Health Care Law And Legislation DB Week three

Health care law and legislation discussion board week 3

Hospital Department and Allied Health Professionals Options Menu: Forum

Describe and discuss the most common negligent error by any allied health professional of your crossing.

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Soil Invertebrate Diversity

1

Formal Lab

Foundations of Biology: Evolution, Ecology, and Biodiversity Lab

Soil Invertebrate Diversity

LEARNING OUTCOMES During this three-day laboratory exercise, you will:

1. Sample the invertebrates in soil and leaf litter using field and laboratory techniques. 2. Use a dichotomous key to identify the soil invertebrates. 3. Calculate and compare the invertebrate diversity within soil samples taken from habitats

with different water availabilities. 4. Statistically analyze the collective data from all lab sections to serve as the basis for a

formal lab report. BACKGROUND Invertebrates are one of the dominant groups of organisms in soil food webs. Probably the most common invertebrate groups in the soil are arthropods and nematodes, but other phyla are represented as well. Soil invertebrates may be predators, herbivores, or detritivores, or may feed specifically on fungi and bacteria that are abundant in the soil. Of course, soil invertebrates live where they do not only for the food, but also for the shelter—they require the shade, moisture, and stable temperatures that soil and leaf litter provide. The diversity of soil invertebrates can affect the properties of the very soil in which they reside, due to the fact that they influence key soil processes such as nutrient cycling, nutrient retention, the formation of soil structure, and decomposition rates. To sample soil invertebrates, you first need to obtain a small quantity of soil or leaf litter. The tricky part is then extracting all of the small invertebrates from the soil. To get them to come out of their otherwise optimal habitat, you need to make the soil unpleasantly hot and dry. An apparatus called a Berlese funnel will help with this job. The Berlese funnel does not extract all of the organisms from the soil. Fungi and bacteria are not motile enough to escape, and some invertebrates are also connected to the soil particles. However, this technique does give a good estimate of the true soil invertebrate diversity. EXERCISES Activity 1 (Week 1) – Sampling a Soil Habitat for Invertebrates

1. You will work with your lab partner to obtain a soil and leaf litter sample from one of three local campus habitats. Your lab instructor will lead you to all three locations so that everyone is able to observe the conditions encountered and methods employed at each.
2. The three locations sampled will be habitats that differ in water availability. The first site

2

will be a manicured grove that receives an optimal amount of water on a regular basis. The second site will be a natural woodland that on occasion has a small stream trickling through, so there is some (but not an abundant amount of) water present much of the time. Therefore, even when water is not present, the soil remains somewhat damp. The third and final site will be a very dry grassland / shrubland location that gets minimal water throughout the year. Note that you may not sample from these three locations in this particular order.

1. All lab sections will sample from these same three habitats—data will be combined for

all sections. As each lab section has twelve groups of two, four groups from each section will sample from one particular location. Specific sampling spots within each habitat will be chosen randomly by each group. Following the directions given by your instructor, obtain a leaf litter sample from your sampling spot. Fill about three-fourths of a plastic bag with soil and leaf litter scooped from the ground surface.

1. Spend a few minutes at each location examining the habitat that was just sampled. Do

you see any invertebrates crawling on the surface of the soil or in the leaf litter? How wet or dry does the site appear? Begin thinking about which habitat may contain the greatest invertebrate diversity.

Activity 2 (Week 1) – Constructing and Using a Berlese Funnel A Berlese funnel is a simple device used for extracting small invertebrate animals from soil and leaf litter samples. The Berlese funnel creates a very hot and dry environment at one end of the funnel, driving the invertebrates to the other end. Here they will fall out into a container of alcohol that is set up to collect them. Once you have extracted the invertebrates from your sample, you can observe them using a dissecting microscope and, with the aid of a dichotomous key, identify what kinds of invertebrates are present in the sample. This process, along with calculating the Shannon index, will allow you to determine your soil invertebrate diversity. First, though, the Berlese funnel must be set up—follow the procedure below to construct your own funnel.

1. Cut an empty and clean 2-liter bottle 3 cm below the top of the label using a sharp scalpel. Then cut off the neck by cutting along the middle of the curvature. The bottom of the bottle will serve as the jar. The top of the bottle with the neck removed will serve as the funnel. The neck of the bottle can be discarded.
2. Fill approximately one-fourth of the jar with 70% isopropyl alcohol.
3. On a strip of tape placed on the jar, write a label for your sample. Include your names,

lab section, and the habitat from which you sampled.

