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Rev 12/19

Biologist at Work! Name____________________________________Skills: your mastery of scientific method, use of metric system, and measurement by microscopy,

balance, and caliper technology protocols (appendices) will be tested during finals week!

Observation: Organisms have parts, which can be measured in terms of length. Suppose you previously made some measurements on yourself. With those measurements in mind, you would now have a “human ruler.” You could measure a centimeter at a time with one of your fingernails, and could measure longer lengths by “walking” with your thumb and index finger.

Which of your fingernails comes closest to 1 cm in width? What is the length between your thumb tip and extended ________ finger tip?       .     cm

Question: Is my right hand the same size as my left hand?Hypothesis: H0=My hands are the same size; H1=My hands are ______________________________.Prediction: If my hands are the same size, then the width across my left hand should be the same as

the width across my right hand. Note: to get more precision, we will use a vernier caliper.

Experiment: Width across knuckles of: left hand       .        cm ... right hand       .        cmNote: do not include the thumb in measuring with the caliper, but do use its full precision !

Was this really an experiment?

If no, why not?_____________________________________________________

_____________________________________________________

If this is not an experiment, what is it? _____________Analysis: With a sample size of one (n = 1) we cannot do a statistical test, so we will simply decide

based on a simple comparison of the two sizes measured.The width of my left hand is: that of my right hand.

Decision: The hypothesis (H0): “My hands are the same size” is:

There is very little doubt about the outcome here because you have asked a discrete question with a measurable answer.

Did the prediction thoroughly test the hypothesis? If not, what else might we measure to more thoroughly test the hypothesis?(hint: the key word is “size”!)

1. __________________ 2. __________________Most investigations yield not only answers but more questions as well. Scientists are curious people! We might also wonder whether the results of our study can be generalized to the entire human population, for example.

H

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Page 2

Observation: You now know something about your own two hands. You also notice that not everyone (Homo sapiens sapiens) in the room is the same size overall.

Question: In spite of different absolute body sizes, does everyone have hands of equal width?

Hypothesis: The human population has hands of equal width; this is the:   H0    H1  

Prediction: If the human population has hands of equal width, then a sample of the human population should have hands of equal width.

Notice that we cannot go out and measure the hands of the entire human population, so we must settle for a sample. We hope we can take a representative sample (that is a random sample). Our sample will be all the people in this laboratory.

Would this be a random sample of the population? If it is not a random sample, why not? A truly random sample would have a wider range of:

1. _____________________________________________________________________

2. _____________________________________________________________________We also hope that our sample is sufficiently large. In spite of any shortcomings in our sample, we will continue our analysis since we lack a better sample.

Experiment: Your instructor will help you post your hand width data along with your classmates’ data on the screen. Additional data will be recorded on a computer.

By collecting lots of data, do we now have an experiment?

If no, why not?_____________________________________________________

_____________________________________________________

If this is not an experiment, what is it? _____________

Analysis: Clearly we have various widths in each sample and must now include an assessment of this variation in preparing for our decision. Calculate the mean (average) width and the standard deviation of the samples. The latter gives us some measure of the variation (or spread) around the mean. Most calculators will determine the mean and standard deviation for you, using the formulae shown below, but we will let a computer do this work for us!

mean = x= standard deviation = We will use Microsoft Excel™ to help us with these calculations.

After powering up the computer, select Excel from the dock at the bottom of the screen. This should open a dialog box, which you can dismiss by clicking on the blue “Open” button. A blank spreadsheet will appear on the monitor screen. In the cell A1 type “Left” and in the cell B1 type “Right.” Enter the data from the screen in the columns beneath the words (left hand data in A2 to A21, and right hand data in B2 to B21).

To calculate the means: In A26 type “=average(A2:A21)” and hit return. Copy A26 and paste it into B26. To calculate the standard deviations: In A27 type “=stdev(A2:A21)” and hit return. Copy A27 and paste it into B27. To fix the rounding problems, select A26:B27 and then select Format-Cells-Number- (Format Tab on Ribbon) and set the decimal places to one more than we have precision in our measurements (in this case millimeters, so we want two decimal places—the default). Record your values in the table (next page):

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Page 3

Left hands in sample: Right hands in sample:

Mean width (cm) . .

Standard Deviation (cm) . .

Student’s t-test value of p . same     different

In general, if the spread about a mean (Standard Deviation) is greater than the difference between the two means, we worry whether what we are observing is meaningful or not. But how will we know with reasonable certainty? We need to do a statistical test of our hypothesis.

