EXPERIMENTATION AND MODELS THE NEED FOR HYPOTHESES (POSSIBLE EXPLANATIONS OF OBSERVED PHENOMENA) CLARITY, TESTABILITY THE LOGICAL ORIGINS OF HYPOTHESES INDUCTIVE METHOD - PROCEEDS FROM SPECIFIC OBSERVATIONS TO A GENERAL CONCLUSION E.G., FROM SPECIFIC OBSERVATIONS THAT BIODIVERSITY OF AQUATIC SPECIES IS UNUSUALLY LOW WHERE SEVERE POLLUTION OCCURS TO THE GENERAL HYPOTHESIS THAT SEVERE POLLUTION REDUCES BIODIVERSITY DEDUCTIVE METHOD - PROCEEDS FROM A GENERAL PRINCIPLE TO THE PREDICTION OF A SPECIFIC EVENT E.G., GIVEN THE GENERAL NOTION THAT BIODIVERSITY IS REDUCED BY POLLUTION, IT MIGHT BE PREDICTED THAT DIFFERENT LEVELS AND/OR TYPES OF POLLUTANTS WILL AFFECT BIODIVERSITY DIFFERENTLY (I.E., TO DIFFERENT DEGREES) THE COLLECTION OF DATA FOR THE TESTING OF HYPOTHESES DIRECT OBSERVATION THE USE OF "NATURAL EXPERIMENTS" E.G., TEST THE HYPOTHESIS THAT HERBIVOROUS INSECTS REDUCE THE YIELD OF AGRICULTURAL CROPS BY OBSERVING THE YIELDS OF DIFFERENT FIELDS OF THE SAME CROP THAT DIFFER IN DENSITY OF HERBIVOROUS INSECTS EXPERIMENTATION MANIPULATION OF AN INDEPENDENT VARIABLE AND MEASUREMENT OF THE EFFECT ON A DEPENDENT VARIABLE E.G., TEST THE HYPOTHESIS ABOVE BY ESTABLISHING DIFFERENT PLOTS (FIELDS) OF A CROP SPECIES THAT DIFFER ONLY IN THE DENSITY OF HERBIVOROUS INSECTS (MANIPULATED BY THE EXPERIMENTER) AND MEASURE THE YIELDS OF THE PLOTS REQUIRES REPLICATION TO CONTROL FOR GENETIC VARIABILITY (IN THIS CASE REPLICATE PLOTS FOR EACH TREATMENT - DENSITY OF HERBIVORES) BUT THE REPLICATES MUST BE INDEPENDENT SO THAT THE RESPONSE IN ONE DOES NOT INFLUENCE THE OUTCOME IN ANOTHER PSEUDOREPLICATION - THE USE OF NONINDEPENDENT REPLICATES REQUIRES CONTROL PLOTS - TO DETERMINE WHAT YIELD WOULD BE WITHOUT INSECTS PRESENT MAY BE CARRIED OUT IN "NATURE" (FIELD EXPERIMENTS) OR IN THE LABORATORY FIELD EXPERIMENTS MAY BE MORE REALISTIC BUT THEY ARE MORE DIFFICULT TO CONTROL FOR OTHER CONDITIONS AND THE MANIPULATION OF THE INDEPENDENT VARIABLE IS HARDER THE TESTING OF HYPOTHESES CREATION OF A NULL HYPOTHESIS NULL HYPOTHESIS (Ho) - A STATEMENT THAT SAYS THAT NO DIFFERENCE BETWEEN THE CONTROL AND EXPERIMENTAL TREATMENTS IS EXPECTED I.E., THE INDEPENDENT VARIABLE HAS NO SIGNIFICANT EFFECT ON THE DEPENDENT VARIABLE ALTERNATIVE HYPOTHESIS ALTERNATIVE HYPOTHESIS (H1) - THE INDEPENDENT VARIABLE HAS A SIGNIFICANT EFFECT ON THE DEPENDENT VARIABLE WHY A NULL HYPOTHESIS? LOGIC REQUIRES THE REFUTATION OF EITHER THE NULL OR ALTERNATIVE HYPOTHESIS ONE CANNOT PROVE A POSITIVE - BUT ONLY DEMONSTRATE THAT A HYPOTHESIS IS NOT TRUE DEALING WITH INHERENT VARIATION IN THE DEPENDENT VARIABLE TEXT EXAMPLE OF THE EFFECT OF CO2 ON THE GROWTH OF INDIVIDUALS OF A PLANT SPECIES ASSUME THAT NORMAL VARIATION IN GROWTH