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Quadrat sampling & the Chi-squared test

Quadrat sampling & the Chi-squared test. 4.1.S3 Testing for association between two species using the chi-squared test with data obtained by quadrat sampling. Quadrat Sampling. Quadrats are square sample areas, often marked by a quadrat frame

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Quadrat sampling & the Chi-squared test

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  1. Quadrat sampling & the Chi-squared test 4.1.S3 Testing for association between two species using the chi-squared test with data obtained by quadrat sampling

  2. Quadrat Sampling • Quadrats are square sample areas, often marked by a quadrat frame • Quadrat sampling involves repeatedly placing a quadrat frame at random positions in a habitat and recording numbers of organisms present • Goal is to obtain realistic estimates of population sizes • Not useful for motile organisms

  3. Quadrat Sampling • In our example, students wanted to see if the presence of ferns was statistically significantly larger in the shaded areas (the woodland) compared with the areas in direct sunlight (the prairie). • First we must state the “null hypothesis” • The null hypothesis basically says that there is a high probability that any deviation from the expected values can be attributed to chance • Null hypothesis: The two categories (presence of fern and presence of shade) are independent of each other. • Now we will use the data provided to do a statistical test called a chi-squared test to determine if shade and fern distribution are related.

  4. Chi-Squared Testing Draw a contingency table of observed frequencies Observed: # of quadrats that had ferns present

  5. Chi-Squared Testing Draw a contingency table of observed frequencies Observed: # of quadrats that had ferns absent

  6. Chi-Squared Testing Draw a contingency table of observed frequencies Observed: Sum of the rows (ex: 14+7)

  7. Chi-Squared Testing Draw a contingency table of observed frequencies Observed: Sum of the columns (ex: 14+6)

  8. Chi-Squared Testing Draw a contingency table of observed frequencies Observed: Total sample size (Grand total)

  9. Chi-Squared Testing • Calculate the expected frequencies for each of the possible contingency table scenarios • (Row Total) x (Column Total) / Grand Total Expected: (20x21)/40 = (20x21)/40 = Column totals (20x19)/40 = (20x19)/40 = Total sample size (Grand total) Row totals

  10. Chi-Squared Testing Calculate number of degrees of freedom (# Rows – 1)(# Columns – 1) = df (2 – 1)(2 – 1) = Shade & Sunlight = 2 Present or Absent = 2 1

  11. Chi-Squared Testing • Calculate the Chi-Squared value: Observed: (14-10.5)2 + …… 10.5 X2 = Expected:

  12. Chi-Squared Testing Find the critical value for the Chi-squared test (0.05) Find the degrees of freedom (df) you calculated earlier Find the p value of 0.05 Determine the critical value (3.841)

  13. Chi-Squared Testing • Compare the Chi-squared value with the Critical Value • If the X2 < CV, then ACCEPT the Null Hypothesis • (i.e. there is NO Association between the variables) • If the X2> CV, then REJECT the Null Hypothesis • (i.e. there is a significant Association between the variables)…aka ACCEPT the Alternative Hypothesis Chi-squared vale = 4.91 Critical value = 3.841

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