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BIOLOGY 1001
FALL 2004
LABORATORY 7
Midterm Practical Examination
Collection and Statistical Analysis of GA Data
Final Observations of Tobacco Clones
When measurements are made in a scientific experiment, questions always arise as to how reliable
they are. If I ask you to run from the main gate to Altschul Hall and you do so in 256 seconds, we
may wonder whether this is typical of your running ability. Suppose I were to ask you to run the
distance again, and you found it was a different time. How could we reconcile the second with the
first in coming up with an idea of your running time? Suppose I asked you to try a new pair of
running shoes or a special diet. How could we compare your running times under the new
conditions with those seen originally? Or, more specific to our needs, how can we compare the
growth of tall and dwarf pea plants with and without the influence of gibberellic acid. For these
measurements and investigations, we will need to utilize statistics and calculate means, standard
deviations, and, to compare results, employ the t-test.
In laboratory today, you will make the final measurements of GA-treated and control dwarf and
tall pea plants and will utilize the t-test to see if the GA was effective. You will also make your
last observations on the tobacco cultures now that they have been growing for three weeks.
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** Lab 7 begins with a LAB PRACTICAL EXAMINATION on Laboratories 1 to 6. The exam will
consist of timed stations, each asking multiple short answer questions.**
Following the exam, there will be a five-minute break. Then, lab will begin with a short pre-lab quiz
as usual!
I.
II.
III.
IV.
Midterm lab practical examination
5-minute break, then prelab quiz
The effect of gibberellic acid on stem growth (conclusion): FORMAL LAB REPORT #2
Observations of tobacco leaf cultures (conclusion)
============================================
Tobin and Dusheck, Third Edition: pp. 658, 669-673.
Lab 7-1
III. EFFECT OF GIBBERELLIC ACID ON STEM GROWTH (conclusion)
Before we measure and analyze the results of the gibberellic acid test, let us return to the
question of your running ability. If I ask you to run from the main gate to Altschul Hall and you
do so in 256 seconds, we may wonder whether this is typical of your running ability. In fact, you
may have had a terrible time, tripping on wet leaves and running into classmates studying their
laboratory notes on the lawn. Suppose I ask you to run a second time and this time you complete
the distance in 44 seconds. Which is your typical time? Clearly, the answer is to have you run
the course a number of times more and compute the average or mean, which turns out to be 83
seconds.
The mean gives us a more reasonable idea of what your typical running time might be. Indeed,
we have used averaging several times during the semester. But the mean alone does not tell us
that you are capable of running that distance in almost half that time (you did it on the second
try) and, at other times, at three times the mean time. Other information is needed and one which
can supplement the mean with the standard deviation.
Suppose I ask you to run the distance again, a number of times, but this time with a special type
of running shoe we have developed. We can again calculate the mean to give us some idea of
what you are typically capable of doing, and the standard deviation, to give some idea of how
much variation there is. But how can we know that the times you clocked without the shoes are
the same or different from the range of times you ran with the shoes? For that, there are a
number of statistical tests, one being the t-test.
A. FINAL MEASUREMENTS
Make the final measurements of your treated and control pea plants and record these
observations in Table 6-2 (from last week’s handout).
The class results will be pooled (on the chalk board) in order to calculate means. The
means should be plotted as a bar graph. A bar graph is one in which the mean value for
each treatment group is represented as the height of a column on the y-axis. The x-axis
is not incremental; it is only a place for labeling each bar. Use the graph paper
provided in Figure 7-C.
Next, you will measure the internode lengths of your treated and control pea plants.
Gently place a ruler next to the stem and, starting from the bottom of the plants
(between the surface of the soil and the lowest leaf), measure and record the distance
between the leaf nodes. Observe where the largest internodes occur and record these
observations in Table 6-3.
Lab 7-2
B. THE t-TEST
1. INTRODUCTION
The t-test is a statistical test for determining if two means are significantly different from one
another. It is not enough to say two means are "pretty different" or "fairly close."
The t-test is designed to see if the difference between the means of two groups is due simply to
variation in the entire group or to the experimental factor, the independent variable. In our case,
the independent variable is the addition of GA. The dependent variable is that factor which
changed in response to treatment. In our case this is the height of the treated plants.
In order to use the t-test, however, we must first consider the concept of a null hypothesis. The
NULL HYPOTHESIS simply states that there is no difference between the means of the
groups for the dependent variable. In our experiment, it would mean that there is no
difference in the mean height of GA-treated genetic dwarf plants and control dwarf plants, or
between GA-treated genetic tall plants and control tall plants. We must test the null hypothesis
since we do not know how different the two means really are.
If the difference in height between treated and control plants is due to chance, then we can accept
the null hypothesis. If we find a significant difference between mean heights of treated and
control dwarf plants or between treated and control tall plants, we can reject the null hypothesis.
If we reject the null hypothesis, we can say that there is a significant difference between the
GA-treated and control plants due to our independent variable, GA treatment.
2. CALCULATIONS
First, obtain the class results, i.e., final height measurements, and enter them on the data sheets in
Table 7-1 (talls) and Table 7-2 (dwarfs). To calculate the two t values, one for the dwarf and one
for the tall pea plants, it is first necessary to calculate the mean height (X) of experimental and
control groups.
The experimental groups are:
GA-treated dwarf pea plants
GA-treated tall pea plants
The control groups are:
untreated dwarf pea plants
untreated tall pea plants
Lab 7-3
To obtain the mean height (X) of a group of plants, the sum of the heights of the plants is divided
by the total number (N) of the plants in the group. Having obtained the mean, simply follow the
instructions in Table 7-1 and Table 7-2 to calculate the t value.
