Department of Plant Biology
502 Life Sciences
Louisiana State University
Baton Rouge, LA 70803-1705
ph (504) 388-8563 FAX (504) 388-8429
btmarsh@lsuvm.sncc.lsu.edu or sundberg@life.jsc.nasa.gov
Title: Hypothesis testing and the scientific method
Keywords: hypothesis testing, sampling, replication, descriptive statistics
Credits: This activity was developed with support of NSF Grant BBS-9155920 to MDS.
Abstract: Cooperative group learning is used in this non-threatening introduction to hypothesis testing and the scientific method. Students are introduced to the problem of which automobile (or clothing, bookbags, umbrellas, etc.) dealership might be most profitable at a site near campus. An initial survey and vote by the class determines the hypothesis to be tested - the most common make. Further discussion generates a list of possible ways to test the hypothesis. Sampling is encouraged as the method of choice which leads to a discussion of anticipated problems and limitations of various sampling techniques. When a concensus on approach is reached, the class is divided into research teams and given a specified time period to collect data and return to pool data by the end of the class period. The homework assignment is to calculate descriptive statistics for the four most frequently sampled models in the pooled data. Results and limitations are discussed at the beginning of the following period. Finally, the procedures used in this activity provide a framework for introducing the technique of concept mapping as both a research and study skill.
FAIR USAGE
This exercise may be freely copied and disseminated for all non-commercial educational activities provided that appropriate credit is given to the author, this source (BIOLAB BBS), and NSF grant USE-9156094. Its use is explictly permitted in laboratory manuals and compiled class handouts sold at or below the cost of printing or duplication.
INSTRUCTOR'S GUIDE
BACKGROUND INFORMATION
Investigative laboratories will probably be very different for your students from those in any previous science course most of them have taken. It may be very frustrating for them, at first, because they will not have specific directions to follow or lists of terms and concepts to learn. Instead, you will have to force them to become self-reliant in making observations, forming questions, proposing hypotheses, in particular null hypotheses, designing tests of their hypotheses and analyzing and interpreting the results of their tests. THEY ARE EXPECTED TO DO THE WORK. IT IS YOUR JOB TO GUIDE THEM, BUT NOT TO TELL THEM WHAT TO DO!!
OBJECTIVES
There are two primary objectives of this activity. First is to introduce and reinforce the concept of hypothesis testing as an extension of common sense problem solving. The second is to introduce the technique of concept mapping. There are three secondary objectives. First, is to introduce sampling techniques and the concept of replication. Second is to introduce basic descriptive statistics as a means of summarizing data. Third is to develop a sense of teamwork and cooperation among small research teams of students.
CONCEPTS AND RELATED CONCEPTS ACCURACY
When making measurements or collecting data one hopes to obtain estimates which approach the true value of the unknown. An accurate measurement is one which does this. It is important to note, however, that accuracy is not the same thing as precision (see PRECISION). An accurate measurement is not necessarily precise.
BIAS
A bias is a preconception which can influence your ability to make observations or to interpret data. Try to recognize what your biases might be when designing an experiment, then design your experiment in such a way as to avoid as many biases as possible.
CONCEPT MAPPING
Concept mapping is a special learning tool based on the supposition that knowing is a process of making mental maps of ideas and relationships. This tool allows students to visually record the relationships between concepts. For example, the concept of a wooden pencil can be mapped as follows:
The task for the student is first to identify the key concepts (wood, "lead", graphite, clay, etc.), and the way these concepts are related (called the proposition, which in this case includes the verbs made of, composed of, surrounding, etc.) Long or wordy propositions are hard to remember and often unclear. Most of your time will be spent trying to decide on just the right word that best describes the relationship between the concepts. The lines that are broken, and point across the map are called cross-links. Cross-links represent insight. Because the concepts are represented visually, students can see all of the concepts simultaneously. This creates new opportunities for generating new knowledge. Such cross-links represent a new depth of understanding. Look for cross-links once you have completed a C-map, since what you might think is an insight could very well be a solid relationship.
