Manyh animals engage in aggressive, or agonistic ...



LEARNING TO BE WINNERS OR LOSERS

The scientific study of animal behavior developed into a distinct discipline in the 1930s, arguably reaching a milestone in 1973 when the Nobel Prize was awarded to Konrad Lorenz, Niko Tinbergen and Karl VonFrisch for their pioneering studies of ethology. If you are interested, the Nobel acceptance speeches are available on the Courses Server (or online at ).

A major contribution of these ethologists was to supplement qualitative descriptions of behavior, which are necessary but insufficient, with quantitative measures of behavior.

Tinbergen also presented the concept of four fundamental problems, or questions, to be addressed by the study of behavior:

(1) Development / Ontogeny - How does the behavior arise during the lifetime of the individual?

(2) Mechanistic causation - How do internal and external causal factors elicit and control behavior in the short term?

(3) Evolution / Phylogeny – What is the evolutionary history of the behavior?

(4) Adaptive Value (function) - What is the current utility or survival value of the behavior?

These four questions engender different experimental approaches and provide complementary insights. The most insightful studies in animal behavior address more than one of these questions and employ methods that blur the distinctions between them. The crayfish have been a model organism for many studies on agonistic behaviors involving all 4 levels of investigations (e.g. Huber et al., 2001; Baranaga, 1996).

Theory

As you learned from Bob Kaplan’s lectures, evolution through natural selection works to favor traits that increase the organism’s fitness (overall reproductive success). The theory of natural selection can be used as a framework for developing hypotheses about the evolution of behavior. Evolution, through natural selection, should favor those behaviors that maximize some beneficial currency (e.g. food intake, predator avoidance, mate choice etc.) or minimize cost. Thus existing phenotypes are likely to have high, adaptive value. Rigorous tests of this hypothesis constitute the basis of “the adaptionist approach.”

This “adaptationist approach” can be applied to agonistic interactions with conspecifics. Animals may fight over prey, territories, mates or any other limited resource. The outcome, escalation and intensity of agonistic contests may depend on many factors; for example, animals may differ in their relative fighting ability, motivation, or territorial advantage. Their displays may range from ritualized fights with threat displays through to fully escalated fights with costly physical attacks. (When would it be advantageous (have high survival value) to not fight?) The major cost of escalated fighting is risk of injury, and the major benefit is access to resources (e.g. territory, shelter, food, mates). If these costs and benefits are different for particular individuals in particular encounters, then graded levels of escalation, ranging from ritualized fighting through all-out attacks are expected. Graded levels of aggression allow individuals to settle disputes in a less costly manner.

Empirical research on shelter-dwelling crustaceans, such as lobsters, crayfish, and hermit crabs, has consistently demonstrated dominance hierarchies. When two individuals encounter each other, they respond behaviorally in a manner appropriate for their rank. One question that has been difficult to answer is how such inter-individual assessments of dominance are made. There are three plausible explanations. First, individuals may have dominance recognition. This is the ability to quickly determine the rank of the opponent. Second, individuals may have an internal assessment of their own dominance rank based on past experience. Third, animals may rely on individual recognition, the ability to recognize an individual previously encountered, remembering the relative rank of that individual.

Animals that have recently won aggressive interactions may often be more likely to win against new opponents that have not had recent winning experience; that is, winners keep winning. This phenomenon has been found in a variety of taxa, including juncos, chickens, paradise fish, red deer, spiders, and crickets (reviewed in Jackson, 1991). The proximate reasons and mechanisms for this phenomenon are the current topic of many research programs (e.g. Stevenson et al., 2000) most recently employing the awesome power of Drosophila genetics (Chen et al., 2002; Dierick, and Greenspan 2006). Historically, crustaceans have been used widely in agonistic behavioral investigations. The advantageous characteristics of crustaceans include the relatively large size that facilitates behavioral observation and measurement. Due to the concerted efforts of many researchers, the aggressive behaviors are now well described. Furthermore, these animals are hardy and exhibit a broad range of their natural agonistic repertoire even in a lab setting. Perhaps the most important characteristic of crustaceans is their relatively accessible nervous system for physiological experiments. Studies examine species-specific ritualized displays (e.g. Huber and Kravitz, 1997), inter and intra-sexual interactions (e.g. Cushing and Reese, 1998), and how fighting behavior is influenced by the environment (e.g. predation risk and time of day (e.g. Spanier et al., 1998)).