1. Invert the funnel end of the bottle into the jar (see Figure 1).
2. Place an approximately 30 cm × 30 cm piece of square screening into the funnel so that it lines the entire inside. The screening has mesh large enough for invertebrate animals to

3

fall through but will keep much of the soil and leaves from falling into the alcohol. Use masking tape to secure the square screening onto the outside of the funnel by taping down all four corners.

1. Transfer your leaf litter sample from your plastic bag into the lined funnel.
2. Place the entire funnel apparatus underneath a heat lamp. This heat source will drive the

invertebrates to the lower end of the soil sample, causing them to fall through the screening and the mouth of the funnel into the alcohol, where they will be collected as your sample. Adjust the lamp so that the bulb is about three to four inches away from the top of your leaf litter.

1. Let the Berlese funnel sit under the heat lamp for one week. Most of the invertebrates

should be extracted in that amount of time.

Figure 1: Diagram of a Berlese Funnel Activity 3 (Week 2) – Identifying the Invertebrates in Your Soil Sample

1. Remove the jar containing the extracted soil invertebrates from your Berlese funnel.
2. Carefully pour a small amount of alcohol from the jar into a Petri dish. Only pour enough to fill half of the Petri dish.
3. With your lab partner, observe the Petri dish under a dissecting microscope. Be sure to

adjust the light source, magnification, and focus for optimal viewing.

1. As you find the invertebrates in your sample, make a sketch or detailed notes of each one so that you are very familiar with the organisms you are observing. Use a small paintbrush to move around or pick up the small animals in the Petri dish. Using forceps

4

is not likely to be effective and may actually crush some of the individuals in your sample.

1. Use the dichotomous key provided by your lab instructor to identify the invertebrates in

your sample. As most of your sample will consist of arthropods, the key is specifically for this phylum. Key out the arthropods to the class level. As the class Insecta will be the most abundant, the key enables you to identify insects to the order level. All other phyla can simply be recorded as such. Record the name of each phylum, class, or order that you identify in Table 1. Keep a tally of the number of individuals in each taxonomic group that you encounter in your sample. You will probably want to remove the organisms from your Petri dish once you have recorded them so that you can keep an accurate tally, but do not discard them completely in case you need to recheck any of your work.

1. Repeat steps 2 through 5 until all of the alcohol is drained from your jar. If necessary,

you may have to add additional alcohol to “rinse” out any invertebrates or small particles that stick to the walls of the jar.

1. Once completed, count your tallies and record the total number of individuals from each

taxon in Table 1. Sum these counts to determine the total number of individuals in your entire sample.

Activity 4 (Week 2) – Calculating the Soil Invertebrate Diversity You will use the Shannon index (H′) to calculate the diversity of your soil / leaf litter sample. Recall the equation for this diversity index: abundance of a given taxon (i) where pi = H′ = -ΣS (pi ln pi) total abundance of all taxa and S = the # of different taxa Complete Table 1 by calculating pi, ln pi, and pi ln pi for each invertebrate taxon. Determine the total diversity by summing all of the pi ln pi values and reversing the negative sign. This will yield the diversity for your sample. Your lab instructor will indicate the proper procedures for cleaning up / discarding / putting away funnels, mesh, soil, leaf litter, alcohol, invertebrates, and lamps. Have your work checked by your lab instructor prior to disassembling your Berlese funnel and cleaning up your lab bench. Be sure to give your diversity value, as well as the habitat from which the value came, to your instructor. All of the diversity values from all lab sections will be combined to produce one large set of data.

5

Table 1: Shannon Diversity Index Calculations Lab Partner Names Habitat Sampled

Invertebrate Taxon (Phylum, Class, or

Order)

of Individuals of

this Taxon pi ln pi pi ln pi

Total # of individuals

(add the second column)

H′ = – ΣS (pi ln pi) (add the last column and reverse the – sign)

pi = # of individuals of a particular taxon / total # of individuals in the entire sample