Concept mapping is hierarchical. This means that the most general concept (the superordinate), is placed at the top of the map. All other concepts that make up or are related to the superordinate are placed below. Ideally, all C-maps (concept map(s)) are grounded with examples at its bottom-most level (cedar, carpenters glue). As a rule, concepts are placed in solid lined figures and examples are placed in broken line figures.
Interestingly enough, concept maps are based on the personal knowledge of individual students. The implications of this are important. Different students reading the same material will have different concept maps. The differences can be slight or radical, but none could be considered wrong. After all, they represent the way that a person understands the given concepts a the given time. On the other hand, these personal maps do change over time, especially when the person obtains new information.
How to make a C-map:
1. From the reading, extract the key concepts.
2. Rank order these concepts from general to specific.
3. Relate each of these concepts in a branching pattern with short propositions. Be sure to start with the superordinate at the top and end with examples at the bottom.
4. Look for crosslink insights.
5. Be sure to include examples - i.e. go through reading and underline the key words, then list this on separate slips of paper.
How to evaluate a C-map: Ask yourself the following questions:
1. Is there a valid hierarchy?
2. Are there valid relationships?
3. Are there valid examples?
4. Are the concepts in a branching pattern or is it stringy?
5. Are there opportunities for crosslinks?
CONTROL
When designing an experiment you want something to compare your results against - this is the control. For instance, if you are interested in the effect of a particular color of light on the rate of photosynthesis, you would design an experiment using particular colored light filters. As controls you would used white light (all colors combined) and complete dark (no light). By comparing your experimental results against the controls, you would be able to determine if a particular color had any effect. When designing your experiment, be sure to keep all variables constant, except the one you are interested in examining. For instance, in an effect of light quality (color) experiment, all treatments, including the control, would be run at the same temperature, with the same amount of nutrients, etc.
ERROR
This term has a common usage which is equally applicable in biology -- making a mistake. In science, however, there are other, more specific definitions. When analyzing the results of an experiment, we are interested in the experimental error - that error due to the specific design of the experiment or the equipment used. For instance, if we are using a thermometer to record temperatures during an experiment, and the instrument was out of calibration, our results will be consistently in error. Another example of experimental error would arise if different members of a group make successive readings of an instrument and they do not read consistently. For instance, one person may misread the meter by not viewing it direct on while another person may round off readings. A third person may interpolate (estimate a fraction between two numbers on the scale) to one additional significant figure, while a fourth may interpolate two additional significant figures. When the data from this group is pooled, there will be an inherent experimental error due to the different instrument reading techniques of the individual group members. Additional errors commonly encountered in biology have to do with statistical testing.
We use statistical tests to help us determine if observed results are sufficiently close to the expected results to be accepted or sufficiently different to be rejected. A type I error is when we reject a null hypothesis (see HYPOTHESIS) when it is true. The probability of making a type I error is the level of significance of a statistical test. A type II error is when we accept a null hypothesis when, in fact, the alternative is true. We can avoid a type I error by making our statistical test more rigorous - but of course, that increases the likelihood of making a type II error!
EXPERIMENTAL DESIGN
Experimental design deals with selection of variables to be studied and the choice of a sampling program. It does not deal with experimental techniques used to gather data. The most commonly used experimental design is the two-sample comparison. To do this you select two situations in which all conditions but one are the same. One situation, usually more "normal" serves as the control and is the basis for comparison. The other situation is the experimental in which you vary the factor of interest. By comparing data obtained from the experimental situation with the control, you can make some conclusions about the effect of the variable you altered on the organism being studied. Be careful, though, to consider other possible explanations. For instance, you may do an experiment growing plants under two different lighting conditions. The control may be normal daylight, and the experimental may have additional supplemental lighting from a floodlight. Plants in the latter situation may grow more rapidly. This may seem to support the hypothesis that the greater the amount of light, the faster a plant will grow. The supplemental floodlight certainly will provide more light intensity - but it also provides heat. Is it the light, the heat, or both that made the experimental plants grow faster?