Student’s T-Test:Excel can quickly carry out a t-test, which compares the means of two samples and

gives us a probability (p) value that the result we observed could be observed again with the null hypothesis. In A28 type: “=ttest(A2:A21,B2:B21,2,1)” hit return, and set the cell to show 3 decimal places. In general we choose to reject a null hypothesis when this value is less than the arbitrary value () of 5% (0.05…so now you see why we chose three decimal places).

In B28 type: “=if(A28>0.05,"Same","Different")” and hit return. You can see that Excel can even automate your decision making. The beauty of a spreadsheet is that once you have produced it, you can change any of the raw data numbers and the rest of the calculations are repaired automatically!

Some details: the ttest function in Excel compares the two data ranges you told it were of interest (A2:A21 and B2:B21). We told it to perform a two-tailed (2) test because we had no a priori reason to suspect the one array would have to be different from the other. We told Excel that our data were paired (1), meaning we had left and right hand data from the same person in each row of our data dataset. The returned value of p was compared to an value, which is suitable for everyday biology projects. In some kinds of projects you might want to allow more error (more than 5%), but in others you might want to allow less error. Allowing 5% gives a reasonable balance between Type I and Type II statistical errors for “typical” tests of null hypotheses.

It is also important to note that the value of p returned by the ttest function may be shown in one of several possible "number formats." If you received a returned value of 6.02E23, the E indicates that this value is in scientific notation. The E indicates that the numbers after it are the exponent on a 10. So this value would be equivalent to 6.02 x 1023, also happening to be Avogadro's number. It is a huge number; you move the decimal point of 6.02 by 23 decimal places to the right! One mole of a substance (such as 18 grams of water) contains this many molecules of H2O. It is more likely that your ttest will return a very small number. A value of 6.02E-23 indicates 6.02 x 10-23. We convert this to a common decimal by moving the decimal point of 6.02 by 23 decimal places to the left (because of the negative sign). This result is a very small number! It would round off to 0.000 when comparing it to an α of 0.05, right?!

Decision: Based upon Student’s T-test, the hypothesis:“The human population has hands of equal width”   is    is not   rejected.

There are two reasons for this:

1._________________________________________________________________

2._________________________________________________________________

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Page 4

Observations: A single bag of beans (Phaseolus vulgaris ‘Roman’) was purchased from the store. Some of the beans were soaked in water overnight, the rest from the same bag remain dry. Clearly the soaking has had some effect upon width.

Question: Does soaking beans cause them to expand?

Hypothesis: H0=Soaking does not cause beans to expand; H1=Soaking ________________________.

Prediction: If soaking causes beans to expand, then beans will be significantly larger when they are soaked than beans which have been kept dry.

Experiment: A sample of beans was divided into two sub-samples. One sub-sample was placed in water, the other sub-sample was kept in dry conditions overnight. Use the reticule in the ocular lens of the dissection microscope (Appendix) and a balance to their greatest precision to determine the width and weight of each of 10 beans from each sub-sample as indicated below. Be sure to use leading 0s and round calculated answers correctly!

Bean Widthsoaked dry

Bean Weightsoaked dry

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

. mm . mm .       g .       g

Was this a true experiment?   yes    no  

Soaked Dry

Mean Width (mm) . .

Standard Dev. . .

Soaked DryMean Weight (g)

. .Standard Dev.

. .

Analysis: Carry out a t-test to see whether there is any significant difference between the mean weights of the two sub-samples. In this case the formula for t-test needs to end with 1,3. We get to do a one-tailed test as our subjects clearly must have gained water during the treatment, but we do not have paired data this time. Therefore the 3 tells Excel that our two data sets come from different samples.

Review last paragraph on page 3! Value of p: ___.________ Value of : ___.______Based on the t-test, are the two mean weights significantly different?

Decision:Based on Student's T-test, the hypothesis:

“Soaking does not cause beans to expand” is:   rejected    not rejected  

Our hypothesis used the term “expand” and our prediction used the term “larger.” In our experiment we measured the weight of the beans. What weight adjective would describe the soaked beans?

The soaked beans are _________________________________than the dry beans.Homework: redo all Excel work at home, check rounding and leading 0 for all data!!

Complete this homework early enough to get instructor help if needed!

Appendix: Using the Leica Dissection Microscopenote: your mastery of this skill will be tested during finals week!