Many investigations of agonistic behavior in crustaceans have focused on crayfish, which are especially easy to maintain in the laboratory. The outcome and nature of crayfish fights are influenced by a multitude of factors. These include differences in reproductive status; the relative intensity of light conditions (related to circadian behavior); relative body size; and previous contest experience. Contest experience may affect subsequent behavior by modifying development and activity of the nervous system (e.g. Baranaga, 1996; Huber et al., 1997). Because crayfish fights are decided, in part by the relative size of the contestants, it is possible to provide crayfish with a series of training fights that generate individuals that have had either winning or losing experiences.

QUANTIFYING BEHAVIOR

Quantifying behavior is not easy, particularly if you need to watch many focal subjects, note many behaviors, or record behaviors that occur frequently or quickly. Hence, one must choose a sampling rule. Your task in this lab is made simpler by employing a focal animal sampling rule (i.e. you watch just one individual). Other possible sampling rules are scan sampling, in which one periodically scores behavior for a series of individuals, or behavior sampling, in which one scores all instances of particular behavior(s) in a group of individuals. These different sampling rules are appropriate for different questions, different organisms and different situations. The details guiding such decisions will be discussed in lecture and more detail can be found in chapter 6 of Measuring Behavior by Martin and Bateson (on reserve in the library).

Quantifying behavior also requires one to make decisions about recording rules. A continuous recording of all behavior is impractical when many individuals or many behaviors are being scored, or when behaviors are occurring quickly. Furthermore, continuous recording for long periods can be tedious. Therefore, a common alternative is instantaneous recording in which the behavior is noted at regularly spaced time points and the intervening periods are ignored. Today each student will watch only one animal at a time and will use focal sampling with continuous recording. Try to think about how other sampling and recording rules could yield different data.

General Lab Instructions:

BEFORE HANDLING the animals, please thoroughly wash and rinse your hands. Lotions, soaps, and general campus grime can be deadly to critters.

Get to Know Your Crayfish Ethogram:

An ethogram is a catalog of species-typical behaviors. In the early days of ethology, (the study of animal behavior) comprehensive ethograms of all behaviors exhibited by a species would constitute publishable scientific research. Today, most ethograms represent only a subset of the behavioral repertoire that is related to the specific behavior being tested. For example, our ethogram, will not be concerned with mating or feeding, but rather will focus on agonistic behaviors. Each behavior should be clearly defined and described by recognized postures and movements. In an ethogram, the descriptions of each behavior should avoid statements of intent, avoid anthropomorphism, and be clearly defined by neutral characteristics.

We will spend a few minutes observing the animals on video. Discuss the defined behaviors with your team until you are confident that you will not introduce observer bias by disagreement on definitions.

|SCORE |BEHAVIOR |DESCRIPTION |

|-3 |Tailflip | Rapid ventral movement of the tail results in the crayfish shooting backwards (away from opponent).|

|-2 |Tailtuck |Tail is tucked under the abdomen (no rapid resulting movement) |

|-1 |Avoidance |Crayfish slowly moves away from opponent (gives a wide berth) usually moves in reverse. |

|0 |Separate |Crayfish is at a distance from opponent and makes no directed movement. |

|1 |Approach |Crayfish slowly moves toward opponent (may include contact without the claw display) |

|2 |Threat |Crayfish approaches opponent with outspread claw and may strike opponent without locking claws. |

|3 |Fight |Crayfish locked claw(s) over opponent and attempt to flip opponent. |

Read the ENTIRE handout before beginning your training and experiments

-Use focal sampling with continual recording (described above) for both training and testing.

-All fights will be observed for 10 minutes.

-Use the data collection sheets provided and staple these into your own lab notebook.

-Be sure that every student does at least one focal observation

-Because the team results include only 2 animals, a class data set is necessary for statistical tests.

