BIOLOGY 1001FALL 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.
* * *
** 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!
- 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)
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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 yaxis. The xaxis 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 7-1
B. THE tTEST
1. INTRODUCTION
The ttest 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 ttest 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 ttest, 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 GAtreated genetic dwarf plants and control dwarf plants, or between GAtreated 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 GAtreated 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:
GAtreated dwarf pea plants
GAtreated tall pea plants
The control groups are:
untreated dwarf pea plants
untreated tall pea plants
Lab 7-1
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 ttable and test the null hypothesis.
3. THE tTABLE
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 ttest 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 7-1
TABLE 7-1. CLASS DATA – FINAL HEIGHTS OF TALL PLANTS
Group / Height ofTreated Tall (cm) / Height2 / Height of
Control Tall (cm) / Height2
1
2
3
4
5
6
7
8
TOTAL / D= / E= / F= / G=
CALCULATION OF t VALUE
TREATED / CONTROL# of Treated Groups = NT= / # of Control Groups = NC=
MeanT=D/NT= / MeanC=F/NC
SST=E-[(D)2/NT]= / SSC=G-[(F)2/NC]=
t= MeanT - MeanC =
SST +SSC 1 + 1
NT+NC –2 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):
TABLE 7-2. CLASS DATA – FINAL HEIGHTS OF DWARF PLANTS
Treated Dwarf (cm) / Height2 / Height of
Control Dwarf (cm) / Height2
1
2
3
4
5
6
7
8
TOTAL / D= / E= / F= / G=
CALCULATION OF t VALUE
TREATED / CONTROL# of Treated Groups = NT= / # of Control Groups = NC=
MeanT=D/NT= / MeanC=F/NC
SST=E-[(D)2/NT]= / SSC=G-[(F)2/NC]=
t= MeanT - MeanC =
SST +SSC 1 + 1
NT+NC –2 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
TABLE 7-3. t-TABLE
FIGURE 7-C. BAR GRAPH OF FINAL HEIGHT MEASUREMENTS
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 7-1