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7I am trying to edit the question to add the numbers but it will not update. Am I doing it wrong?Ive updated it 4 times and it is not showing up.
How would I Use the ATTITUDE data set to run a SPANOVA at the .05 level of significance. For the within subjects affect use Math 1 and Math2. For the between subjects effect use TRTCON and then plot my interaction to identify any differences between the plot and the statistical results?
2Explanation / Answer
The ANOVA procedure tests these hypotheses:
H0: 1 = 2 = ... = r, all the means are the same
H1: two or more means are different from the others
Let’s test these hypotheses at the = 0.05 significance level.
We need r simple random samples for the r treatments, and they need to be independent samples.The underlying populations should be normally distributed. However, the ANOVA test is robust and moderate departures from normality aren’t a problem, especially if sample sizes are large and equal or nearly equal.
The samples should all have the same standard deviation, theoretically. Because the ANOVA test is robustif the largest standard deviation is less than double the smallest standard deviation.When sample sizes are equal but standard deviations are not, the actual p-value will be slightly larger than what you find in the tables. But when sample sizes are unequal, and the smaller samples have the larger standard deviations, the actual p-value “can increase dramatically above” what the tables say, even “without too much disparity” in the standard deviations. Balance the experiment [equal sample sizes] if at all possible.”
A 1-way ANOVA tests whether the means of all groups are equal for different levels of one factor, using some fairly lengthy calculations.
There are many software packages for mathematics and statistics that include ANOVA calculations. One of them, R, is highly regarded and is open source.
When you use a calculator or computer program to do ANOVA, you get an ANOVA table
Note that the mean square between treatments,is much larger than the mean square within treatments. That ratio, between-groups mean square over within-groups mean square, is called an F statistic (F = MSB/MSW). It tells you how much more variability there is between treatment groups than within treatment groups. The larger that ratio, the more confident you feel in rejecting the null hypothesis, which was that all means are equal and there is no treatment effect.
The p-value is below your significance level of 0.05: it would be quite unlikely to have MSB/MSW this large if there were no real difference among the means. Therefore you reject H0 and accept H1, concluding that the mean absorption of all the fats is not the same
Now that you know that it does make a difference which fat is used, you naturally want to know which fats are significantly different. This is post-hoc analysis.
Perform post-hoc analysis only if the ANOVA test shows a p-value less than your . If p>, you don’t know whether the means are all the same or not, and you can’t go fishing for unequal means.
The easiest thing is to compute the confidence interval first, and then interpret it for a significant difference in means (or no significant difference). You’ve already seen this relationship between a test of significance at the level and a 1 confidence interval:
If the endpoints of the CI have the same sign (both positive or both are negative), then 0 is not in the interval and you can conclude that the means are different.
If the endpoints of the CI have opposite signs, then 0 is in the interval and you can’t determine whether the means are equal or different.
Now estimate the difference of means
If you have r treatments, there will be r(r1)/2 pairs of means. The “/2” part comes because there’s no need to compare
The row heading tells you which treatments are being compared in this row, and the direction of comparison.
The next column gives the point estimate of difference, which is nothing more than the difference or the two sample means.
Next is critical q, from the confidence interval formula. q(,r,dfW) depends on the number of treatments and total number of data points, not on the individual treatments, so it’s the same for all rows in any given experiment.
The standardized error square root of 0.5 times MS sub w times quantity 1 over n sub i plus 1 over n sub j is the square-root term from Tukey’s formula for confidence interval.The endpoints of the confidence interval, as usual, are the point estimate plus or minus the critical q times the standardized error. The last column applies the relation between confidence interval and significance test to say whether there’s a significant difference between the two treatments.
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