HYPOTHESIS
An hypothesis is a tentative statement or assumption which is made in order to be tested. To formulate a hypothesis is to make a testable prediction about the relationship between variables. A hypothesis is usually stated before any sensible investigation or experiment is performed because the hypothesis provides guidance to an investigator about the data to collect. A hypothesis is an expression of what the investigator thinks will be the effect of the manipulated (independent) variable on the responding (dependent) variable. A workable hypothesis is stated in such a way that , upon testing, its credibility can be established or refuted. Hypotheses can usually be formed as an "if...then" statement.
Because it is not possible to prove a hypothesis scientifically, in the same way a mathematician can prove a theorem, scientists frequently phrase their hypothesis as a null hypothesis (H:O), in opposition to an alternative hypothesis (H:A). A null hypothesis is simply a statement of "no difference" between the experimental and control. If there is a difference, we must reject the null hypothesis and accept the alternative. The concept of hypothesis testing is basic to all of science; it is also the most misunderstood by the public. The word "prove" should not exist in the scientist's vocabulary, an infinite number of examples are needed to prove a hypothesis. No matter how much evidence we gather to support a specific hypothesis, we can never be certain that the same data would not equally support any number of unknown alternative hypotheses. On the other hand, only one piece of evidence is necessary to disprove, and thus reject, a null hypothesis. If we demonstrate that the null hypothesis is invalid, then the alternative must be true - although, in fact, this simply means we must rexamine the alternative to define and test additional null hypotheses - ever refining our understanding of the concept or process involved.
PRECISION
Results which are predictable and repeatable are precise, but precise results may or may not be accurate. For instance, if your measuring instrument is not calibrated properly you may get exactly the same result on ten successive measurements, which would be extremely precise, but your results would be inaccurate to the degree that the instrument was out of calibration. (see ACCURACY).
RANDOM
Random means without definite aim, direction, intention, or method; of equal probabilities. In other words, without bias. Random selection is a key assumption of statistical analysis, and as such, is critically important in designing scientific experiments and analyzing data. If one cannot be reasonably certain that samples were obtained in a randomized manner, the results obtained will be questionable.
In designing experiments, treatments should be randomized. For instance, if three pots of plants serve as a control and an additional three plants receive a fertilizer treatment, the three treatment pots should not all be next to the window while the control plants are lined up away from the window. To do so biases the experiment because the treatment plants would receive more light in addition to fertilizer. If the pots were set out in a random manner, however, it would be just as likely for a control plant as an experimental plant to be next to the window.
In sampling, it is important to decide where, how much and how many samples should be made ahead of time so as not to bias samples, eg. subconsciously choosing to sample where the largest bacterial colonies are located on a Petri dish. One way to do this is to lay out grid coordinates and then choose sample coordinates with a random numbers table.
In a table of random numbers, each integer from 0-9 has an equal and independent chance of occurring anywhere in the table. Likewise each two digit number 00-99 is randomly distributed as are three digit numbers 000-999, etc. To use the table, decide ahead of time: 1) what direction you want to read (either horizontally, vertically or diagonally, 2) how many digits are appropriate, and 3) where you want to begin in the table (the table should be entered randomly so as not to begin at the same point everytime you need to sample). For example, if you lay out grid coordinates 15 X 15, you want to use 2 digit numbers and use the first 2-digit number between 00 and 15 as your first coordinate and the second number between 00 and 15 as your second coordinate.
SAMPLING
A scientist can rarely collect all of the data about which she wants to draw conclusions. For example, it may be of interest to draw conclusions about the body weight of all 18 year old males in the United States. The only way to make statements about body weight of these men, with 100 % confidence is to weigh each individual - an impossible task. Instead, only some of the total number of 18 year old males are weighed and we infer from the results the total weights of all the individuals of interest. The men who are actually weighed are a statistical sample of the population.
The key to having a sample accurately represent the population is to obtain a random sample. Random sampling implies that each individual in the population has an equal chance of being selects as part of the sample, that is, there is no bias for or against any individuals being sampled. If samples are taken at random from a population, valid conclusions may be drawn about that population from a small sample - with a known chance of error. We can control the amount of error by varying the size of the sample. In general, the smaller the sample, the larger the chance of error; the larger the sample, the smaller the chance of error.