1. Carefully remove the microscope from the cabinet. Remove and set aside the dust cover. Plug the power cord into the nearest electrical outlet. There is a switch on the back of the base of the microscope to power up the microscope.

2. On the right side of the deck is a switch array to control the direction and brightness of the illumination of the specimen. The epi-illumination and trans-illumination lamps allow you to direct light upon or through the specimen, respectively. For this day, you want bright epi-illumination.

3. Remove any eyeglasses you wear; the microscope will correct your vision for you. Adjust the ocular lenses by pushing them closer together, or pulling them farther apart to match the inter-pupillary distance between your two eyes. You will know when you have achieved this when you see just ONE circle of light as you look through the microscope.

4. Place the metric ruler on the stage and use the large black knobs on the arm of the microscope and your left eye and left ocular lens to focus sharply on that ruler’s measuring scale (cm divided in mm).

5. Adjust the focus of the right ocular lens by using the fingers of both hands; use the fingers of your anti-dominant hand to hold the base of the ocular lens steady, and the fingers of your dominant hand to turn the knurled ring (clockwise or anti-clockwise as needed) to sharply focus the view of your right eye on the measuring reticule scale.

6. Using your right eye and right ocular lens, adjust as needed the white magnification knob on the head of the microscope to a position “near” the 1.0x mark to super-impose the 100-subdivision optical reticule scale across exactly 1 cm of the metric ruler, to measure to a precision of 0.1 mm.

7. The accuracy of measurements depends on you sharply focusing on the specimen. Double check the focus on the ruler (step 4), the focus on the reticule (step 5), and that the magnification is precisely adjusted so that the reticule is calibrated to cover exactly 1.00 cm (step 6).

8. To measure an object, make sure you have calibrated the microscope properly (steps 4-7). Place the object to be measured, say a Roman bean seed, in a half-Petri dish on the stage. Focus sharply on the surface of that object using the black focusing knob on the microscope arm while using your right eye and the right ocular lens only! You can now measure the sharply-focused image of that object directly using the reticule. If the bean seed you are using is too wide for the reticule (soaked ones likely!), use a razor blade to make a shallow cut about half-way across the bean width; measure edge to cut, and cut to opposite edge, and add the measures together!

9. Turn the switch on the back of the base of the microscope off. Unplug the wire from the outlet by wiggling and pulling on the plug body only! DO NOT PULL ON THE WIRE ITSELF! Cover the microscope with the dust cover and return the microscope to the cabinet.

Appendix: Using the Vernier Calipernote: your mastery of this skill will be tested during finals week!

1. This vernier caliper is a measuring instrument with a precision of 0.1 mm (0.01 cm) 2. Close the jaws lightly on the object to be measured (this example is a left index finger) 3. You may tighten the thumbscrew to lock the jaws to the precise measure. 4. Notice that the caliper has a fixed scale and a short, sliding vernier scale with a window. 5. Ignore the top scales; we NEVER use English units, such as inches, in biology! 6. In biology use only the bottom scales, which are calibrated in metric units. 7. The numbers on the fixed scale are centimeters, its black scale subunits are millimeters. 8. There are ten silver tick marks in the sliding (vernier) scale window. The left-most silver

tick mark in the sliding scale window shows the finger diameter measurement at the black tick marks on the fixed scale:

9. In the example above, the leftmost silver tick mark on the sliding vernier scale window is between 2.1 and 2.2 cm on the fixed scale, indicating 21 whole millimeters (2.1 cm).

10. To find full precision, we must determine the tenths of millimeters. Notice that the ten silver tick marks in the window of the vernier sliding scale measure the same width as only nine black tick marks on the fixed scale. This means that only one of the silver tick marks on the vernier scale will align perfectly with a black tick mark on the fixed scale. The rest of the 10 silver tick marks on the sliding scale will be at least slightly misaligned.

11. The number of the best-aligned silver tick mark on the sliding scale shows the tenths of millimeters. In the example above, the 4th silver tick mark on the sliding scale is aligned quite accurately with the black tick mark on the black scale, so the full-precision caliper measurement shown is 21.3 mm (2.13 cm).

12. On the quite-rare occasions when the full-precision measurement just happens to be exactly 8 cm, you must record your data with the full precision of the instrument. In that case you would not record 8 cm, or even 8.0 cm, but rather 8.00 cm or 80.0 mm.