biol 202 lab 3: scientific inquiry: formulating a...

BIOL 202 LAB 3 Scientific Inquiry - Formulating a Hypothesis FINAL DIST W17.docx page 1 of 15

BIOL 202 LAB 3: Scientific Inquiry: Formulating a Hypothesis (Prepared with contributions from Cassandra Cook, Lynda Jensen, Tana Kaiser, and Dineh Judd.) Equipment, Supplies & Materials—Required:

• Compound microscopes • Microscope slides (2 per student) • Millimeter scale (e.g., clear metric ruler, preferably with 0.1 mm increments) • Leaves, young (unexpanded) and old (fully expanded), of maple, oak, etc.; at least one of

each age/size from one kind of plant (make sure leaves are clean of any dust or debris and that the abaxial surfaces are dry); 1 each per student (Note: Leaves of salal [Gaultheria shallon], an evergreen broadleaf species, work well and are available during the winter quarter [see Figures 1, 2, and 3 below].) These should be clean and free from damage.

• Clear fingernail polish • Pencil or pen (and label tape, if necessary) to mark microscope slides • Clear cellophane tape (not the translucent or "magic" adhesive tape) • Data sheet (included in this document, where Xa = stomatal count per observation for

young leaves and Xb = stomatal count per observation for old leaves) • Calculators • Computer with Internet access (to access the t-test webpage of VasserStats, an online

statistical computation site from Vassar College, Lowry, n.d.) Equipment, Supplies & Materials—Ancillary:

• Raven Biology of Plants Laboratory Manual Topic 1 The Microscope (Evert, Eichhorn, & Perry, 2012)—one copy per student—Exercise II, Part B, step d, on p. 1-6 (to calculate the diameter of field of view [abbreviated as dFOV], or visual field, for each objective of your microscope) (Note: "9. Diameter of the low-power field:" should read "9. Diameter of the medium-power field.")

• Raven Biology of Plants Laboratory Manual Topic 2 Scientific Inquiry: Formulating a Hypothesis (Evert, Eichhorn, & Perry, 2012)—one copy per student

• Raven Biology of Plants Laboratory Manual Appendix B Basic Statistics for the Botany Lab (Evert, Eichhorn, & Perry, 2012)—one copy per student

Activities: • Overview of Lab 3 (Hypothesis: Young and old leaves of a species do not have

significantly different stomatal densities.) • Follow procedure as described in lab manual (and as indicated by instructor)

Assignment: • Lab Report #3 (final version to be submitted to instructor as indicated in class)

Introductory Figures:

Figure 1. Salal plant Figure 2. Salal leaves Figure 3. Stomata ("Stomata (Ripe Berries, n.d.). (Young salal, n.d.). on Epidermis," n.d.).


Comparing the Density of Stomata on Young Versus Old Leaves In statistical hypothesis testing, two hypotheses are compared. These are called the null hypothesis and the alternative hypothesis. The null hypothesis also may be represented as H0, where the letter H stands for hypothesis and the subscript 0 means zero change. It states that there is no relation between the phenomena under investigation, or no difference will be observed. The alternative hypothesis also may be represented as or Ha or H1, where the letter H stands for hypothesis and the subscript a or 1 takes the opposite point of view. It is the alternative to the null hypothesis, which states that there is some kind of relation or difference. Hypothesis: Young and old leaves of a species do not have significantly different stomatal densities. Or, more formally: Alternative hypothesis: _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ Null hypothesis: _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ Dependent variable: _________________________________________________________ Independent variable: _________________________________________________________


Overview of Calculations (images are not to scale): This lab involves several quantitative measurements and calculations, as indicated below:

• 1. Measurement: Measurement of diameter of field of view (dFOV, or visual field, i.e., what you can see through the eyepiece[s] of your microscope) at low-power (scanning) magnification, i.e., 4X (see #1 below, where the dFOV is 4 mm)

• 2. Ratio and Proportion: Calculation of dFOV (or visual field) at medium-power (or perhaps high-power) magnification (based on a ratio as compared to the low-power magnification) (see #2 below)

• 3. Density per Area: Number of stomata counted in a visual field (based on the number of stomata visible in an entire field of view, which does not yield stomatal density based on unit area) (see #3 below)

• 4. Density per Unit Area: Calculation of stomatal density based on unit area as a conversion from the number of stomata in an entire visual field (#stomata/1.0 mm2, where density refers to the number of stomata per unit area, i.e., square millimeter [1.0 mm2], rather than the entire visual field—the green square is 1.0 mm2) (see #4 below)

mm

4X objective (40X overall magnification)

10X (or 40X) (100X or 400X overall magnification)

10X (100X overall magnification) – not to scale

10X (100X overall magnification) – not to scale


Details Regarding Calculations: Note: These calculations do not involve the overall image magnification that you may experience by looking through a microscope eyepiece (e.g., 4X for a low magnification objective vs. 4X x 10X [eyepiece magnification] for a total magnification of 40X).