6

Activity 5 (Week 3) – Analyzing Differences in Diversity Among the Habitats A statistical technique known as ANOVA will be used to determine if there is a difference in the diversity of invertebrates among the three habitats (which do differ in the amount of water that they receive). Let us explore the topic of statistics further using a simple example so that you feel comfortable with the analysis that you will be performing. Suppose you want to know if there is a difference between the mean (average) height of all of the male students on campus and the mean (average) height of all of the female students on campus. Here, the heights of all of the male students on campus and the heights of all of the female students on campus are termed populations, and the means of these populations are termed parameters. A parameter is a numerical summary of a population. You can probably imagine that it might be challenging to obtain the height of every single male student and every single female student on campus. Because populations are often very large (as in this example), population parameters will likely not be able to be determined. To resolve this, a sample (random subset) needs to be taken from each of the populations. You could sample 30 male students and measure their heights and then sample 30 female students and measure their heights. Here, the heights of the random subsets from the populations are termed samples, and the means of these samples are termed statistics. A statistic is a numerical summary of a sample. Sample statistics are therefore estimates of population parameters. Statistics will rarely if ever equal the parameters exactly. The difference between the statistic and the parameter (which a researcher would not know, as parameters are not known) is termed sampling error. Not only will statistics estimate the parameters of interest, they will allow for an objective method of dealing with this sampling error. Statistics are therefore very important tools, as they enable scientists to make conclusions about entire populations, though they are working with just samples. Statistics will reveal how reliable these conclusions are. How exactly are these conclusions determined? All hypotheses formulated in biology are set up as null and alternative hypotheses. A null hypothesis is a hypothesis of no difference or no relationship. In the student height example, the null hypothesis would be that there is no difference between the mean male height and the mean female height of all students on campus. An alternative hypothesis must accompany each null hypothesis, and together these two hypotheses must account for all possibilities. In this example, the alternative hypothesis would be that there is a difference in the mean heights of male and female students on campus. As you can see, there are no other possibilities—there either is a difference or there is not a difference between male and female heights. Based on the type of data, the number of samples collected, and the question of interest, a particular statistical test will be performed. Remember, for our soil invertebrate study you will be utilizing a test known as ANOVA. For the student height example, a different statistical test (known as a t-test) would be employed. Understanding when to use which type of statistical test need not concern you here—you will deal with that when you take a biostatistics class. What is important now is to understand the results that the tests give you.

7

Each statistical test will yield a result known as a p-value. A p-value is a probability value and therefore always ranges between 0 and 1. Again, the calculation of the p-value is beyond the scope of this course (we will let Microsoft Excel calculate it for us). However, you do need to be able to interpret it. A p-value is the probability (percent chance) that a sample could have been taken from a population in which the null hypothesis is true. Remember what the null hypothesis is—the hypothesis of no difference. If the p-value in the height example turned out to be 0.85, then there would be an 85% chance that the samples were taken from populations in which there is no difference in the mean heights of male and female students. This is a very high probability, so we would accept the null hypothesis and conclude that there is no difference between the mean height of males and the mean height of females on campus. Suppose the p-value was instead 0.01. This would mean that there is only a 1% chance that the samples came from populations in which the null hypothesis (no difference in the mean heights) is true. This is a very small probability, so we would therefore reject the null hypothesis, concluding instead that there is in fact a difference between the mean height of males and the mean height of females on campus (the alternative hypothesis). Where is the line drawn between accepting and rejecting the null hypothesis? It is standard practice in biology to only reject the null hypothesis if the p-value is less than or equal to 0.05. The reason for 0.05 will become apparent in a biostatistics course. For now, rest assured that there is a solid mathematical basis for this value. Once it is known that there is a difference between the populations (if in fact there is one), how can it be determined what that difference is? Go back and look at the mean values from the samples. If the males have a higher mean value, then it can be concluded that males on campus are significantly taller than females. If the females have a higher mean value, then it can be concluded that the females on campus are significantly taller. Again, remember that this is the goal of statistics—making overall conclusions about populations using data obtained only from samples. It is a very important tool, as we need to make conclusions about entire populations, but they are just too large to work with. Practice your understanding of statistics using another example: Is there a difference in photosynthesis rates among plants grown in low, medium, and high light levels? The sample mean photosynthesis rate from plants in low light is 20 units, the sample mean from medium light is 25 units, the sample mean from high light is 30 units, and the p-value is 0.03. (Units of photosynthesis = μmol/m2/sec.) What is the null hypothesis?

What is the alternative hypothesis?

8

Is the null hypothesis accepted or rejected? What conclusion can you make based on these results?

