Scientific Method

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Scientific Method Statistical Evaluation of
Data
2
Scientific Methods in Environmental Science

• Controlled experiments
• Isolation models (mini-ecosystems, etc.)
• Modeling
• Multivariable analysis to evaluate interactions
• Creating computer simulations based upon data and
  observations mathematical modeling

3
How are the data analyzed?

• Depends upon the research how it was set up
• Decisions on analysis are made PRIOR to research
• We will look at three of the popular method for
  evaluating data from controlled experiments
• Correlation (are variables associated?)
• t-Test (are the quantitative results
  significantly different than hypothesized?)
• X 2 Test (are the qualitative results
  significantly different than the expected?)

4
Correlation

• Are two parameters correlated significantly?
• Create graph of IV (x axis) and DV (y axis)
• Get line of best fit (may not be linear).
• Find R2 value (closer to 1.00 shows Strength of
  association, but not necessarily causation).
• NOT FOR HYPOTHESIS TESTING....

5
Using Excel for Correlation

• Data for input into Excel

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Create a graph of IV versus DV

• Directions follow my example in the spreadsheet
• Online tutorial for Excel use later
• http//www.ncsu.edu/labwrite/res/gt/graphtut-home.
  htmleaf

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What About Hypothesis Testing?

• Null is ---
• Ho No difference of DV between levels of IV
• Example If fish live with varying DO, none will
  die.
• Research is ---
• H1 Difference between the DV for the levels of
  IV
• Example If fish live with varying DO, some DO
  level fish will die more than others.

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Reject or Fail to Reject Ho

• Statistics is odd all of these mathematical
  methods attempt to evaluate the data against your
  null hypothesis.
• Most tests provide a calculated test statistic
• ( a t-value, X2 value, F-value, etc.)

9
Reject or Fail to Reject Ho

• The test statistic is then compared (in the
  calculator or software) and a p value is then
  determined. This is the important piece of
  information.
• Lower the p value, the more you can feel
  rejecting Ho
• is appropriate.
• probability that these data sets are due
• to chance and not IV
• Usually p
• p
• this limit should be established PRIOR to
• running the analysis
• Excel gives ONLY the p-value for a stats test

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Main Stats. Tests To determine if Ho is rejected
or failed to reject

• Student t-Test to compare two means
• 2-sample control group data vs. experimental
  group
• paired - if before after type study
• 2-tailed for normal distribution (We will use
  this for our data)
• X2 test (chi-square test) to test for
  independence for qualitative data matrix or
  goodness of fit

11
Comparing samples by mean variance

• Student's t-Test assumes the samples are
  independent, the variances constant, and the
  errors normally distributed. This test can also
  be used for paired data (before, after same
  subjects).
• 2 sample t-Test will give t value for each pair
  of lists compared. (more levels of IV, the more
  t-Tests you run)
• Lower the p value, the more feel comfortable that
  you can reject Ho
• (again, usually psituations, psafety related)

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Using Excel or TI-84 for t-Test

• Excel t-Test example today Are states CO2
  emissions significantly different depending upon
  fuel use?
• Excel for paired t-Test Comparison of reported
  and confirmed malaria cases in all reporting
  countries for 2003
• Tutorials for statistics on TI calculators
• http//calculator.maconstate.edu/mean_test_t/index
  .html

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Chi-square

• Deals with count data. (how many are faded)
• Suppose evaluating one characteristic (flower
  color). The null hypothesis is that
  objects/subjects are just as likely to be any of
  the values of the characteristic.
• Example 20 bees, 2 colors of flower expect if
  random selection by bee that 10 bees will go to
  each color.
• Create a matrix that contains the data and apply
  X2 test (goodness of fit).
• This will give you a p-value for given the
  deviation from expected.

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Example Chi Square Goodness of Fit

• Is the distribution of pine trees related to soil
  type?
• The expected frequency of soil types in plots
  with pine trees is 50 dry, 30 loamy, and 20
  wet established via other research
• Let's also say that 50 plots had pine trees on
  them. Among the 50 plots with pines, then, the
  expected distribution of soil types would be 25
  dry, 15 loamy, and 10 wet.
• You observed that of the 50 plots with pine
  trees, 31 were dry, 17 loamy, and only 2 were wet

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Is the distribution of pine trees related to soil
type?

• Calculation is the sum of the (expected
  observed)2 expected
• Here, we get 36/25 4/15 64/10 8.11
• We need to consider the degrees freedom, of
  categories minus 1
• Here dry, loamy, wet are 3 categories, d.f.
  3-12
• Use the Critical Values Table _at_ d.f.2, and your
  sig. level
• OR, use Excel