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Design of Fish and Wildlife
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Terms in this set (43)
Pseudoreplication
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Replication
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Laboratory experiments
-Conducted on small scale
-Use test tubes, beakers, aquaria, microcosms
Advantages of laboratory experiments
-Complete control
-Experimental units are "exactly" the same before treatment
-Easy to do replication (required for statistics)
-Generate hypotheses and provide support for broader ecological theory
Limitations of lab experiments
-Lack of realism (do results apply to nature?)
-Small spatiothermal scale (probably okay for aquatic insects but not for long-term studies with larger organisms)
Field Experiments
-Conducted outdoors with natural populations
-Manipulate directly
-Goal is to manipulate one variable while all else remains constant
-Cages, habitat improvements, whole ecosystem experiments
Advantages of field experiments
-Greater realism
-Larger scale
-Broader scope
Limitations of field experiments
-Expense and logistics
-Low replication
-Site matching (have to assume all sites are identical before manipulation)
-Artifacts
Natural experiments
-Selected sites where "treatment" already exist -> provided by nature
-Looking at allopatric vs. sympatric populations
-Allopatric: related species/populations occurring in separate non-overlapping geographical areas
-Sympatric: related species/populations that occur in the same geographic area and thus frequently encounter one another
Advantages of natural experiments
-Greater realism
-Vast temporal scale (10^2 - 10^6 years. That is not possible with field experiments)
-Spatial scale (field experiments often limited to small areas wheras natural experiments can include an entire island chain)
-Lead to ecological and evolutionary questions
Limitations of natural experiments
-Only a snapshot of current conditions. You can't evaluate trajectory (how did we get there?)
-Limited site matching and replication
-Shows correlation but not causation
Assumptions of parametric statistics
-The data has a normal distribution (The data were sampled from a specified distribution)
-Homogeneity of variances: Data from multiple groups have the same variance (The data collected represents random, independent samples)
Type I error
-Falsely rejecting a null hypothesis that is true
-Making a false claim that some factor above and beyond random variation is causing patterns in our data
-When you determine theres a statistical difference when there isn't one
-Probability of committing a type I error is denoted by alpha (the smaller the alpha value, the smaller the chance of a type I error)
Type II error
-Not rejecting a null hypotheses that is false
-incorrectly concluding that only random variation among observations is present
-Denoted by beta
Importance of Type II error (especially in applied research)
-If you collect too few samples you are unable to show a statistically significant effect when there is one
Interpretation of standard deviation
-What makes S large? Low sample size, the more observations you have that are far away from the mean
-What does a large S mean? Low confidence in determining if the results actually mean anything
How do you determine the necessary sample size?
1.) Degree of confidence desired (typically use alpha of .05 which means theres a 5% chance of type I error)
2.) Variability of the data
3.) How much difference do you wish to detect
What makes n large (the number of samples you need)
-Large standard deviation
-Large t-statistic (small alpha value)
-Small d (proportion difference)
Treatment effect
-Difference between means (how far apart those means are)
Sampling variation
Variation within a population
All parametric statistical tests come down to one thing...
-Ratio of treatment effect to natural (sampling) variation
test statistic
= variation between/variation within
-how much of a treatment effect you have (how big a difference is there between your populations, relative to how much variation there was in those populations)
t-value and interpretation
-Large t-values means you reject the null hypothesis and conclude that there is a significant difference (t-stat must be larger than critical value)
-What makes t large? Small standard deviation, large number of samples, and a large difference between the average for population 1 - the average for population 2
When to use t-test
-when you compare the means of two sampled groups
Categorical variable
-Variables that are classified into one of two or more unique categories
-Exs.) Sex (male,female), trophic status (producer, herbivore, carnivore), and habitat type (shade, sun)
Continuous variable
-measured on a continuous numerical time scale
-Can take on a range of real numbers or integer values
-Exs.) Measurements of individual size, species richness, habitat cover, and population density
Discrete
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ANOVA (analysis of variance)
-goal is to compare the means among groups that have been sampled randomly (more than 2 groups)
-Use when the independent variable (x) is categorical and the dependent variable (y) is either discrete or continuous
-The independent (predictor) variable may have multiple treatment levels (control, low, high)
-There may be more than one predictor variable
F statistic
= treatment variation/sampling error
= variation between/variation within
-If the F value is larger than the critical value you can conclude that there is a real difference
-The larger the F statistic is, the more confidently we can conclude there is a difference between those groups
Graph of one way ANOVA
bar graph
Multiple comparison tests
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Two way ANOVA
-Accounts for multiple treatment (independent) variables
-2 X 2 factorial design
-End up with 3 F-statistics
-The interaction F-stat is comparing the slopes of the two variables
Two way ANOVA graph
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BACI design (Before-After-Control-Impact)
-Sample locations before a treatment and compare that to the results after the treatment
-Take samples at a control site and an impact site before anything happens and then take samples at the same two sites after the impact took place at the impact site
-When graphed you would expect the control site to look the same before and after
-When graphed you would expect the impact site to be similar to the control site before. After the impact the impact site will be different
-Get 3 separate F statistics: Time (before vs after), Treatment (control vs impact) and interaction
Regression
-Used to analyze the relationships between continuous variables
-Looking at the degree to which one variable depends on another variable
-Allows us to describe the relationship between two variables (compare slopes of two lines, shape of the line)
-Can make predictions about the dependent variable
-Most of what we look at is linear regression
Linear regression
-A linear relationship between a dependent variable (Y) and an independent variable (X)
-Implicit hypotheses: X causes Y (not simply a correlation)
-Dependent and independent variables should be obvious
-Can make predictions (given X, predict Y)
-Fit a straight line to the data
least squares regression line
-Find the best straight line through a set of points
-Regression line should pass through the average of X values and the average of the Y values (where they intersect)
-Want to minimize the vertical distance between points and the line
-Also want to minimize residuals (distance between individual points and the line
Y= Bo + B1X (Bo= Y intercept & B1 = slope)
Non-linear regression
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Multiple regression
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Comparing ANOVA vs regression
-T-tests and ANOVA are looking at the differences between or among groups (control vs treatment, effects of clear cut at 2 elevations, large small and small and far islands)
-If you are interested in a specific treatment you would use ANOVA
-Regression allows you to determine to what degree does one variable depend on another variable
-If you are interested in a predictable relationship you would use regression
Wilcoxan Rank sum test
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Confounding variables
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Bias
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