1. Measurement: Measurement of Diameter of Field of View (dFOV, or visual field, using, e.g., a 4X scanning, or low-power objective)

Follow instructions in Raven Biology of Plants Laboratory Manual Topic 1 The Microscope (or as indicated by your instructor). 2. Ratio and Proportion: Calculation of Diameter of Field of View (dFOV, or visual field, at

a higher power of magnification [cf. Microscope Calculations, 2013]) Higher powers of magnification include medium (denoted by diametermed) and high (denoted by

diameterhigh; note: low = diameterlow). If the dFOV at low power is 4.0 mm, you now know how large an object can be seen with the scanning field. The diameter of field of view using the scanning objective (A) can be used to calculate the diameter using any other objective (B), e.g., medium (10X) or high (40X) using the following equation:

dFOV A x magnification A = dFOV B x magnification B We can rearrange the equation to solve for dFOV B as follows:

magnification A ____________________ x dFOV A (or diameterlow) (mm) = dFOV B (or diametermed) (mm) magnification B

For example, to calculate the diameter of field of view at medium magnification:

dFOV A x magnification A = dFOV B x magnification B Or, rearranged:

4X (magnification at low power) ______________________________________________ x 4.0 mm = 0.4 x 4.0 mm = 1.6 mm (field of viewmed) 10X (magnification at medium power)

Or, to calculate the diameter of field of view at high magnification:

4X (magnification at low power) ______________________________________________ x 4.0 mm = 0.1 x 4.0 mm = 0.4 mm (field of viewhigh) 40X (magnification at high power)


3. Density per Area: Stomatal Density (i.e., number of stomata counted in a field of view, or visual field)

To determine the stomatal density per observation, you will count the number of stomata per field of view (e.g., where the field of view has a diameter of 1.6 mm at medium power). To calculate the stomatal density per area, you will need to:

• Use your stomatal counts and the formula for the area of a circle (A = πr2 where π = 3.14) to determine the number of stomata/area

For example, if (at medium magnification) …

Stomatal Density (number of stomata per non-overlapping field of view at medium magnification)

Count # Young Leaf (Xa) Old Leaf (Xb) 1 60/1.6 mm diametermed 55/1.6 mm diametermed

Then the area of the field of view (at medium magnification, with diameter = 1.6 mm and radius = 0.8 mm) is: Area of a Circle: A = πr2 (where π = 3.14 and r = radius, which is half the diameter of a circle [see figures below].)

Figure 4. Diameter, etc. of a circle. Figure 5. Area of a circle (A = πr2). Therefore: A = 3.14 x 0.82 mm A = 3.14 x 0.64 mm A = 2.0 mm2

Therefore, 60 stomata/1.6 mm diametermed = 60 stomata/2.0 mm2

And, 55 stomata/1.6 mm diametermed = 55 stomata/2.0 mm2


Non-overlapping Fields of View:

Figure 6a. Leaf of salal with circles indicating 10 non-overlapping fields of view to observe and

record stomatal density (also see Figure 6b below). (Note: These images are not to scale, so your fields of view will be much smaller than indicated in this image.)

Figure 6b. Magnified view (at medium magnification) of Gaultheria shallon stomata from a leaf

impression produced using clear fingernail polish and cellophane tape with circles indicating non-overlapping fields of view to observe and record stomatal density. This will require moving the leaf impression mount on the microscope stage to observe non-overlapping fields of view. (Note: These images are not to scale, so your fields of view may differ from this image depending upon characteristics of your microscope and the magnification used.)


Figures 7a, b and c (from left to right). Stomata of young Gaultheria shallon leaf viewed using

low (4X), medium (10X), and high (40X) objectives (preparations by D. Judd, images by B. Compton). (Note: These images do not represent the entire field of view.)

Figures 8a, b and c (from left to right). Stomata of old Gaultheria shallon leaf viewed using low

(4X), medium (10X), and high (40X) objectives (preparations by D. Judd, images by B. Compton). (Note: These images do not represent the entire field of view.)


4. Density per Unit Area: Stomatal Density per 1.0 mm2 (calculation of stomatal density per square millimeter)

To calculate the stomatal density per unit area (where the unit area will be based on 1.0 mm2), you will need to:

• Convert your calculations to be based on 1.0 mm2 of area (Note that your field of view will not be 1.0 mm2).

Based on the above calculations, to convert the value indicated above to #stomata/1 mm2, state the ratios as fractions, set the two fractions equal to each other, cross-multiply, and solve the resulting equation for x. For example, to convert 60 stomata counted in a field of view of area 2.0 mm2 to be expressed as the number of stomata per a unit area of 1.0 mm2, set the two fractions equal to each other:

60 stomata x stomata _____________ = __________

2 mm2 1 mm2 Then:

60 = 2x And, dividing by 2 …

60 _____________ = x

2 Therefore …

30 = x

So, 60 stomata/2.0 mm2 = 30 stomata/1.0 mm2 = Stomatal density based on unit area

Stomatal Density Per Unit Area

Count # Young Leaf (Xa) Old Leaf (Xb) 1 30/1.0 mm2

(based on a calculation of 60 stomata/field of view)

28/1.0 mm2 (based on a calculation of 55

stomata/field of view)


