Name: _____________________
The Moldy Bread
Statistical Worksheet
Question of the lab: Does temperature and/or humidity effect fungal growth?
Brand of Bread? ______________________________________________________________________________
Based on what you know, how do you think temperature will effect fungal growth? How do you
think humidity will effect fungal growth? Note these are the general hypotheses (Think science
fair). They will be the ones you focus on and report in your lab report.
HA1:__________________________________________________________________
Lower temperatures will cause a decrease in fungal growth and higher
temperatures will cause increased fungal growth. Direct relationship between
____________________________________________________________________
the two.
_________________________________________________
HA2:__________________________________________________________________
High levels of humidity will cause an increase in fungal growth showing a direct
relationship between the two.
____________________________________________________________________
_________________________________________________
We are using two treatments and comparing them to a control group. Write out the null hypotheses.
Note: this is not to report in your lab report.
H01:___________________________________________________________________________
Temperature change will have no effect on fungal growth.
_____________________________________________________________________________
Increased humidity will not impact fungal growth.
H02:___________________________________________________________________________
_____________________________________________________________________________
You can use the following table as an idea for how to write your data.
Date:
Zip locks
(sample #)
R1
R2
R3
Room
Temperature
Percent cover
# of squares
covered
Refrigerated
Zip locks
(sample #)
Percent cover
# of squares
covered
F1
F2
F3
Humidity
Zip locks
(sample #)
H1
H2
H3
1
Percent cover # of
squares covered
R4
R5
Average
F4
F5
Average
H4
H5
Average
Observations:__________________________________________________________________
The refrigerator samples developed no mold across the 21 days while the room temperature
______________________________________________________________________________
samples developed a small/medium amount of mold and the humidity samples developed the
______________________________________________________________________________
most.
Record all the averages you calculated before in the table below. This will be the table you use to make
your graph. The results show amount of mold growth on each bread sample and compare it to the
number of days that have passed. Although you are free to use any software you like to produce your
graph, most students will use Excel. For the time being, draw your graph in the space below.
Day
Room Temp
Refrigerated
0
3
6
9
12
15
18
Percent Fungi Growth(%)
21
2
Humidity
Name: _____________________
Day
STOP THE REST OF THE WORKSHEET SHOULD BE DONE WITH YOUR TA OR WHILE WATCHING YOUR LECTURE.
Please copy the data given to you from your lab instructor into the table below. This is the
information you will be using for your stats test. You will not be taking information from any
other day. Note that you have a total of 5 samples. This value is known as N. So N=5. Calculate
the average by dividing the sum (calculated in the table to the left) by N. Record this value in
the spaces given to the left of the table. Recall that in statistics, ! refers to the value and !"
refers the mean. Therefore the sample # will be put in for !.
Sample #
Room
temperature
Percent cover
Refrigerated
Humidity
Percent cover
Percent cover
!̅!""# %&#'&()*+(& =
1
2
3
4
5
Σ &!""# %&#'&()*+(&
5
=_________________
Σ !!"#$%&"$'(")
5
=_________________
#̅!"#$%&"$'(") =
Sum (S)
#̅*+,%)%(- =
Σ !*+,%)%(5
= ___________________
Now square each of those values, then determine the sum.
Room
temperature
Sample #
(Percent cover-Mean)^2
Refrigerated
(Percent cover-Mean)^2
1
2
3
4
5
Sum (S)
3
Humidity
(Percent cover-Mean)^2
Now calculate the variance (S2) for each treatment as indicated. Record the values in the table
below. Recall that in statistics, ! refers to the value and !" refers the mean. Therefore the
sample # will be put in for !.
S ! "##$ &'$(')*+,)' =
S ! "'6)78')*+'9 =
S ! :,$797+; =
∑(.X ,--. /0.10234520 / 01,--. /0.10234520 2 6 )
4/5
∑(.X ,07289:023409 / 01,07289:023409 2 6 )
4/5
∑(.X ;5.8984< / 01;5.8984< 2 6 )
4/5
Room Temperature
Refrigerated
Humidity
Mean
*12345627128
)
Variance
+ 9 12345627128
Standard Deviation
(square root the Variance)
√(+ 9 12345627128 )
Calculate the T-statistic for each pairwise comparison:
# Refridgerated,RDDE FGEHGIJKLIG =
|=̅ ,07289:023409= =̅,--. /0.10234520 |
?
6
>6
,07289:023409 ?>,--. /010234520
# @ABCDCEF,H##$ &'$(')*+,)' =
=
@
|=̅ ;5.8984<= =̅,--. /0.10234520 |
?