A random number table is useful in obtaining random samples (see RANDOM and APPENDIX 1). Decide ahead of time how you will use the table, eg. read the last three digits down a row or the first three digits across line, etc., then enter the table at a random point and begin to sample. A randomly selected number could represent an individual in a row of plantings, number of feet from a starting point, number of measurements taken of a dimension, etc.
A single measurement is not adequate to draw conclusions about a population. This is because it is not possible to know how reliably a character was measured. Repeated measurements may vary greatly, especially if made by different people. Therefore a series of repeated measurements, or replicate measurements, should be taken. From the collection of replicates, the mean and standard deviation will provide an estimate for the population as a whole. There are techniques to determine how many replicates are needed to achieve a certain level of reliability. As a general rule, three is a minimum number.
STATISTICS
There are three reasons statistics are important to scientists: first, they allow data to be quantitatively described and summarized; second, they allow generalized conclusions to be drawn based on relatively small sets of data; third, the differences and relationships between sets of data can be objectively analyzed.
VARIABLE
A variable is any factor in a situation that may change or vary. Investigators in science and other disciplines try to determine what variables influence the behavior of a system by manipulating one variable, called the independent variable and measuring its effect on another variable, called the dependent variable. As this is done, all other variables are held constant. If there is a change in only one variable and an effect is produced on another variable, then you can conclude that the effect has been brought about by the changes in the manipulated (independent) variable. If more than one variable changes, there can be no certainly at all about which of the changing variables causes the effect on the responding variable.
In a scientific investigation, measurements of the variables are made; however, you, the investigator, must decide how to measure each variable. An operational definition of a variable is a definition you determine for the purpose of measuring the variable during an investigation. Thus, different operational definitions of the same variable may be used by different investigators. For instance, in a growth rate experiment, you may decide to measure length of an organ at daily intervals while in another group, they may decide to measure the same dimension at six hour intervals. In many cases it is important that you choose an appropriate operational variable in order to observe a phenomenon. If the time interval you choose is too long, for example, you may miss an important stage of a processes you were looking for.
FACTUAL BACKGROUND
Descriptive Statistics
Living things are, by their nature, variable; a single individual, population, community etc. will not be exactly the same as any other. In order to describe any group of living things, statistics, descriptive measures derived from sample data, must be computed. One of the most common descriptive statistics is the mean, or average. If represents a datum (e.g. the height of a plant in cm) the mean of a sample of several plants is where (X bar) is the symbol of the mean, (sum of X's) is the total of all the plants' heights in the sample and (sample size) is the number of plants sampled.
e.g. The heights of five plants were 10.1, 11.4, 11.7, 12.1 and 13.3 cm respectively. Thus the average height of the plants in this sample was 11.72 cm. If these 5 plants were randomly selected from a larger group of plants, we may assume that the average for the larger population is also approximated by 11.72 cm.
As a general rule, the mean should not be considered more accurate than 1 significant figure beyond the accuracy of the original data. In the above example each plant was measured to within 1/10 cm (0.1). Therefore, the mean may be rounded to the nearest 1/100 (0.01).
Calculating a mean only gives a partial description of the data - the average value. It is usually necessary to also describe how much variability there is around the mean. The following two sets of data have the same mean: 1, 6, 11, 16, 21, and 10, 11, 11, 11, 12. You will probably agree that the mean is not enough to meaningfully describe both sets; some measure of variability is also necessary. Two measures of variability are commonly used, standard deviation(s) and standard error (S.E.). In each case the first step is to calculate the sum of squares (SS) - the sum of squared deviations from the mean. SS = _(x-)2 For the plant height data above, SS = (10.1 - 11.72)2 + (11.4 - 11.72)2 +(11.7 - 11.72)2 + (12.1 - 11.72)2 + (13.3 - 11.72)2 = 5.37 cm2. A simpler way to calculate SS is to use the formula SS = _X2 - (_X)2/n. Again using the data above:
_X = 10.1 + 11.4 + 11.7 + 12.1 + 13.3 = 58.6 cm
_X2 = (10.1)2 + (11.4)2 + (11.7)2 +(12.1)2 + (13.3)2 = 692.16 cm2
n = 5
SS = 692.16 cm2 - (58.6 cm)2/5
= 692.16 cm2 - 686.79 cm2
= 5.37 cm2
Standard deviation = _(SS/DF) where DF (degrees of freedom) = n - 1
In our example s = _(5.37 cm2/4) = 1.16 cm
The standard error (S.E.) is calculated by the formula: S.E. = s/_n, which for our example is 1.16 cm/_5 = 0.52 cm. Our data may now be accurately expressed either by stating
the mean and standard deviation ( = 11.72 cm, s = 1.16 cm) or by the mean and standard error
( = 11.72 _ 0.52 cm).
