AGRI 2400 Lecture 11 - A Statistical Analysis

Common Analysis Workflow

• most analyses follow a similar general pattern

  • 1. establish statistical hypotheses based on your expectations/predictions

  • 2. perform appropriate analysis to generate test statistic

  • 3.use test statistic to determine p-value

  • 4. use p-value to determine whether null hypothesis will be retained or rejected

  • 5. report what those conclusions mean in the context of the study

Experimental Design

• CRD common garden experiment

  • 100 seeds were planted into indiv. pots

    • soil in pots was iron deficient such that normal varieties in it will always show signs of iron deficiency chlorosis(IDC)

  • all plants were then asses at the V5 plant stage for signs of IDC

  • the dep. var. (nominal,categorical) was whether or not each plant showed signs of IDC

    • plants showing no digns of IDC were assumed to possess the new trait, plants with signs of IDC were assumed to not possess the trait

Analysis Expectations

• if close to 3 out of every 4 plants show signs of the trait (3:1 ratio), this result would provide evidence to retain the null hypothesis

• if the ratio of plants showing the trait is much higher or lower than 3:1, then there may be sufficient evidence to reject the null hypothesis since it is unlikely to see large deviations from the expected ratio if the null hyp is true

Results

• 64/36 is different frm expected 75/25 ratio, but is the difference due to:

  • random chnace

  • an incorrect null hypothesis

• we must use a statistical test to help is decide if this result is significantly different from the one expected based on our null hypothesis

Chi-Square Test for Goodness of Fit

• compares observed ratio to expected ratio for normal scaler (categorical) data

• by comparing the observed values to the expected values (from our null hypothesis), we generate a test statistic (in this case, a x² statistic)

The Test Statistic

• is then used to estimate the probability (p-value) of the observed deviation, or an even more extreme deviation, from the expected outcome, if the null hypothesis is true

From Test Statistic to P-Value

• for a chi-square analysis where there are 2 indep. categories, the critical value of chi-square, when your alpha is 0.05, is 3.84

Calculated vs Critical Test Statistics

• for a given alpha value and test result:

  • if x² calc>X² crit, p<alpha (reject Ho)

  • if x² calc<X² crit, p> alpha (retain Ho)

Sample Size and Significance

• caution - a statistically significant difference does not necessarily mean a biologically significant difference

• that is up to your interpretation and should be based on knowledge of the system being studied

• as sample size increases, this is often something one should think about