The t value takes into account both the difference between the means and the deviation
(variation) around each mean. Once a t value is obtained, it must be compared to a standard to
determine if the two means are significantly different. The degrees of freedom (df) takes into
account the sample size in determining whether the t value is significant. The number of degrees
of freedom is always two less than the total number of classes present in your data set. After you
have obtained your t and df values, you are ready to consult the t-table and test the null
hypothesis.
3. THE t-TABLE
Use Table 7-3 to test the null hypothesis. First, locate the correct df value for your experiment.
Read across that row until you find the number closest to the number you calculated for t. Then
read up the column to the heading to determine probability or P.
Probability (P) refers to the percent of the time when differences between observed and expected
data are due to chance. P is expressed in values between 0 and 1. One means that 100% of the
time the deviation is due to chance, while 0.20 means that 20% of the time the deviation is due to
chance. In general, the larger the t, the less probable it is that an event is due to chance. The
more to the right side of the table your t value is, the more statistically significant is the
difference between means.
Statisticians have chosen P = 0.05 as the dividing line between accepting and rejecting the null
hypothesis. If the calculated t is equal to or larger than the t value in the table for P = 0.05, you
reject the null hypothesis. The deviations are significant.
Note that we say that the deviations or difference between the means are significantly different.
It is incorrect to say that the results or means are significant or not significant. Remember that
the t-test is testing differences between means, not the means themselves.
If your calculated t is smaller than the t value in the table for a P of 0.05, you cannot reject the
null hypothesis and must conclude that the means are not statistically different. Any differences
in height are due to chance. If, on the other hand, your calculated t value is greater than the
tabulated value, then the null hypothesis is rejected and the alternative is accepted. The
differences in height are due to the GA treatment.
After you have calculated the t value for the dwarf plants, calculate the t value for the tall plants.
Lab 7-4
TABLE 7-1. CLASS DATA – FINAL HEIGHTS OF TALL PLANTS
Group
Height of
Treated Tall (cm)
Height of
Control Tall (cm)
Height2
Height2
1
2
3
4
5
6
7
8
TOTAL
t=
D=
E=
F=
G=
TREATED
# of Treated Groups = NT=
CALCULATION OF t VALUE
CONTROL
# of Control Groups = NC=
MeanT=D/NT=
MeanC=F/NC
SST=E-[(D)2/NT]=
SSC=G-[(F)2/NC]=
MeanT - MeanC
SST +SSC
NT+NC –2
=
1 + 1
NT NC
df = NT + NC – 2 =
P-value for Experiment = __________
Did the GA have a statistically significant effect on the growth of the tall plants? Yes or No
Describe in your own words what the P-value means (it is VERY important that you understand this):
Lab 7-5
TABLE 7-2. CLASS DATA – FINAL HEIGHTS OF DWARF PLANTS
Group
1
Height of
Treated Dwarf (cm)
Height2
Height of
Control Dwarf (cm)
Height2
2
3
4
5
6
7
8
TOTAL
t=
D=
E=
F=
G=
TREATED
# of Treated Groups = NT=
CALCULATION OF t VALUE
CONTROL
# of Control Groups = NC=
MeanT=D/NT=
MeanC=F/NC
SST=E-[(D)2/NT]=
SSC=G-[(F)2/NC]=
MeanT - MeanC
SST +SSC
NT+NC –2
=
1 + 1
NT NC
df = NT + NC – 2 =
P-value for Experiment = __________
Did the GA have a statistically significant effect on the growth of the tall plants? Yes or No
Lab 7-6
TABLE 7-3. t-TABLE
Lab 7-7
FIGURE 7-C. BAR GRAPH OF FINAL HEIGHT MEASUREMENTS
Lab 7-8
4. THE REPORT
Write up this exercise as a formal lab report using class data. Refer to the instructions from Laboratory
3 for the format to use.
Please note that the formal lab report of the effect of gibberellic acid on stem growth is due at the
beginning of lab 9 the week after Fall Break, 11/8-11/12. You are encouraged to NOT wait until
the last minute to write up your report.
In your results, include the data on dwarf and tall plants (Tables 7-1 and 7-2) and the bar graph
showing final height measurements (Figure 7-C). Also explain what your P-values mean (students
have often lost points for incorrect explanations—be sure you understand what the P-values mean; if
you have questions, ASK!). The proper use of the word “significant” in writing a scientific report
always pairs the word with “statistically” and a P-value. “Significant” alone is too ambiguous. Note
that even if there is a statistically significant difference, there is not necessarily a biologically
significant different. Proper usage example: “There was a statistically significant difference between
the pigs treated with buttermilk and those treated with water (P=0.005).” Remember NEVER to use
the word “prove.”
Your discussion should include answers to the following questions:
1.
Did your results confirm that gibberellic acid affects stem growth in genetic dwarfs?
2.
Did GA have an effect on stem elongation in tall plants and, if it did, was it similar to or
different from its effect on genetic dwarfs?
3.
How might you explain the response of tall plants?
4.
Were there any differences in internode lengths of the treated and control plants?
5.
If you were to repeat the experiment, what would you change and why?
IV. OBSERVATION OF TOBACCO CLONES
Make your final observations of the tobacco clones today. Record your observations on the
appropriate data sheets from Laboratory 4. Do NOT forget to turn these data sheets in at the beginning
of lab 9 after fall break.
1. Attach your completed tobacco leaf culture observation sheets.
2. What conclusions can you draw from your observations over this three-week period? Did your
results support your expectations/hypotheses? If there were any discrepancies, speculate on what
might account for them. Please write a one-page (maximum) summary of your observations over
the three-week period.
Lab 7-9