As you can see by the equation for standard error, the magnitude of this variation is
inversely proportional to the sample size. That is, the larger the sample size, the more precise the estimate of the population mean (i.e. large samples generally give better results than small samples!)
Comparing Two Means
It is frequently of interest to compare the means of two samples to draw conclusions about similarities or differences. For instance, are the results of a particular experimental treatment significantly different from the control? In some cases the difference may be very large and obvious, but in other cases the means and variances may be quite similar and an objective method is required to determine the degree of difference or similarity.
Student's t-test is commonly used to compare two means where the null hypothesis, Ho:1 = 2, is that the means are the same.
The t-statistic is calculated as: where the numerator is the absolute value of the mean of experiment 1 less the mean of experiment 2. The denominator is the standard error of the difference between the means and is calculated as: where n1 and n2 are the two sample sizes and sp2 is: where SS is the sum of squares and DF is the degrees of freedom for the two data sets.
The value obtained for "t" is now compared to the table of critical values of Students'-t. Values smaller than the critical value indicate a high probability that the null hypothesis, is supported. If the calculated t-value is greater than or equal to the critical value, then the null hypothesis is rejected and the alternate hypothesis, is accepted. The appropriate degrees of freedom, DF, is DF1 + DF2 (DF1 = N1-1; DF2 = N2-1; DF = N1 + N2-2).
Critical Values of Students'-t
DF
_ = 0.10
_ = 0.05
DF
_ = 0.10
_ = 0.05
1
6.31
12.71
11
1.80
2.20
2
2.92
4.31
12
1.78
2.18
3
2.35
3.18
13
1.77
2.16
4
2.13
2.78
14
1.76
2.14
5
2.01
2.57
15
1.75
2.13
6
1.94
2.45
16
1.75
2.12
7
1.89
2.36
17
1.74
2.11
8
1.86
2.31
18
1.73
2.10
9
1.83
2.26
19
1.73
2.09
10
1.81
2.23
20
1.72
2.09
(Note: About, the level of significance. Rejecting the null hypothesis, when it is in fact true, is called a Type I error. The probability of making a Type I error is called the level of significance; _ = 0.05 means the probability of a false rejection is only 5%. Unfortunately, by reducing the probability of making a Type I error, you are increasing the chance of accepting the null hypothesis when it is not true- a Type II error!).