6
>6
;5.8984< ?>,--. /010234520
=
@
The next step is to determine whether the t statistic exceeds the critical value for that test. You
need two pieces of information to determine the critical value for the T test. First, we need to
decide the significance level, or α (alpha). The significance level is the probability of rejecting
the null hypothesis when it is true (i.e., saying there is an effect when there actually wasn’t
one). By convention, in science, we use a significance level of 5% (or 0.05). In practical terms,
4
Name: _____________________
this means we are willing to accept a 5% risk of mistakenly concluding that a difference exists
when there isn’t one. Second, we need to determine the degrees of freedom of our test, which
is the number of independent observations (or pairs of observations) being compared: in this
case it is N-1.Thus, your degree of freedom is 4.
You now have enough information to determine the critical value for t in this experiment. To do
this find the row and column with your degrees of freedom and alpha level respectively. For
example, if you have 10 degrees of freedom and have decided to use α=20%=0.20, your critical
value would be 1.372. Use this approach to determine the critical value for t in your
experiment. Circle it on this table!
5
Your critical value for t is _________________________________.
Now compare this critical value to the test statistics you calculated above. If your t value is >
than the critical value in the chart, then your p value is below 0.05, and you can reject the null
hypothesis.
T Statistic for Treatments VS Room
Temperature
t Refrigerated, Room Temperature :
t Humidity, Room Temperature :
t ≥ critical value
t ≥ critical value Thus,
p-value <0.05
or
t < critical value
t < critical value Thus,
p-value >0.05
Indicate for each comparison if the p-value is greater or less than 0.05.
T refrigerated, room temperature: ________________________________________
T humidity, room temperature: __________________________________________
Indicate which of the two null hypotheses (if any) were rejected.
H01: ________________________________________________________
H02: ________________________________________________________
When we reject the null hypothesis, what we are in fact doing is stating that we did detect a
significant difference between the means for two treatments. If we fail to reject it, we state
that we have not detected a significant difference between the two means (or, put another
way, that the observed difference between the means was statistically significant).
6
Name: _____________________
Reporting statistical tests in BIOL 1510
§
§
§
In the methods section of your lab report: after describing the experiment and how you collected
your data, it is usually sufficient to simply state that you used a T-test to determine whether the
mean percent growth differed significantly among treatments, and that you assumed a statistical
significance level of 5% (i.e. α=0.05).
In the results section of your lab report: you should always summarize your results in a narrative
format in your results section; don’t just show graphs, and don’t report your raw data either. The
first thing you should do is summarize the means (± the standard deviation) for each treatment. You
should then orient the reader towards any supporting figures that you have produced. Lastly, you
should summarize the results of your statistical tests.
Please use the requirements from the rubric below to guide your writing: Average for each
treatment (3pts), StDev. for each treatment (3pts), t-statistics (2pts), P-value, crit. t-value, deg. of
freedom (3 pts), Rate of growth from trendline equation (3pts), Clearly explains results (2pts).
For this lab your results paragraph should only consist of your narrative and your line graph. In
the text box, write out a first draft of the narrative results of your lab report, including the
statistical results:
The average mold production for the room temperature samples were 28.04, while for the
refrigerated condition it was 0, and for the humidity condition the average was 61.84. Additionally,
for the room temperature condition the standard deviation was 5.129, and that of the refrigerated
condition was 0, while the standard deviation of the humidity samples was 3.09. Since standard
deviation represents the variation in the data, the small standard deviations mean that the class
was precise in their data collection, but shows more precision in their collection of the refrigerator
samples than the room temperature and humidity samples. The most standard deviation is
present in the room temperature condition, meaning the data had the most variation in the class
and was collected in the least precise manner in comparison to the other 2 conditions. Moreover,
the standard deviation was used to calculate the t-test statistic for the room temperature and
refrigerated pair, which was found too be 12.24 and for the room temperature and humidity pair,
which was 12.50. Using the t-test statistics and the 4 degrees of freedom, the critical value was
found to be 2.776. Since both t-test statistics were higher than the critical value, the p-value is
less than 0.05 for both as well. This means that both the null hypotheses can be rejected and the
data is statistically significant.
The graph depicts the fungal growth of the
refrigerated condition to be none, while in
humidity the growth rate is the fastest. In
room temperature there is a medium
amount of fungal growth on the bread, less
than in humidity but more than in the
refrigerator
Room
temp
7
Refrigerated
Humidity