% mass change/cost in dollars).
8. Repeat for each brand of towel.
Questions to consider:
Why not simply compare the changes in mass when assessing towel performance?
Performance is better assessed by a ratio, taking into account the change with respect to
mass.
How might the cost efficiency be more accurately reported (what further information
might you need)? How many sheets are in each roll.
What two kinds of variation are necessary to consider when comparing the performances
of the brands? Variation within each group (results of tests of one brand), and variation
of the means between groups.
What is the null hypothesis in this study? The brands will not vary in performance
outside of chance, or the brands are equally effective at absorbing water.
What statistical analysis is most appropriate for comparing the means (performances) of
each brand, assuming more than two brands are tested? ANOVA.
How might ecologic considerations be addressed in this study? Composition of towels,
how towels are produced (chlorine bleached for whiteness, etc.), packaged, shipped.
Also, performance (water absorption) should be addressed.
On the next page, an ANOVA analysis is presented for a study as described above. In the
first, towels A, B, C, and D are compared. Their % change in mass are as follows:
Towels (%mass
change)
Trial 1
Trial 2
Trial 3
Trial 4
Avg.
Brand A
Brand B
Brand C
Brand D
960
900
980
920
940
800
770
850
810
808
1050
1100
990
1020
1040
780
740
720
730
743
The ANOVA results, generated by using Microsoft excel and described on the following
sheet are as follows (this table is directly from the program printout):
Anova: Single Factor
SUMMARY
Groups
Column 1
Column 2
Column 3
Column 4
Count
4
4
4
4
ANOVA
Source of
Variation
SS
Sum
3760
3230
4160
2970
df
Between Groups
Within Groups
213350
15950
3
12
Total
229300
15
Average
940
807.5
1040
742.5
Variance
1333.333
1091.667
2200
691.6667
MS
F
71116.67
1329.167
53.5047
P-value
3.22E07
F crit
3.4903
Notice that the average, count, and sum of each set are given. This will students to
confirm that they entered the data on the spreadsheet correctly (vertically, in the first four
columns).
Notice the Between Group and Within Group variation is shown (SS = sum of squares, df
= degrees of freedom).
**In the above study, the F value is greater than the F critical, indicating that the null
hypothesis can be rejected (the variation appears greater than chance and probably due to
inherent differences in the towels). The low p value, 3.22 x 10-7, indicates a high degree
of confidence in this interpretation. A p of .05 (95% confidence interval) is usually
accepted as a cutoff.
ANOVA
To perform an ANOVA stat analysis on your data set, using a computer program:
1.
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8.
9.
Go into Microsoft excel.
Enter your data sets in the vertical columns provided (the spread sheet).
Go into “tools”, select “add-ins”.
Select “analysis tool pack”. (hit OK)
Go back into “tools”, select “data analysis”.
Select “anova single factor”. (hit OK)
Highlight your data on the spread sheet (dotted line margin will surround data).
Hit OK.
Your analysis will appear. You can print out and/or save this as a document.
Interpretation:
If the F value is larger than the F-critical, the null hypothesis can be rejected. This
indicates that the variation seen in your data sets (i.e. your experimental treatments)
appears to be real. The variation seems to be due to the treatment and not just to random
chance such as sampling error (variation).
Conversely, if the F is equal to or lower than F-critical, the null hypothesis can be
accepted. This suggests that the variation observed between your data sets is likely due
to chance (sampling). You cannot say with confidence that the experimental treatments
varied in effect.
Also, p value gives a confidence level. Typically, a 0.05 number (95% confidence level)
is used as a cutoff, though more stringent studies might wish to use a 0.01 cutoff. If your
obtained p value is less than 0.05 (your cutoff), you are more than 95% confident that the
null hypothesis can be rejected, meaning that you think the variation is a real effect.
Conversely, a p value greater than 0.05 suggests that you are not confident that the
variation is real, so you tend to accept the null hypothesis.
Reminder: the null hypothesis states that the experimental groups do not vary. That is,
your treatment does not produce an effect outside of normal variation.