-Be sure that crayfish are returned to the tanks and bowls where you found them.

-Students not directly doing the focal observation should, in their own lab notebook, note the location of the raw data (the collaborator’s notebook).

[pic]

Figure 2. Map of work-station includes 4 experimental crayfish and represents the concerted effort of 8 students

TRAINING -

Each team of 4 students will train two crayfish to be either a winner or a loser. The winner’s training is accomplished by repeatedly fighting your focal crayfish (one of the size matched animals in the isolated bowls) against different smaller opponents. The loser’s training is accomplished by repeatedly fighting your focal crayfish against different larger opponents. Training is complete after 3 consecutive wins (or losses) against 3 different individuals! After each training, store the opponent in a ziplock with water box so that you can be sure to take a new opponent each time (you will have to share opponents with the other training team across the bench from you). If you fight your focal crayfish for 5 trials and fail to achieve 3 consecutive wins or losses, continue with the experiment but make note of the unexpected fight results for final data analysis.

EXPERIMENT Winners vs. Losers

Two size-matched sized crayfish (one with winner’s training and one with loser’s training) will be tested in the experimental fights. Because there are 4 students, you can have 2 students recording focal behavior observations for each crayfish. How similar are your results? When you enter your data to the class data set, enter the mean of the two scores. Another student should be timing the first contact and first tail flip.

As you work today, in your lab notebook, record each step of your protocol, and any additional information that helps you to define the behaviors. This information would be helpful for reproducing your work even if you lose this handout.

PROTOCOL

Sampling and Recording for Training and Experimental Fights.

The data collection sheets (provided in lab) contain entry space for information you may not think that you need for every experiment, but it is better to collect the data and not use it, than not collect it and wish that you had. While it is best to always state a clear hypothesis before your experiment, you may find there are additional hypotheses that can be addressed by your data. You will have to communicate with your partner to identify which animal is the first to tail flip and record that event accurately.

PROTOCOL CONT.

• Leave the tank divider in place until you are ready to begin recording your data.

• Allow crayfish a 5-minute acclimation period (be careful not to bang on the bench or tank, or make any movements near the tank. Sit at least 2 feet back from the tank. You cannot expect crayfish to behave naturally if they are threatened).

• Two students will work together for the training fights using a focal sample and continuous recording rule, each student will observe a single individual crayfish.

• Remove the tank divider and start your timer to count 10 minutes.

• Use the descriptions above, and record behavioral events directly onto the data collection sheet that will be stapled into your lab notebook.

• Each time that you observe your focal animal perform one of the described behaviors, put a tick mark in the appropriate box on your own data collection sheet. (Do not worry about the scoring until the end of the trial).

• The student with the timer will be responsible for noting the time and ID of the crayfish that does the first contact as well as the first tail flip.

• Notice that the data collection sheet includes additional information: Animal ID, weight, type of fight, as well as which animal performed the first tailflip. Because you are watching only your own animal, you will need to verbally communicate with your partner who is watching the other animal when this occurs. Be sure that ALL information is recorded.

• Continue recording for the entire 10 minutes.

• Replace the divider separating the two crayfish when 10 minutes has passed.

• Remove the opponent and weigh the opponent. Record the weight on the data sheet.

• Put the opponent in a ziplock box with water.

• Leave the focal animal in the tank and allow it 5 minutes of rest.

• While your focal animal is resting, tally your tick marks, and multiply the number of events by the score for that behavior.

• REPEAT training for 3 consecutive wins (or losses) or 5 trials (which ever comes first).

Data Entry

As a team of 4, log into the computers as yourself. Connect to the Courses Server as yourself.

Drag the file crayfish data template from the Courses Server/Bio101 102/Beavior-Renn/Week3_Crayfish to your desktop.

Open it and Save As yourname_Ned_Tues_crayfish or yourname_Carey_Wed_crayfish etc.

When you finish recording and saving your data, put that file in the Crayfish data dropbox.

Don’t forget that the class is waiting for your data set.

For each fight you will enter:

• The identifier number of the focal animal (A1 – D6).