Now for some more details as to how ANOVA in particular works. ANOVA is used when you are analyzing differences in means among three or more samples. As we have data from three different samples (the three different habitats), ANOVA is the appropriate statistical test for our study. ANOVA stands for analysis of variance, which indicates what the test does—it analyzes the variances of the samples. Variances are measures of variability. If there is much variability among all of the samples, then it should make sense that the samples are not the same—there is a difference in the diversity of invertebrates, for example, among three sites that differ in water availability. Take a look at the following example, which shows hypothetical values for invertebrate diversity at three locations (only five values are shown for each in this example, but remember that our data set will be much larger as we are combining data from all lab sections): High H2O Low H2O No H2O 7 3 2 7 3 2 7 3 2 7 3 2 7 3 2 Mean: 7 3 2 In the above example, there is variation among the three habitats. The habitat with much water has the highest mean invertebrate diversity, the habitat with no water has the lowest mean invertebrate diversity, and the habitat with intermediate water availability have intermediate invertebrate diversity. In this case, the null hypothesis of no difference among the habitats would be rejected and we would instead conclude that there is a difference in diversity. Now consider another example, which also shows variation, but variation of a different kind: High H2O Low H2O No H2O 7 4 3 6 3 2 4 2 7 3 7 6 2 6 4 Mean: 4.4 4.4 4.4 In the above example, there is variation within each sample rather than among the samples. Notice that within each habitat, various different diversity values are obtained, but the mean

9

diversity value among all three habitats is identical. In this case, the null hypothesis of no difference among the samples would be accepted—there is no difference in invertebrate diversity among habitats with differing water availabilities. What causes the variation within each sample in this example? Perhaps it is different availabilities of other nutrients. Perhaps it is differing temperatures. However, as these factors are not being tested for in our study, we cannot say with certainty what is causing the variation. What can be said with certainty is that what we are testing for, a difference in water availability, has no effect on invertebrate diversity. In the first example, there was variation among the samples but no variation within each sample, and we rejected the null hypothesis of no difference. In the second example, there was variation within each sample but no variation among the samples, and we accepted the null hypothesis of no difference. A much more likely scenario is that there will be some variation among the samples and some variation within each sample: High H2O Low H2O No H2O 6 4 3 7 2 3 6 5 2 8 3 2 7 4 2 Mean: 6.8 3.6 2.4 You should convince yourself that, in order to reject the null hypothesis and conclude that there is a difference among the three habitats, there must be greater variation among the samples rather than within the samples. How is it determined which is greater? This is where the calculation of a p-value by Microsoft Excel comes into play. Enter the raw data into an Excel spreadsheet and then select Tools → Data Analysis → Anova: Single Factor. When you are asked to input the range, highlight your data. Click OK and find the p-value in the output table. Practice using the data analysis feature in Excel by entering the above example (the one with some variation among the samples and some variation within the samples). You should find a p- value of 1.18×10-5 (0.0000118) in the output table. Will you accept or reject the null hypothesis of no difference in this example? Why?

Is there more variation among the habitats or within each habitat in this example?

What conclusion can you make about invertebrate diversity in habitats with different water

availabilities? Note that the means for each sample are given in the output table as well.

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You are now ready to input the actual invertebrate diversity data from the three different habitats sampled by the entire class. Don’t be overwhelmed by all of this background information—after all, Excel is doing the work for you. You just need to have a big picture understanding of the results that Excel gives you. Ask your instructor about your results to make sure that you are interpreting them correctly. Activity 6 (Week 3) – Searching for Sources as Background Information You will be writing your lab report in the form of a formal scientific paper. Your lab instructor will discuss the required components of a scientific paper. One requirement is to find other papers that have performed studies similar to yours, citing them in your own paper as background information or to compare results. Cited sources must be peer-reviewed scientific journal articles. Textbooks and websites are not permitted. While in lab, you will start to look up journal articles and have your lab instructor confirm that they are indeed relevant sources for your paper. Two good locations to begin your search for sources are:

1. The Cal Poly Pomona website. From the homepage, search for the University Library, then begin searching for journal articles by typing in some keywords (for example, invertebrate diversity and water availability). The search results will indicate which sources are peer-reviewed journal articles.
2. Google Scholar. Go to https://scholar.google.com/, type in some keywords, and examine

the peer-reviewed articles that result to determine which may be appropriate for inclusion in your paper.

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What is the alternative hypothesis?