Randomly Assorted Digits
00-04
05-09
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
00
54463
22662
56905
70639
79365
67382
29085
23248
47058
08186
01
15389
85205
11885
39226
22490
90669
96325
56891
60933
26927
02
85941
40756
82414
02015
13858
78060
16269
62773
10389
15345
03
61149
69440
11286
88218
58928
03638
52862
72095
33451
77455
04
05219
81619
10651
67079
92511
59888
84502
20002
83463
75577
05
41417
89326
87719
92294
46614
50948
64886
05217
97365
30976
06
28357
94070
20652
35774
16249
75019
21145
62481
47286
67305
07
17783
00015
10806
83091
91530
36466
39981
62660
49177
75779
08
40950
84820
29881
85966
62800
70629
84740
96488
77379
90279
09
82995
64157
66164
41180
10089
73417
78258
32940
88629
37231
10
96754
17676
55659
44015
47361
37032
86679
22885
53249
27083
11
34357
88040
53364
71726
45690
66334
60332
48888
90600
71113
12
06318
37403
49927
57715
50423
67372
63116
73947
21505
87018
13
62111
52820
07243
79931
89292
84767
85693
54440
22278
11551
14
47534
09243
67879
00554
23410
12740
02540
73443
32949
13491
15
98614
75993
84460
62846
59844
14922
48730
70158
48167
34770
16
24856
03648
44898
09351
98795
18644
39465
53342
90638
44105
17
96887
12479
80621
66223
86085
78285
02432
21434
42846
94771
18
90801
21472
42815
77408
37390
76766
52615
41943
30268
18106
19
55165
89522
83666
36028
28420
70219
81369
89872
47366
41067
20
75884
03033
84318
95108
75305
64620
91318
87894
45375
85439
21
16777
38804
56882
42859
21460
43910
01175
03164
81378
40620
22
46230
43877
80207
88844
89380
32992
94380
60137
98656
59637
23
42902
66892
46134
01432
94710
23474
20423
19774
60609
43449
24
81007
00333
39693
28039
10154
95425
2230
97017
31782
41550
25
68089
01122
51111
72373
06902
74676
96199
87236
41273
21546
26
20411
67081
89950
16944
93054
87687
96693
58680
77045
33848
27
58212
13160
06468
15718
82627
76999
05999
12696
96739
69700
28
70577
42866
24969
61210
76049
67699
42054
05437
93758
03283
29
94522
75628
71659
62038
79643
79169
44741
32404
39038
13163
30
42626
86819
85651
88678
17401
03252
99547
48769
17918
62880
31
16051
33769
57194
16752
54450
19031
58580
55781
54132
60631
32
08244
27647
33851
44705
94211
46716
11738
17805
95374
72655
33
59497
04392
09419
89964
51211
04894
72882
82171
21896
83864
34
97155
13428
40293
00998
58434
01412
69124
39435
59085
8285
35
89409
66162
95769
47420
20792
61527
20441
61203
11859
41567
36
45476
8882
56109
96597
25930
66790
65706
66669
53634
22557
37
89300
68799
50741
30329
11685
23166
05400
65578
48708
03887
38
50051
95137
91631
66315
97428
12275
24816
45153
71710
33258
39
361753
85178
31310
89642
98364
02306
24617
09609
83942
22716
40
79152
53829
77250
20190
56535
18760
69942
77448
33278
48805
41
44560
38750
82635
56540
64900
42912
13953
79149
18711
68618
42
38328
83378
63369
71381
39564
05615
42451
64559
97507
65747
43
46939
38689
58625
08324
30459
85863
20781
09284
23666
91777
44
83544
86141
15707
96256
23068
04372
08467
89496
93848
55376
45
91621
00881
04900
54224
46177
55309
17852
27491
89415
23466
46
91869
67126
04151
03795
59077
01848
12630
98375
52068
60427
47
55751
62515
21108
80830
02263
29303
37204
96926
30506
97111
48
85156
87689
95493
88842
00664
55017
55539
17771
69448
01117
49
07521
56898
12236
60277
39402
62315
12239
07105
11844
44517
PROCEDURE
Prelaboratory.
Start out with a hypothetical scenario that will force students to think about solving problems and introduce them to sampling and some basic statistics at the same time. For instance, relate a scenario similar to the following. You have to supplement your meager GTA income and are thinking about opening up a car dealership (shoe store, clothing shop, sunglass shop, etc.) catering to the college community. You want some data to determine what company (lines, brands, items, etc.) you should carry - and you need this information by the end of the hour in order to secure your small business loan.
To get a rough idea you could survey the students in your recitation - make a list of how many drive: Chevys, Fords, Hundais, Hondas, Nissans, Toyotas, etc. Ask the class to make a suggestion, based on the list, of what would be the best choice. Their consensus response is the class hypothesis.
Now, how to test the hypothesis? Allow groups to brainstorm among themselves for about 5 minutes to generate a list of possibilities. Then go group to group, listing possible suggestions on the board. The constricting factors are the time and the fact that you're keying in on the university community. A variety of survey methods will probably be suggested, including the library, telephone calls to theDepartment of Motor Vehicles, etc.