• The sex of the combatants (male, female, mixed).

• The type (not the outcome) of fight (W=winner training L=loser training E=experiment).

• Is this the first training fight (first, second, third, fourth, fifth or experiment)?

• Weight of the focal crayfish. (for the experimental fight focal = winner’s training)

• Weight of the opponent crayfish. (for the experimental fight opponent = loser’s training)

• Total Behavior Score of the focal crayfish.

• Total Behavior Score of the opponent crayfish.

• Which crayfish tailflipped first (F=focal O=opponent N=Neither tailflipped)?

• What was the highest intensity score for this fight (-3 – +3)?

• Which crayfish initiated the FIRST contact (F=focal O=opponent N=No contact)?

• Which crayfish won the fight (F=focal; O=opponent; T = tie)?

• What was the duration (seconds) from first contact to first tailflip?

Hypotheses and Predictions:

Many hypotheses can be tested with the data you will collect during this experiment.

You will be recording categorical data (nominal) such as winner/loser, first to tail flip, male/female. You will also be recording numerical variables (continuous) such as the number of specific behaviors, the overall behavioral score, the weight of the individual. For some of these variables you may be interested in the mean value for a group of individuals, such as the mean time to first tail flip for a winner’s training compared to a loser’s training. For other variables you may be interested in the relationship between two continuous variables, for example, the relationship between weight of the opponent and the duration of time until the first tailflip. Different statistical tests are appropriate for different types of data. The following flowchart should help you decide when each test is appropriate.

[pic]

While you wait for the class data set, work as a team to discuss the following questions.

Record some of your ideas in your lab notebook.

• How would you redesign this experiment in order to determine if crayfish rely on individual recognition, the ability to recognize an individual previously encountered?

• How would you test if familiarity is more or less important that an individual’s recent experience?

• How would you design an experiment to determine if relative size of the opponent is more or less important than recent experience?

While you continue to wait for the class data set, work as a team to choose the correct statistical test for each biological question. You can begin writing the hypothesis and methods for the assignment.

A) Chi-square test of independence (two (or more) categorical descriptions).

B) Correlation analysis (Regression) to test for a relationship between two continuous variables.

C) The unpaired t-test compares the mean of one sample set against the mean of another sample set.

D) The paired t-test compares the means of two samples in which each datum in the first set can be matched with a corresponding datum in the second set (often the same individual measured before and after an experimental manipulation).

During training, you fought crayfish that are not size matched.

The answers to these questions are all predictions about a staged fight. These results may support hypotheses that are related to the adaptive value of different aspects of agonistic behavior. You will need to use the class dataset. In most cases you will want to use data from the first training fight rather than subsequent training fights. (Why do I suggest this?)

Which test would you use to address each of the following questions?

1) Was the type of fight independent of which animal would tailflip first?

2) Was there a relationship between the opponent's weight and the duration between first contact and tailflip?

3) Was there a relationship between the focal animal's weight and the highest score in the battle (escalation)?

4) Was the outcome of the fight independent of type of fight? (if it is, we aren't doing a very good "training")

5) Is there a difference in the mean Total Behavior Score for focal crayfish in winner and loser training?

6) Is there a difference in the mean Total Behavior Score for the opponent crayfish for the 3rd training fight compared to the 1st training fight?

*7) Was there a relationship between the weight difference of the two individuals and the time between first contact and tailflip? *(You would have to add a column to the data table and use a dynamic formula in order to calculate the size difference between the focal and opponent animals.)

**8) Is there a difference in the Total Behavior Score for the focal crayfish for the 3rd training fight compared to the 1st training fight for the focal crayfish in loser’s training?

** This would require rearrangement of the StatView template. You should be able to figure out what the appropriate statistical test is, but you may need to seek help if you want to complete the analysis.

In the Experimental fight, the crayfish were size matched.

As a class we will test a hypothesis about the value of previous experience in agonistic encounters. If fight outcome is not independent of past experience, we predict that the crayfish with “winner’s” training will win.