1

Formal Lab

Foundations of Biology: Evolution, Ecology, and Biodiversity Lab

Soil Invertebrate Diversity

LEARNING OUTCOMES During this three-day laboratory exercise, you will:

1. Sample the invertebrates in soil and leaf litter using field and laboratory techniques. 2. Use a dichotomous key to identify the soil invertebrates. 3. Calculate and compare the invertebrate diversity within soil samples taken from habitats

with different water availabilities. 4. Statistically analyze the collective data from all lab sections to serve as the basis for a

formal lab report. BACKGROUND Invertebrates are one of the dominant groups of organisms in soil food webs. Probably the most common invertebrate groups in the soil are arthropods and nematodes, but other phyla are represented as well. Soil invertebrates may be predators, herbivores, or detritivores, or may feed specifically on fungi and bacteria that are abundant in the soil. Of course, soil invertebrates live where they do not only for the food, but also for the shelter—they require the shade, moisture, and stable temperatures that soil and leaf litter provide. The diversity of soil invertebrates can affect the properties of the very soil in which they reside, due to the fact that they influence key soil processes such as nutrient cycling, nutrient retention, the formation of soil structure, and decomposition rates. To sample soil invertebrates, you first need to obtain a small quantity of soil or leaf litter. The tricky part is then extracting all of the small invertebrates from the soil. To get them to come out of their otherwise optimal habitat, you need to make the soil unpleasantly hot and dry. An apparatus called a Berlese funnel will help with this job. The Berlese funnel does not extract all of the organisms from the soil. Fungi and bacteria are not motile enough to escape, and some invertebrates are also connected to the soil particles. However, this technique does give a good estimate of the true soil invertebrate diversity. EXERCISES Activity 1 (Week 1) – Sampling a Soil Habitat for Invertebrates

1. You will work with your lab partner to obtain a soil and leaf litter sample from one of three local campus habitats. Your lab instructor will lead you to all three locations so that everyone is able to observe the conditions encountered and methods employed at each.
2. The three locations sampled will be habitats that differ in water availability. The first site

2

will be a manicured grove that receives an optimal amount of water on a regular basis. The second site will be a natural woodland that on occasion has a small stream trickling through, so there is some (but not an abundant amount of) water present much of the time. Therefore, even when water is not present, the soil remains somewhat damp. The third and final site will be a very dry grassland / shrubland location that gets minimal water throughout the year. Note that you may not sample from these three locations in this particular order.

1. All lab sections will sample from these same three habitats—data will be combined for

all sections. As each lab section has twelve groups of two, four groups from each section will sample from one particular location. Specific sampling spots within each habitat will be chosen randomly by each group. Following the directions given by your instructor, obtain a leaf litter sample from your sampling spot. Fill about three-fourths of a plastic bag with soil and leaf litter scooped from the ground surface.

1. Spend a few minutes at each location examining the habitat that was just sampled. Do

you see any invertebrates crawling on the surface of the soil or in the leaf litter? How wet or dry does the site appear? Begin thinking about which habitat may contain the greatest invertebrate diversity.

Activity 2 (Week 1) – Constructing and Using a Berlese Funnel A Berlese funnel is a simple device used for extracting small invertebrate animals from soil and leaf litter samples. The Berlese funnel creates a very hot and dry environment at one end of the funnel, driving the invertebrates to the other end. Here they will fall out into a container of alcohol that is set up to collect them. Once you have extracted the invertebrates from your sample, you can observe them using a dissecting microscope and, with the aid of a dichotomous key, identify what kinds of invertebrates are present in the sample. This process, along with calculating the Shannon index, will allow you to determine your soil invertebrate diversity. First, though, the Berlese funnel must be set up—follow the procedure below to construct your own funnel.

1. Cut an empty and clean 2-liter bottle 3 cm below the top of the label using a sharp scalpel. Then cut off the neck by cutting along the middle of the curvature. The bottom of the bottle will serve as the jar. The top of the bottle with the neck removed will serve as the funnel. The neck of the bottle can be discarded.
2. Fill approximately one-fourth of the jar with 70% isopropyl alcohol.
3. On a strip of tape placed on the jar, write a label for your sample. Include your names,

lab section, and the habitat from which you sampled.

1. Invert the funnel end of the bottle into the jar (see Figure 1).
2. Place an approximately 30 cm × 30 cm piece of square screening into the funnel so that it lines the entire inside. The screening has mesh large enough for invertebrate animals to

3

fall through but will keep much of the soil and leaves from falling into the alcohol. Use masking tape to secure the square screening onto the outside of the funnel by taping down all four corners.

