Data Analysis

A Few Necessary Terms

Categorical Variable: Discrete groups, such as Type of Reach (Riffle, Run, Pool)

Continuous Variable: Measurements along a continuum, such as Flow Velocity

What type of variable would “Mottled Sculpin /meter2” be?

What type of variable is “Substrate Type”?

What type of variable is “% of bank that is undercut”?

A Few Necessary Terms

Explanatory Variable: Independent variable. On x-axis. The variable you use as a predictor.

Response Variable: Dependent variable. On y-axis. The variable that is hypothesized to depend on/be predicted by the explanatory variable.

Statistical Tests: Appropriate Use

For our data, the response variable will always be continuous.

T-test: A categorical explanatory variable with 2 options.

ANOVA: A categorical explanatory variable with >2 options.

Regression: A continuous explanatory variable

Statistical Tests

Hypothesis Testing: In statistics, we are always testing a Null Hypothesis (Ho) against an alternate hypothesis (Ha).

Test Statistic:

p-value: The probability of observing our data or more extreme data assuming the null hypothesis is correct

Statistical Significance: We reject the null hypothesis if the p-value is below a set value, usually 0.05.

Tests the statistical significance of the difference between means from two independent samples

Student’s T-Test

Cross Plains Salmo Pond

Mottled Sculpin/m2

Compares the means of 2 samples of a categorical variable

Precautions and Limitations

• Meet Assumptions

• Observations from data with a normal distribution (histogram)

• Samples are independent

• Assumed equal variance (boxplot)

• No other sample biases

• Interpreting the p-value

Analysis of Variance (ANOVA)Tests the statistical significance of the difference between means from two or more independent samples

ANOVA website Riffle Pool Run

Grand MeanMottled

Sculpin/m2

Precautions and Limitations

• Meet Assumptions

• Observations from data with a normal distribution

• Samples are independent

• Assumed equal variance

• No other sample biases

• Interpreting the p-value

• Pairwise T-tests to follow

Simple Linear Regression

• What is it? Least squares line

•When is it appropriate to use?

•Assumptions?

•What does the p-value mean? The R-value?

• How to do it in excel

Simple Linear Regression

R2 = 0.6955

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Mottled Sculpin/Meter^2

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Tests the statistical significance of a relationship between two continuous variables, Explanatory and Response

Precautions and Limitations

• Meet Assumptions

• Observations from data with a normal distribution

• Samples are independent

• Assumed equal variance

• Relationship is linear

• No other sample biases

• Interpret the p-value and R-squared value.

Residual Plots

Residuals are the distances from observed points to the best-fit line

Residuals always sum to zero

Regression chooses the best-fit line to minimize the sum of square-residuals. It is called the Least Squares Line.

R2 = 0.6955

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Mottled Sculpin/Meter^2

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Residuals

Residual vs. Fitted Value Plots

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Fitted Values (MS_CPUA)

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Model Values (Line)

Observed Values (Points)

Residual Plots Can Help Test Assumptions

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“Normal” Scatter

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Curve (linearity)

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Fitted Values (MS_CPUA)

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R2 = 0.6955

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Mottled Sculpin/Meter^2

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er^2

Have we violated any assumptions?

R-Squared and P-value

High R-Squared

Low p-value (significant relationship)

R-Squared and P-value

Low R-Squared

Low p-value (significant relationship)

R-Squared and P-value

High R-Squared

High p-value (NO significant relationship)

R-Squared and P-value

Low R-Squared

High p-value (No significant relationship)

P-value indicates the strength of the relationship between the two variables

You can think of this as a measure of predictability

R-Squared indicates how much variance is explained by the explanatory variable.

If this is low, other variables likely play a role. If this is high, it DOES NOT INDICATE A SIGNIFICANT RELATIONSHIP!