What we are looking for is to have each group go out to some street location on campus and tally the cars going by, or to a parking lot to tally the vehicles parked. Get the class to agree on a sampling technique.
Some things to consider are: Where to sample?, How long to sample?, Cars in both directions or a single direction, How to tally results, eg. which makes?, To sample every car, every other, every fifth, etc.? Once the class agrees on the data collection procedure, send them off, by groups, to collect their data. Set a time limit for them to return to class with their results. Twenty minutes is reasonable to get to a location, collect data for about 5 minutes, and return.
While the students are out collecting data, prepare a table on the board, or an overhead, to summarize class data. An example follows.
Make
Group 1
Group 2
Group 3
Group 4
Chevy
Ford
Honda
Hundai
Nissan
Toyota
others
As student groups return, they should place their data into the appropriate column of the summary table.
Each student should make a complete copy of the summary data to work on before lab.
The student assignment, in preparation for lab, is to calculate two basic summary statistics, mean and standard deviation, using the summary class data table.
Laboratory Activity 1.
During the recitation, students were presented with a problem and asked to find a solution. In actuality they were asked to put the scientific method into practice, without being told that this is what they were doing. During the first part of the laboratory we want them to "discover" the scientific method. Of course, they have been taught the "steps" in their previous schooling and could probably list and describe the steps for you if you asked them to. But teaching it in this way tends to reinforce the misconception that the scientific method is some rigid system that only scientists use. In actuality, it is simply a formalization of every day, common sense problem solving, and it is precisely this point that we want to make.
We want to introduce the concept of the scientific method by reviewing the activities of the recitation session. This will also provide an opportunity to formally introduce concept mapping as a technique. Begin by recalling for your students the problem you asked them to help you solve, eg. which kind of car dealership to open. Place this in a box, high on the board (it will become the principle concept in the map the class develops). Now recall that your preliminary class survey suggested that a particular make would probably be best. This is the hypothesis which can be placed in a second box, under the first, as shown below.
Best Dealership is probably Toyota
Next you decided on how the class could test if indeed these preliminary observations were valid for the broader university community. First, you had to decide on what criteria would be the best to check, given the constraints you set for the problem. Some of the possibilities may have been: most licenses sold, profits of existing dealerships, most vehicles sold, highest profit/car, etc. Next, you had to decide on a sampling method, which itself had several parameters. Once data was collected it had to be summarized and analyzed, and finally a conclusion had to be reached concerning whether or not the data supported the original hypothesis. All of this can be summarized in a concept map such as the one presented below. Work this through on the board or an overhead with your class. Once a consensus map has been agreed upon, have your students copy it in the space provided on their laboratory handout. This will serve as an example to them as they construct their own maps during future activities.
You are now ready to make a very important point to your students. The problem solving approach they used to determine the best business for you to invest in was really application of the scientific method. In other words, the scientific method is not some mystical technique employed only by scientists locked away in a laboratory somewhere (and out of touch with the real world). Instead, it is simply a formalization of common sense problem solving that we all do every day! To illustrate this, first make a concept map of the scientific method (some of your students will surely have memorized the steps in some previous course so they will be able to list them, in order, for you.
Now have your students go back to their concept map of how the problem was solved and draw an enclosing circle around every box that is part of observation. Then do the same for every hypotheses. Repeat for all the boxes that are experimental, and finally those that are conclusions.
Activity 2.
Students' homework assignment between recitation and laboratory was to calculate the summary statistics on their class summary data sheets. Now we want to introduce them to the computer program for statistical analysis, and simultaneously give them an opportunity to check their own work.
There should be one computer workstation for each group of six students per table. Have the students group around their workstation. Specific instructions at this point depends on the hardware and software available. Enter the statistics package and choose "Mean and Standard Deviation". The computer will prompt for data entries. For instance, the first student should enter the data collected for "Chevy". The printout will give mean and standard deviation which will allow students to check their calculated values. They should indicate with a check on their table if their calculated value was correct. If incorrect, they should strike out the incorrect answer with a single line, then write in the correct value.