1. Transfer your leaf litter sample from your plastic bag into the lined funnel.
2. Place the entire funnel apparatus underneath a heat lamp. This heat source will drive the

invertebrates to the lower end of the soil sample, causing them to fall through the screening and the mouth of the funnel into the alcohol, where they will be collected as your sample. Adjust the lamp so that the bulb is about three to four inches away from the top of your leaf litter.

1. Let the Berlese funnel sit under the heat lamp for one week. Most of the invertebrates

should be extracted in that amount of time.

Figure 1: Diagram of a Berlese Funnel Activity 3 (Week 2) – Identifying the Invertebrates in Your Soil Sample

1. Remove the jar containing the extracted soil invertebrates from your Berlese funnel.
2. Carefully pour a small amount of alcohol from the jar into a Petri dish. Only pour enough to fill half of the Petri dish.
3. With your lab partner, observe the Petri dish under a dissecting microscope. Be sure to

adjust the light source, magnification, and focus for optimal viewing.

1. As you find the invertebrates in your sample, make a sketch or detailed notes of each one so that you are very familiar with the organisms you are observing. Use a small paintbrush to move around or pick up the small animals in the Petri dish. Using forceps

4

is not likely to be effective and may actually crush some of the individuals in your sample.

1. Use the dichotomous key provided by your lab instructor to identify the invertebrates in

your sample. As most of your sample will consist of arthropods, the key is specifically for this phylum. Key out the arthropods to the class level. As the class Insecta will be the most abundant, the key enables you to identify insects to the order level. All other phyla can simply be recorded as such. Record the name of each phylum, class, or order that you identify in Table 1. Keep a tally of the number of individuals in each taxonomic group that you encounter in your sample. You will probably want to remove the organisms from your Petri dish once you have recorded them so that you can keep an accurate tally, but do not discard them completely in case you need to recheck any of your work.

1. Repeat steps 2 through 5 until all of the alcohol is drained from your jar. If necessary,

you may have to add additional alcohol to “rinse” out any invertebrates or small particles that stick to the walls of the jar.

1. Once completed, count your tallies and record the total number of individuals from each

taxon in Table 1. Sum these counts to determine the total number of individuals in your entire sample.

Activity 4 (Week 2) – Calculating the Soil Invertebrate Diversity You will use the Shannon index (H′) to calculate the diversity of your soil / leaf litter sample. Recall the equation for this diversity index: abundance of a given taxon (i) where pi = H′ = -ΣS (pi ln pi) total abundance of all taxa and S = the # of different taxa Complete Table 1 by calculating pi, ln pi, and pi ln pi for each invertebrate taxon. Determine the total diversity by summing all of the pi ln pi values and reversing the negative sign. This will yield the diversity for your sample. Your lab instructor will indicate the proper procedures for cleaning up / discarding / putting away funnels, mesh, soil, leaf litter, alcohol, invertebrates, and lamps. Have your work checked by your lab instructor prior to disassembling your Berlese funnel and cleaning up your lab bench. Be sure to give your diversity value, as well as the habitat from which the value came, to your instructor. All of the diversity values from all lab sections will be combined to produce one large set of data.

5

Table 1: Shannon Diversity Index Calculations Lab Partner Names Habitat Sampled

Invertebrate Taxon (Phylum, Class, or

Order)

of Individuals of

this Taxon pi ln pi pi ln pi

Total # of individuals

(add the second column)

H′ = – ΣS (pi ln pi) (add the last column and reverse the – sign)

pi = # of individuals of a particular taxon / total # of individuals in the entire sample