You can also ask many questions concerning specific aspects of the fight (duration, intensity, specific behaviors etc.). Again, the type of data available to answer these questions determines what statistical test to use.

1) Was the mean Total Behavior Score for the focal animal different for fights that were won by that animal?

2) Was the outcome of the experimental fight independent of which animal initiated contact?

3) Is there a relationship between the intensity of the fight and the duration between first contact and tailflip?

**4) Was the mean Total Behavior Score different for crayfish with winner’s training or loser’s training?

** This interesting question requires rearrangement of the StatView template. You should be able to figure out what the appropriate statistical test is, but you may need to seek help if you want to complete the analysis.

***5) Is there a relationship between the number of “Threats” and “Strikes” for the focal animal?

***We did not enter data for individual behaviors for the class data set, but you can determine which statistical test is required. There is a wealth of individual variation in fighting patterns that is omitted from our analysis.)

Assignment:

Prepare a write up as a team (the 4 students training 2 focal crayfish).

The report is due 1 week after this exercise is performed.

The report should include:

1) A formal hypothesis (one from above or one that your team devised).

2) A brief explanation (4 – 5 sentences) concerning the adaptive value of the behavior that might explain the ultimate function of the decision to fight or not to fight. There are some primary literature papers on the Courses Server that are referenced in this handout that may be helpful. If you use information from those references (or others that you find on your own) don’t forget to cite those references appropriately with the authors last name(s) and year in the text and the full citation provided at the end of your write up.

3) A methods section that clearly states which aspects of the data set were analyzed (did your team use the results for the first training fight for every focal animal, did your team use total behavioral scores for all training fights, did your team use only data from the experimental fights etc.). Clearly state the statistical analysis that was applied to the data in order to determine if there was a significant effect.

Do not write out the training and testing methods in your Lab Report. That information should be in your lab notebook. Unless you have changed the protocol, your write up you can simply state, “Behavioral training, scoring and testing was conducted according to standard Bio102 Crayfish protocol”.

4) A figure that accurately presents the data that are relevant to your hypothesis and statistical test.

5) A figure legend that sufficiently describes the experimental design so that a knowledgeable scientist could interpret the figure without having to refer back to the rest of the report.

6) A brief discussion of your statistical results in relation to your hypothesis.

StatView Instructions for Correlation Analysis with Small Sample Size

Click Analyze / Nonparametrics and choose Spearman Correlation

In the Variables window assign the two continuous variables you are testing for correlation.

Click OK

As with ANOVA and t-tests that you have seen before, the P-value tells you if the relationship between your two variables is significantly different than would be expected by random chance.

To graph your data: use Bivariate / Scattergram

Display a line for the Regression, but do NOT check mean or slope.

Assign one of your continuous variables to be the X Variable and the other to be the Y Variable.

StatView Instructions for Chi-Square Test of Independence for two categorical variables

Click Analyze / New View

Choose Contingency table / and while holding down the apple key click Summary Table / Observed Frequencies / Expected Values.

Then select Coded raw data.

Click OK.

The summary table includes the Chi-square P-value.

The Observed Frequency table includes the tally of your data

The Expected Frequency table includes the values that you would have expected if these two variables were independent (i.e. if the null hypothesis was true).

StatView instructions on the paired and unpaired t-test are the

t-test: used to compare the means of two distributions given the between group and within group variances

Factorial ANOVA is an extension of the t-test for >2 groups.

Analyze-> New View

Unpaired Comparisons

Unpaired t-test

Hypothesized difference: 0

Tail: Both OK

Assign a continuous variable and a nominal variable with the Add button.

Paired t-test: used when multiple response variables are measured for each individual

Repeated measures ANOVA is an extension of the paired t-test for > 2 groups.

Analyze-> New View

Paired Comparisons

Paired t-test

Hypothesized difference: 0

Tail: Both OK

Assign two continuous variables with the Add button.

To make your graphs, you will use Cell Plot->Point Chart to plot the two means with 95% Confidence Intervals. While the t-test tables are still selected, Point Chart will use the same two variables already selected.

