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D courses a a.com/af/servlet/quiz?quiz action takeQuiz&quiz.; probGuid ONAPCOA8010100000036c7fa70080000&ctx; thomas myers1-00038 Aa Aa 5. Using calculations to compare samples with different sources of variation Abbey Alkon, a professor at the University of Califomia, San Francisco, studies the effects of pesticide exposure on young children's autonomic nervous system reactivity as a part of the Center for the Health Assessment of the Mothers and children of Salinas (CHAMAcos) research project. Autonomic nervous system reactivity is the way the autonomic nervous system responds to stress, and individual differences in autonomic reactivity have been associated with a variety of types of psychopathology. suppose that you select matched sets of children with no exposure, low level exposure, and high-level exposure to pesticide. The three children in each set are matched according to their ages. The methods of the repeated-measure ANovA can also be used in the case of a matched-subjects design. In this matched subjects design, there are n 4 matched sets who are tested in k 3 tre ent conditions, producing a total of N 12 scores. Each of these scores is a measure of the child's autonomic nervous system reactivity. Although the scores within the matched set come from three different children, you can use the methods of the repeated-measure ANOvA by considering the scores as coming from the same child with three repeated measures. The following data are two hypothetical outcomes for the experiment. For each outcome, compute the between-treatments variance, between subjects variance, and error variances. Then compute the F-ratio. Outcome B Outcome A Pesticide Exposure Exposure None Love Level High Level Set Total A 92 101 110 P 30 93 124 102 112 92 Type here to search

Explanation / Answer

The between-treatments variance, first we need to calculate mean of each treatment.

So Mean-none = (77+92+107+122+92+93+92+95)/8 = 96.25

Mean-low = (93+78+125+110+101+102+104+106)/8= 102.375

Mean-high= (124+109+80+91+110+112+112+115)/8 = 106.625

Then, we calculate de overral mean, to make it easier we will take the total in each treatment

Overal mean = (398+406+404+372+413+449)/24=101.75

Then we calclate the estimated effects, this mean the difference between treatments means and overall mean.

EE-none = 96.25-101-75=-5.5

EE-low=102.375-101.75=0.625

EE-high=106.625-101.75=4.875

Now we can claculate the sum of squares between treatment groups (better now as SStreat), as follows

=SUM( EE^2)*(# measures)=(-5.5^2)(8)+(0.625^2)(8)+(4.875^2)(8)=435.25

Then we calculated the sum of squares within treatment groups (SSres), as follows:

=Sum(Sum(observation - treatment mean)^2)=(77-96.25)^2+(92-96.25)^2+(107-96.25)^2+(122-96.25)^2+(93-102.375)^2+(78-102.375)^2+(125-102.375)^2+(110-102.375)^2+(101-102.375)^2+(102-102.375)^2+(104-102.375)^2+(104-102.375)^2+(106-102.375)^2+(124-106.625)^2+(109-106.625)^2+(80-106.625)^2+(91-106.625)^2+(110-106.625)^2+(112-106.625)^2+(112-106.625)^2+(115-106.625)^2=3885.25

The total sum of squares(SStot) is = SStreat + SSres = 435.25+3885.25=4320.5

To obtain the mean square it is necessary to calculate the degrees of freedom as follow

Degrees of freedom of treatment= 3 different treatments = 3-1=2

Total Degrees of freedom = 24 measurements = 24-1=23

Degrees of freedom of responses = dftot-dftreat=24-2=22

Now, we can calculate mean square of treatments and responses as follow:

MStreat= SStreat/ dftreat=435.25/2=217.625

MSres=SSres/dfres=3885.25/22=176.60

F-value is calculated by diving MStreat between MSres= 217.625/176.60=1.2322

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