6

Activity 5 (Week 3) – Analyzing Differences in Diversity Among the Habitats A statistical technique known as ANOVA will be used to determine if there is a difference in the diversity of invertebrates among the three habitats (which do differ in the amount of water that they receive). Let us explore the topic of statistics further using a simple example so that you feel comfortable with the analysis that you will be performing. Suppose you want to know if there is a difference between the mean (average) height of all of the male students on campus and the mean (average) height of all of the female students on campus. Here, the heights of all of the male students on campus and the heights of all of the female students on campus are termed populations, and the means of these populations are termed parameters. A parameter is a numerical summary of a population. You can probably imagine that it might be challenging to obtain the height of every single male student and every single female student on campus. Because populations are often very large (as in this example), population parameters will likely not be able to be determined. To resolve this, a sample (random subset) needs to be taken from each of the populations. You could sample 30 male students and measure their heights and then sample 30 female students and measure their heights. Here, the heights of the random subsets from the populations are termed samples, and the means of these samples are termed statistics. A statistic is a numerical summary of a sample. Sample statistics are therefore estimates of population parameters. Statistics will rarely if ever equal the parameters exactly. The difference between the statistic and the parameter (which a researcher would not know, as parameters are not known) is termed sampling error. Not only will statistics estimate the parameters of interest, they will allow for an objective method of dealing with this sampling error. Statistics are therefore very important tools, as they enable scientists to make conclusions about entire populations, though they are working with just samples. Statistics will reveal how reliable these conclusions are. How exactly are these conclusions determined? All hypotheses formulated in biology are set up as null and alternative hypotheses. A null hypothesis is a hypothesis of no difference or no relationship. In the student height example, the null hypothesis would be that there is no difference between the mean male height and the mean female height of all students on campus. An alternative hypothesis must accompany each null hypothesis, and together these two hypotheses must account for all possibilities. In this example, the alternative hypothesis would be that there is a difference in the mean heights of male and female students on campus. As you can see, there are no other possibilities—there either is a difference or there is not a difference between male and female heights. Based on the type of data, the number of samples collected, and the question of interest, a particular statistical test will be performed. Remember, for our soil invertebrate study you will be utilizing a test known as ANOVA. For the student height example, a different statistical test (known as a t-test) would be employed. Understanding when to use which type of statistical test need not concern you here—you will deal with that when you take a biostatistics class. What is important now is to understand the results that the tests give you.

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Each statistical test will yield a result known as a p-value. A p-value is a probability value and therefore always ranges between 0 and 1. Again, the calculation of the p-value is beyond the scope of this course (we will let Microsoft Excel calculate it for us). However, you do need to be able to interpret it. A p-value is the probability (percent chance) that a sample could have been taken from a population in which the null hypothesis is true. Remember what the null hypothesis is—the hypothesis of no difference. If the p-value in the height example turned out to be 0.85, then there would be an 85% chance that the samples were taken from populations in which there is no difference in the mean heights of male and female students. This is a very high probability, so we would accept the null hypothesis and conclude that there is no difference between the mean height of males and the mean height of females on campus. Suppose the p-value was instead 0.01. This would mean that there is only a 1% chance that the samples came from populations in which the null hypothesis (no difference in the mean heights) is true. This is a very small probability, so we would therefore reject the null hypothesis, concluding instead that there is in fact a difference between the mean height of males and the mean height of females on campus (the alternative hypothesis). Where is the line drawn between accepting and rejecting the null hypothesis? It is standard practice in biology to only reject the null hypothesis if the p-value is less than or equal to 0.05. The reason for 0.05 will become apparent in a biostatistics course. For now, rest assured that there is a solid mathematical basis for this value. Once it is known that there is a difference between the populations (if in fact there is one), how can it be determined what that difference is? Go back and look at the mean values from the samples. If the males have a higher mean value, then it can be concluded that males on campus are significantly taller than females. If the females have a higher mean value, then it can be concluded that the females on campus are significantly taller. Again, remember that this is the goal of statistics—making overall conclusions about populations using data obtained only from samples. It is a very important tool, as we need to make conclusions about entire populations, but they are just too large to work with. Practice your understanding of statistics using another example: Is there a difference in photosynthesis rates among plants grown in low, medium, and high light levels? The sample mean photosynthesis rate from plants in low light is 20 units, the sample mean from medium light is 25 units, the sample mean from high light is 30 units, and the p-value is 0.03. (Units of photosynthesis = μmol/m2/sec.) What is the null hypothesis?

What is the alternative hypothesis?

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Is the null hypothesis accepted or rejected? What conclusion can you make based on these results?

Now for some more details as to how ANOVA in particular works. ANOVA is used when you are analyzing differences in means among three or more samples. As we have data from three different samples (the three different habitats), ANOVA is the appropriate statistical test for our study. ANOVA stands for analysis of variance, which indicates what the test does—it analyzes the variances of the samples. Variances are measures of variability. If there is much variability among all of the samples, then it should make sense that the samples are not the same—there is a difference in the diversity of invertebrates, for example, among three sites that differ in water availability. Take a look at the following example, which shows hypothetical values for invertebrate diversity at three locations (only five values are shown for each in this example, but remember that our data set will be much larger as we are combining data from all lab sections): High H2O Low H2O No H2O 7 3 2 7 3 2 7 3 2 7 3 2 7 3 2 Mean: 7 3 2 In the above example, there is variation among the three habitats. The habitat with much water has the highest mean invertebrate diversity, the habitat with no water has the lowest mean invertebrate diversity, and the habitat with intermediate water availability have intermediate invertebrate diversity. In this case, the null hypothesis of no difference among the habitats would be rejected and we would instead conclude that there is a difference in diversity. Now consider another example, which also shows variation, but variation of a different kind: High H2O Low H2O No H2O 7 4 3 6 3 2 4 2 7 3 7 6 2 6 4 Mean: 4.4 4.4 4.4 In the above example, there is variation within each sample rather than among the samples. Notice that within each habitat, various different diversity values are obtained, but the mean