Have a second student do the same for the second model sampled. A third student does the same for the third model, etc., until each student has entered data and calculated values for one data set.
This sheet will be turned in by students for credit.
HINTS AND SUGGESTIONS
The following ideas frequently come up during the class discussion of how to gather data
Passive sampling - check library for information (eg. sales and/or tax records)
- phone state Department of Motor Vehicles
- phone Auto dealers in area
Active sampling - passing cars on a street corner
- which one?
- one direction or both?
- for how long?
- parking lots
- which one?
- every car or a sub sampling?
MINIMUM MATERIALS NEEDED
Computer with statistical package is handy, but not absolutely necessary.
EXPECTED STUDENT OUTCOMES
Some student groups will probably have data significantly different from that of other groups. Further discussion at this point usually reveals differences in sampling techniques that were not standardized previously. This also allows for discussion of the legitimacy of pooling data in this experiment. Students now will be aware of these kinds of problems and should consider them in designing future experiments.
An example of actual class data:
Make
Group
1
Group
2
Group
3
Group
4
Sum
Mean
St.Dev.
S.E.
TIME FRAME
The activity was originally designed for a one hour recitation followed by the first part of a three hour laboratory period. The actual data collection could be designed as a homework activity for the group so that the problem could be set up during the last 20-30 minutes of a lecture and then the data collated and analyzed during the subsequent laboratory period.
STUDENT PROTOCOL
INTRODUCTION
Investigative laboratories will probably be very different for you from those in any previous science course you have taken. It may be very frustrating, at first, because you will not have specific directions to follow or lists of terms and concepts to memorize. Instead, you and your research team will have to become self-reliant in making observations, forming questions, proposing hypotheses, in particular null hypotheses, designing tests of you hypotheses and analyzing and interpreting the results of your tests.
YOU ARE EXPECTED TO DO THE WORK.
OBJECTIVES
1. You should be able to construct a concept map to show relationships between ideas.
(note: concept mapping is THE BEST way to study and learn new information, eg., after each lecture, map your notes and then go back and connect the day's map to what you learned previously in the course.)
2. You should be able to solve problems in a rational way (i.e., using the scientific
method).
3. You should understand the importance of repeating observations and be able to calculate
and interpret summary statistics.
SPECIFIC INSTRUCTIONS
During this recitation you are asked to collect some data, as a group, then combine the results from your group with that of other groups. Use the table outline below as a guide - add additional columns and/or rows as needed.
Make
Group
1
Group
2
Group
3
Group
4
Sum
Mean
St.Dev.
S.E.
During class, you will decide on how best to collect data to test the hypothesis the class decides upon. Each group, including yours, will have to collect data, then bring it back to class to share with other members of your section. You will need a personal copy of all the group data from your lab section. Therefore, as groups return from collecting data, they will fill in a class summary form, similar to the one above. You should copy this information onto your form.
Your assignment, to be completed BEFORE lab, is to calculate the summary statistics mean and standard error for the four most common car makes. The procedures for doing this are listed under "Statistics" in your resource manual. The first thing you will have to do is add up the total numbers for each row. This is filled in under the column "Sum". The sum divided by the number of samples taken (4, i.e., one for each group) is the mean, or average. The procedures for calculating standard deviation (St. Dev.) and standard error (S.E.) are described in the resource manual.
Your instructor will introduce you to the technique of concept mapping in the laboratory.
QUIZ
NAME: _________________________________________________________
Section #: ___
1. In 1903 a federal commission measured the flow of the Colorado River to determine the
volume of water flow that could be divided by treaty among seven western states and Mexico. Based on that survey, 15 million acre feet of water was partitioned. Currently there are water rights disputes in the West because the average annual water flow of the Colorado River is actually about 14 million acre feet. What basic experimental principle should the government have used, at the turn of this century, to obtain a more accurate measure of volume flow? Describe in one or two paragraphs how you would have determined the amount of water that should have been allocated.