Math 145Math 145

August 5, 2008August 5, 2008

ReviewReviewMethods of Acquiring Data:Methods of Acquiring Data:

1.1. CensusCensus – obtaining information from each – obtaining information from each individual in the individual in the populationpopulation..

2.2. SamplingSampling – obtaining information from a – obtaining information from a part of the population (part of the population (samplesample) in order to ) in order to gain information about the whole gain information about the whole population.population.

Observational Study Observational Study – observes individuals and – observes individuals and measures variables of interest but does not measures variables of interest but does not attempt to influence the responses.attempt to influence the responses.

ExperimentsExperiments – deliberately imposes some – deliberately imposes some treatment on individuals in order to observe treatment on individuals in order to observe their responses.their responses.

Examples of Designed Examples of Designed ExperimentExperiment

Example 1 :Example 1 : Consider the problem of comparing Consider the problem of comparing the effectiveness of 3 kinds of diets (A, B, C). the effectiveness of 3 kinds of diets (A, B, C). Forty males and 80 females were included in Forty males and 80 females were included in the study and were randomly divided into 3 the study and were randomly divided into 3 groups of 40 people each. Then a different groups of 40 people each. Then a different diet is assigned to each group. The body diet is assigned to each group. The body weights of these 120 people were measured weights of these 120 people were measured before and after the study period of 8 weeks before and after the study period of 8 weeks and the differences were computed.and the differences were computed.

Example 2 :Example 2 : In a classic study, described by F. In a classic study, described by F. Yates in the Yates in the The Design and Analysis of The Design and Analysis of Factorial ExperimentsFactorial Experiments, the effect on oat yield , the effect on oat yield was compared for three different varieties of was compared for three different varieties of oats (A, B, C) and four different oats (A, B, C) and four different concentrations of manure (0, 0.2, 0.4, and 0.6 concentrations of manure (0, 0.2, 0.4, and 0.6 cwt per acre).cwt per acre).

Terminologies in Terminologies in ExperimentsExperiments

Experimental UnitsExperimental Units – These are the individuals – These are the individuals on which the experiment is done.on which the experiment is done.

SubjectsSubjects – human beings. – human beings. Response variables Response variables – Measurement of interest.– Measurement of interest. FactorsFactors – Things that might affect the – Things that might affect the

response variable (explanatory variables). response variable (explanatory variables). {new drug}{new drug}

Levels of a factor Levels of a factor – {different concentration of – {different concentration of the new drug; no drug, 10 mg, 25 mg, etc.}the new drug; no drug, 10 mg, 25 mg, etc.}

TreatmentTreatment – A combination of levels of – A combination of levels of factors.factors.

Repetition Repetition – putting more than one – putting more than one experimental units in a treatment.experimental units in a treatment.

Example 1 : Diet StudyExample 1 : Diet Study

Example 1 :Example 1 : Consider the problem of comparing Consider the problem of comparing the effectiveness of 3 kinds of diets (A, B, C). the effectiveness of 3 kinds of diets (A, B, C). Forty males and 80 females were included in Forty males and 80 females were included in the study and were randomly divided into 3 the study and were randomly divided into 3 groups of 40 people each. Then a different groups of 40 people each. Then a different diet is assigned to each group. The body diet is assigned to each group. The body weights of these 120 people were measured weights of these 120 people were measured before and after the study period of 8 weeks before and after the study period of 8 weeks and the differences were computed.and the differences were computed.

a)a) Experimental units : Experimental units : PeoplePeopleb)b) Response variable : Response variable : Weight lostWeight lostc)c) Factor(s) : Factor(s) : DietDietd)d) Levels : Levels : diet A, diet B, diet Cdiet A, diet B, diet Ce)e) Treatments : Treatments : diet A, diet B, diet Cdiet A, diet B, diet C

Example 2 : Oat Yield Example 2 : Oat Yield StudyStudy

Example 2 :Example 2 : In a classic study, described by F. In a classic study, described by F. Yates in the Yates in the The Design and Analysis of The Design and Analysis of Factorial ExperimentsFactorial Experiments, the effect on oat , the effect on oat yield was compared for three different yield was compared for three different varieties of oats (A, B, C) and four different varieties of oats (A, B, C) and four different concentrations of manure (0, 0.2, 0.4, and concentrations of manure (0, 0.2, 0.4, and 0.6 cwt per acre).0.6 cwt per acre).

a)a) Experimental units : Experimental units : FieldsFieldsb)b) Response variable : Response variable : Oat yieldOat yieldc)c) Factor(s) : Factor(s) : Oat variety, Manure Oat variety, Manure

concentrationconcentrationd)d) Levels : Levels : Oat A, B, COat A, B, C ; ; Concentration 0, .2, .4, Concentration 0, .2, .4,

.6.6e)e) Treatments : Treatments : (A, 0), (A, .2), …, (C, .6)(A, 0), (A, .2), …, (C, .6)

Designs of ExperimentsDesigns of Experiments Completely Randomized Completely Randomized – Experimental units – Experimental units

are allocated at random among all treatments, are allocated at random among all treatments, or independent random samples are selected or independent random samples are selected for each treatment.for each treatment.

Double-Blind Study Double-Blind Study – Neither the subjects nor the – Neither the subjects nor the medical personnel know which treatment is being medical personnel know which treatment is being giving to the subject.giving to the subject.

Matched PairMatched Pair – Used for studies with 2 – Used for studies with 2 treatment arms, where an individual from one treatment arms, where an individual from one group is matched to another in the other group is matched to another in the other group.group.

Block Design Block Design – The random assignment of – The random assignment of units to treatments is carried out separately units to treatments is carried out separately within each block.within each block.

BlockBlock – is a group of experimental units that are – is a group of experimental units that are known to be similar in some way that is expected to known to be similar in some way that is expected to affect the response to the treatment.affect the response to the treatment.

Example 1 : Diet StudyExample 1 : Diet Study

Example 1 :Example 1 : Consider the problem of Consider the problem of comparing the effectiveness of 3 kinds comparing the effectiveness of 3 kinds of diets (A, B, C). Forty males and 80 of diets (A, B, C). Forty males and 80 females were included in the study and females were included in the study and were randomly divided into 3 groups of were randomly divided into 3 groups of 40 people each. Then a different diet is 40 people each. Then a different diet is assigned to each group. The body assigned to each group. The body weights of these 120 people were weights of these 120 people were measured before and after the study measured before and after the study period of 8 weeks and the differences period of 8 weeks and the differences were computed.were computed.

Block - GenderBlock - Gender

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