Acknowledgements:

This lab is, in part, based upon a protocol by Elizabeth Jakob and Chad Hoefler “Learning to be Winners and Losers: Agonistic Behavior in Crayfish published in Exploring Animal Behavior in Laboratory and Field. Elsevier Press 2003.

Advice on design was contributed by Donald Edwards (Univ. of Georgia) and Ed Kravitz (Harvard Medical School).

References:

Barinaga, M. (1996). Neurobiology - Social status sculpts activity of crayfish neurons. Science 271:290-291.

Chen, S., A. Y. Lee, Bowens, N. M., Huber, R. and Kravitz, E. A. (2002). Fighting fruit flies: A model system for the study of aggression. Proceedings of the National Academy of Sciences of the United States of America 99:5664-5668.

Dierick, H. A. and R. J. Greenspan (2006). Molecular analysis of flies selected for aggressive behavior. Nature Genetics 38:1023-1031.

Glass, C. W. and F. A. Huntingford (1988). Initiation and Resolution of Fights between Swimming Crabs (Liocarcinus-Depurator). Ethology 77: 237-249.

Hofmann, H.A., and Stevenson, P.A., (2000) Glight Restores Fight in Crickets. Nature 403:613.

Huber, R., M. Orzeszyna, Cobb, J. S. and Clancy, M. (1997). Biogenic amines and aggression: Experimental approaches in crustaceans. Brain Behavior and Evolution 50:60-68.

Huber R & EA Kravitz. 1995. A quantitative study of agonistic behavior and dominance in juvenile American lobsters (Homarus americanus). Brain, Behav., Evol. 46:72-83

Huber, R., K. Smith, Delago, A., Isaksson, K. and Kravitz, E. A. (1997). Serotonin and aggressive motivation in crustaceans: Altering the decision to retreat. Proceedings of the National Academy of Sciences of the United States of America 94:5939-5942.

Jackson, W. M. (1991). Why Do Winners Keep Winning. Behavioral Ecology and Sociobiology 28:271-276.

Karavanich, C. and J. Atema (1998). Individual recognition and memory in lobster dominance. Animal Behaviour 56:1553-1560.

Kravitz, E. A. and R. Huber (2003). Aggression in invertebrates. Current Opinion in Neurobiology 13:736-743.

Smith, I. P., F. A. Huntingford, Atkinson, R. J. A., and Taylor, A. C. (1994). Strategic Decisions During Agonistic Behavior in the Velvet Swimming Crab, Necora Puber (L). Animal Behaviour 47:885-894.

Smith, I. P. and A. C. Taylor (1993). The Energetic Cost of Agonistic Behavior in the Velvet Swimming Crab, Necora (= Liocarcinus) puber. Animal Behaviour 45:375-391.

Spanier, E., T. P. McKenzie, Cobb, J. S. and Clancy, M. (1998). Behavior of juvenile American lobsters, Homarus americanus, under predation risk. Marine Biology 130:397-406.

Stevenson PA, Hofmann HA, Schoch K (2000) The fight and flight responses of crickets depleted of biogenic amines. Journal of Neurobiology 43:107-120.

Appendix

Categorical measurement:

Categorical data fall into distinct mutually exclusive categories that lack quantitative and qualitative intermediates. Names are assigned to the categories. For practical data processing, the names may be numerals, but in that case the numerical value of these numerals is irrelevant. The only comparisons that can be made between categorical values are equality and inequality. There are no "less than" or "greater than", nor addition or subtraction among categorical data. Examples include: the marital status of a person, the make or model of a car, a defined behavioral outcome, response vs non-response etc. Categorical variables are also called “Nominal variables”.

Different Numerical Measurements:

Ordinal measurement:

Numbers are assigned that represent a rank order (1st, 2nd, 3rd etc.) of the entities measured. The numbers are called ordinals. The variables are called ordinal variables or rank variables. Comparisons of greater and less can be made, in addition to equality and inequality. However operations such as conventional addition and subtraction are still meaningless. Examples include the results of a horse race, which say only which horses arrived first, second, third, etc. but no time intervals; and many measurements in psychology and other social sciences, for example attitudes like preference, conservatism or prejudice and social class.