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diversity value among all three habitats is identical. In this case, the null hypothesis of no difference among the samples would be accepted—there is no difference in invertebrate diversity among habitats with differing water availabilities. What causes the variation within each sample in this example? Perhaps it is different availabilities of other nutrients. Perhaps it is differing temperatures. However, as these factors are not being tested for in our study, we cannot say with certainty what is causing the variation. What can be said with certainty is that what we are testing for, a difference in water availability, has no effect on invertebrate diversity. In the first example, there was variation among the samples but no variation within each sample, and we rejected the null hypothesis of no difference. In the second example, there was variation within each sample but no variation among the samples, and we accepted the null hypothesis of no difference. A much more likely scenario is that there will be some variation among the samples and some variation within each sample: High H2O Low H2O No H2O 6 4 3 7 2 3 6 5 2 8 3 2 7 4 2 Mean: 6.8 3.6 2.4 You should convince yourself that, in order to reject the null hypothesis and conclude that there is a difference among the three habitats, there must be greater variation among the samples rather than within the samples. How is it determined which is greater? This is where the calculation of a p-value by Microsoft Excel comes into play. Enter the raw data into an Excel spreadsheet and then select Tools → Data Analysis → Anova: Single Factor. When you are asked to input the range, highlight your data. Click OK and find the p-value in the output table. Practice using the data analysis feature in Excel by entering the above example (the one with some variation among the samples and some variation within the samples). You should find a p- value of 1.18×10-5 (0.0000118) in the output table. Will you accept or reject the null hypothesis of no difference in this example? Why?

Is there more variation among the habitats or within each habitat in this example?

What conclusion can you make about invertebrate diversity in habitats with different water

availabilities? Note that the means for each sample are given in the output table as well.

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You are now ready to input the actual invertebrate diversity data from the three different habitats sampled by the entire class. Don’t be overwhelmed by all of this background information—after all, Excel is doing the work for you. You just need to have a big picture understanding of the results that Excel gives you. Ask your instructor about your results to make sure that you are interpreting them correctly. Activity 6 (Week 3) – Searching for Sources as Background Information You will be writing your lab report in the form of a formal scientific paper. Your lab instructor will discuss the required components of a scientific paper. One requirement is to find other papers that have performed studies similar to yours, citing them in your own paper as background information or to compare results. Cited sources must be peer-reviewed scientific journal articles. Textbooks and websites are not permitted. While in lab, you will start to look up journal articles and have your lab instructor confirm that they are indeed relevant sources for your paper. Two good locations to begin your search for sources are:

1. The Cal Poly Pomona website. From the homepage, search for the University Library, then begin searching for journal articles by typing in some keywords (for example, invertebrate diversity and water availability). The search results will indicate which sources are peer-reviewed journal articles.
2. Google Scholar. Go to https://scholar.google.com/, type in some keywords, and examine

the peer-reviewed articles that result to determine which may be appropriate for inclusion in your paper.

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Attention And Conscious Thought

Select at least one of the research articles listed in this week’s Learning Resources or referenced by the University of Utah, Department of Psychology/American Psychological Association.

Imagine you were a legislator or inventor in the future. You are familiar with the research on attention and distracted driving, but people still need to be able to communicate with others while they travel. What law would you propose or technology would you invent to enable drivers to communicate with those outside the car while reducing the dangers of distracted driving? (No, you cannot just invent a driverless car or hands free cell phone.) What research would inform your proposed law or invention?

Post a 3- to 4-paragraph response to the following:

For your chosen article, summarize how the researchers conducted the study and what they found.

Based on the research article you summarized and on your reading from the text, critique the law that drivers can only use hands-free cell phones while driving.

For the given scenario, what law would you propose or technology would you invent to enable communication with people outside the car while reducing the dangers of distracted driving? What research would inform your proposed law?

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