Data Sheet for Scientific Inquiry: Formulating a Hypothesis Plant Species: ______________________________ Magnification (mag): ______________________________ (e.g., medium, indicated by med; if high magnification is used, indicate with "_____/field of viewhigh")

Table 1: Stomatal Density (number of stomata per non-overlapping field of view at medium magnification)

Count # Young Leaf (Xa) Old Leaf (Xb) 1 _____/field of viewmag _____/field of viewmag

2

3

4

5

6

7

8

9

10

Table 2: Stomatal Density Per Unit Area

(conversion of each count of stomata/field of view to stomata/unit area, i.e., 1 mm2) Count # Young Leaf (Xa) Old Leaf (Xb)

1 _____/mm2 _____/mm2

2

3

4

5

6

7

8

9

10


5. Statistical Analysis Using the t-Test and VasserStats To complete this lab, follow the in-class instructions using the t-test as presented on the VasserStats website (available at http://vassarstats.net/tu.html). Notes: The t-test is a method used to test the differences in means between two sample sets (where the letter t was chosen arbitrarily). It will yield a p-value, or calculated probability (where the letter p refers to probability), of evidence against the null hypothesis. This test allows us to reject or accept the null hypothesis. A small p-value (typically ≤0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. If we reject the null hypothesis, we accept the alternative hypothesis. If we accept the null hypothesis, we reject the alternative hypothesis.

Furthermore, two samples are independent of each other if they are separate samples containing different sets of individual subjects. The individual measures in group A are in no way linked with or related to any of the individual measures in group B, and vice versa. Therefore, we will use the independent t-test in this procedure (cf. http://vassarstats.net/textbook/ch11pt1.html).

Depending on the nature of a hypothesis, either a one-tailed t-test or a two-tailed t-test may be appropriate. A one-tailed test is appropriate if we are expecting a change or difference in one direction (e.g., older leaves will have higher stomatal density); two-tailed is appropriate if the direction is expected in two directions (a) or may be unspecified (b) (e.g., a: younger leaves will have more stomata than older leaves, or b: younger and older leaves will be different, but in which way is not specified—there may be either more or fewer stomata in either sample set). Therefore, in our example with our hypothesis, the two-tailed t-test is appropriate. Procedure Using VasserStats:

a. Select "Independent Samples" in the setup section on the VasserStats webpage for the t-test.

b. Enter your stomatal density per unit area data (from your data table #2) into the two columns for data entry on the VasserStats webpage for the t-test (sample A is for young leaf stomatal counts and sample B is for old leaf stomatal counts).

c. Click "Calculate" to calculate your results. d. Next, be sure to check to make sure your n = 10 for each data set. If for some reason,

numerals other than 10 are indicated, you may need to re-enter your data and click "Calculate" again.

e. A simple next step would be to check the means of your two data sets (i.e., the arithmetic averages of each set of observations). If they are the same, there is no difference between the data sets. If they are different, the p-value can provide information to determine if there is a statistically significant difference between the data sets.

f. Note that the hypothesis used in this lab means that the two-tailed p-value is appropriate (see note below), so consult the p-value for a two-tailed test. Scientists generally agree that two data sets are statistically different when the p-value reported by the t-test is less than 0.05. This means that the likelihood of the experimental results having come about through mere random variability—chance coincidence—is somewhat less than 5%. Hence you can have about 95% confidence that the observed result reflects a genuine difference between two data sets.


g. If your p-value is <.05, this indicates that your data sets are statistically different and the null hypothesis would be rejected, meaning that the alternative hypothesis would be accepted.

h. If your p-value is >.05, this indicates no significance difference between your data sets and the null hypothesis would be accepted, meaning the alternative hypothesis would be rejected.

i. In your lab report, please report the p-value of your t-test and whether the null and alternative hypotheses are accepted or rejected.

j. Also, please print out a copy of your t-test results from the VasserStats website to submit with your lab report.


Appendix: Example Statistical Analysis Using VasserStats Note: In the following example, we will disregard the data summary except for the mean or average values and focus on the p-value for the two-tailed test.


References Evert, R. F., Eichhorn, S. E., & Perry, J. (2012). Laboratory topics in botany (8th ed.). New

York, NY: W. H. Freeman. Lowry, R. (n.d.). t-test for independent or correlated samples. Retrieved from VassarStats:

Website for statistical computation website: http://vassarstats.net/tu.html Microscope calculations: Field of view, object size, drawing magnification. (2013). Retrieved

from Vancouver Community College website: http://library.vcc.ca/learningcentre/pdf/vcclc/MicroscopeCalculations.pdf

Ripe berries of the salal plant, G. shallon [Electronic Image]. (n.d.). Retrieved February 20, 2017, from https://en.wikipedia.org/wiki/Gaultheria_shallon#/media/File:Salal_berries.jpg

[Stomata on epidermis of rose leaf] [Electronic Image]. (n.d.). Retrieved from http://images.fineartamerica.com/images-medium-large-5/2-stomata-on-epidermis-of-rose-leaf-power-and-syred.jpg

Young salal [Electronic Image]. (n.d.). Retrieved February 20, 2017, from https://en.wikipedia.org/wiki/Gaultheria_shallon#/media/File:Gaultheria_shallon_31974.JPG

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