AMONG THE INDIVIDUALS OF A LARGE POPULATION RESULTS IN A NORMAL DISTRIBUTION HOW DOES ONE KNOW IF THE DIFFERENCES BETWEEN CONTROL AND EXPERIMENTAL GROUPS REFLECT DIFFERENT SAMPLES OF THE NORMAL DISTRIBUTION OR AN EFFECT INDUCED BY THE TREATMENT? BY REPEATED SAMPLING (25 PLANTS FROM THE POPULATION IN THE TEXT EXAMPLE) ONE CAN CALCULATE THE PROBABILITY OF ANY TWO SAMPLES DIFFERING BY A PARTICULAR AMOUNT IN MEAN DRY WEIGHT IF THE DIFFERENCES BETWEEN CONTROL AND EXPERIMENTAL TREATMENTS ARE SO GREAT THAT THEY ARE UNLIKELY TO BE DUE TO SAMPLING ERROR THEN THE NULL HYPOTHESIS WOULD BE REJECTED AND THE ALTERNATIVE HYPOTHESIS SUPPORTED TYPES OF ERROR TYPE I ERROR - REJECTION OF NULL HYPOTHESIS EVEN THOUGH IT IS TRUE THE PROBABILITY OF FALSELY REJECTING THE NULL HYPOTHESIS IS TERMED ALPHA AN ALPHA VALUE OF 0.05 (5%) IS USUALLY USED AS THE UPPER LIMIT FOR ACCEPTING A NULL HYPOTHESIS I.E., THERE IS ONLY A 5% CHANCE OF HAVING A DIFFERENCE EQUAL TO OR LARGER THAN THAT OBSERVED BETWEEN THE TWO TREATMENTS IF THE NULL HYPOTHESIS IS TRUE TYPE II ERROR - ACCEPTING THE NULL HYPOTHESIS EVEN THOUGH IT IS FALSE THE PROBABILITY OF ACCEPTING THE NULL HYPOTHESIS WHEN IT IS NOT TRUE IS TERMED BETA STATISTICAL POWER TEST POWER OF A TEST IS 1-§, THE PROBABILITY OF REJECTING THE NULL HYPOTHESIS WHEN IN FACT IT IS FALSE THE LARGER THE VALUE THE GREATER THE POWER OF THE STATISTICAL TEST THE POWER OF A TEST INCREASES AS A FUNCTION OF SAMPLE SIZE AND EFFECT SIZE I.E., THE GREATER THE SAMPLE SIZE AND/OR EFFECT SIZE THE SMALLER THE VALUE OF §, THE PROBABILITY OF MAKING A TYPE II ERROR (ACCEPTING A FALSE NULL HYPOTHESIS) MODELS AND PREDICTIONS MODELS ALLOW FOR PREDICTIONS ABOUT THE RESPONSE OF A DEPENDENT VARIABLE MODELS MAY BE QUALITATIVE E.G., A HYPOTHESIS THAT PREDICTS THE DIRECTION OF CHANGE IN A DEPENDENT VARIABLE AS A CONSEQUENCE OF CHANGE IN THE INDEPENDENT VARIABLE OR, QUANTITATIVE E.G., A STATISTICAL MODEL THAT PREDICTS THE VALUE OF THE DEPENDENT VARIABLE FOR A GIVEN VALUE OF THE INDEPENDENT VARIABLE TEXT EXAMPLE OF A LINEAR REGRESSION MODEL A DESCRIPTION OF CORRELATION BETWEEN THE TWO VARIABLES, NOT A STATEMENT OF CAUSATION E.G., A NONSTATISTICAL MODEL IN WHICH THE BIOLOGICAL AND PHYSICAL MECHANISMS ARE INCLUDED TO EXPLAIN THE ACTION OF THE INDEPENDENT VARIABLE ON THE DEPENDENT VARIABLE (CAUSATION) NONSTATISTICAL MODELS MAY BE: ANALYTICAL MODELS - SOLVABLE EQUATIONS E.G., LOGISTIC POPULATION MODEL SIMULATION MODELS - NOT BASED ON SOLVABLE EQUATIONS E.G., COMPLEX INDIVIDUAL- BASED POPULATION MODELS VALIDATION AN OBJECTIVE TEST OF THE EFFICACY OF A MODEL HOW WELL DOES IT PREDICT THE OUTCOME OF ADDITIONAL EXPERIMENTS OR OBSERVATIONS - ESPECIALLY THOSE INVOLVING INDEPENDENT SITUATIONS