Biostats

Two-Way ANOVAs and Statistical Interactions

• Statistics Modelling: Involves response and explanatory variables. For example, Kid's Height depends on Father's Height and other factors (Mother's Height, Genetics, Diet, etc.).

• Concept of Statistical Interaction: Occurs when the effect of one independent variable on a dependent variable changes based on the level of another independent variable.

• R.A. Fisher's Principles: Includes randomization, replication, blocking, and recognizing statistical interactions.

• Two-Way ANOVA Models:

  • Model form: FITNESS = AGE + EXERCISE + AGE:EXERCISE

  • Hypotheses involve interactions between age and exercise impacting fitness.

• Hypotheses:

  • Interaction Hypothesis:

  • H_0 : No interaction effect between age and exercise on fitness.

  • H_A : There is an interaction effect between age and exercise on fitness.

  • Factor 1 (Age):

  • H_0 : No effect of age on fitness.

  • H_A : Effect of age on fitness.

  • Factor 2 (Exercise):

  • H_0 : No effect of exercise on fitness.

  • H_A : Effect of exercise on fitness.

• Data Analysis:

  • ANOVA table assesses sources of variance (AGE, EXERCISE, AGE:EXERCISE).

  • Significant interaction means that both factors (age and exercise) impact fitness together, without the need for independent assessment of each factor.

• Conclusions from ANOVA Results: Report rejection of the null hypothesis indicating a significant interaction between age and exercise on fitness (e.g., F(1,16) = 7.3; P = 0.016 ).