Interval measurement:

The numbers assigned to objects have all the features of ordinal measurements, and in addition equal differences between measurements represent equivalent intervals. That is, differences between arbitrary pairs of measurements can be meaningfully compared. Operations such as addition and subtraction are therefore meaningful. The zero point on the scale is arbitrary; negative values can be used. Examples of interval measures are the year date in many calendars, and temperature in Celsius scale or Fahrenheit scale.

Ratio measurement:

The numbers assigned to objects have all the features of interval measurement and also have meaningful ratios between arbitrary pairs of numbers. Operations such as multiplication and division are therefore meaningful. The zero value on a ratio scale is non-arbitrary. Most physical quantities, such as mass, length or energy are measured on ratio scales; so is temperature measured in Kelvins, that is, relative to absolute zero.

Statistical Tests in Animal Behavior:

Statistics enable us to objectively evaluate our results.

Descriptive statistics are useful for exploring, summarizing, and presenting data. Descriptive statistics include the mean, mode (most frequent data class), and median (middle value in an ordered set of data). The variance, standard deviation, and standard error are measures of deviation from the mean. These statistics can be used to explore your data

Inferential statistics are used for interpreting data and drawing conclusions about our hypotheses.

A variety of statistical tests can be used to determine if the data best fit our null hypothesis (a statement of no difference) or an alternative hypothesis (the questions we ask). We calculate the test statistic appropriate for our research methods, experimental design, and sample size in order to calculate the probability that the pattern we see in our data is due to chance alone. This probability is called the P value. By convention, most behavioral ecologists agree that when P is equal to or less than 0.05, we can confidently reject the null hypothesis.

Statistical tests are of two basic types: parametric and non-parametric.

Parametric tests, such as Student’s t-test, ANOVA, and Pearson Correlation are usually the most powerful tests if the underlying distributions are “normal”. Parametric tests are based on certain assumptions and often depend upon linear relationships between variables (this is why you needed to log transform data for some of the Regression analyses earlier this year).

Non-parametric tests, such as Mann-Whitney U-test, Wilcoxon matched-pairs test, chi-square and Spearman correlation are generally less powerful. However, because they are free form the assumptions of parametric test they are more “robust”. These tests rely upon the rank rather than measurements on an interval or ratio scale, and they can be used to analyze data measured on an ordinal scale.

The data obtained in animal behavior research often rely upon categorical measurement. Furthermore, the sample sizes are often small, and the data are often not “normally” distributed. In these cases, non-parametric statistical tests are appropriate.

The Spearman rank correlation is a non-parametric statistic requiring measurement on an ordinal scale or higher. A statistical correlation between two variables does not mean that they are directly related in a causal manner. Additional experimentation is required to demonstrate causation. Correlation between two variables, A and B, can arrive for one of three reasons: A causes B; B causes A; or A and B are independently related to a third variable C. The Spearman correlation coefficient is denoted by the Greek letter ρ (rho). It is a measure of how well an arbitrary function could describe the relationship between two variables, it does not require a linear relationship between the two variables, and it can be used for variables measured at the ordinal level. Significance is determined by calculating the probability that the correlation would be greater than or equal to the observed ρ, given the null hypothesis. This can be done repeatedly randomizing the data set in a technique called “permutation testing”, or comparing the observed ρ with published tables for various levels of significance. StatView will do this for you.

Chi-square is a non-parametric test of statistical significance appropriate for categorical data. It can be used for more than two variables. First a table is constructed and the observed frequencies are entered into the appropriate cells. These values are used to calculate the expected frequencies if the variables were independent (i.e. if the null hypothesis is true).

For each cell in the table the expected value is calculated by the following equation.

[pic]

The difference of the observed frequency and expected frequency squared divided by the expected frequency is then calculated for every cell in the table. The Chi-square test statistic is equal to the sum of these values.

[pic]

In order to determine significance (P-value), the Chi-square value is compared with a published table that takes into account the number of variables that were tested. Again, StatView does all of this for you (So don’t bad mouth StatView too much).

-----------------------

Back of Room

Front of room

claw

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download