Question

The next two major topics in this course deal with the ANOVA test. This is an advanced statistical procedure for testing results of studies that use multiple levels for an independent variable, and/or multiple independent variables. Suppose you want to design a study that looks at the effects of depression medication versus placebo. Going beyond a simple placebo/no placebo design, what types of things would you look at? Create a hypothetical study that contains more than 2 levels for the independent variable you will test. Then explain why you can't, or shouldn't, just use a t-test to determine significance. What are the specific issues you would encounter if you tried using a t-test instead of an ANOVA?

Answer 1

here hypothesis-

H0: steel produced in all four plants is same.

against

H1:steel produced in all four plants is not same.

therefore, ANOVA is -

by using R software -

R code is-

observations= c(71.2,70.9,72.0,71.9,72.3,70.9,71.0,72.3,72.7,72.5,72.2,71.5,
70.9,71.5,72.3,71.3,72.0,71.4,74.2,73.7,74.0,73.8,74.2,74.3,73.0)
levels=c(rep(c(1,2,3,4),c(5,6,7,7)))
b=aov(observations~levels);b
summary(b)

and

OUTPUT is-

b=aov(observations~levels);b
Call:
aov(formula = observations ~ levels)

Terms:
levels Residuals
Sum of Squares 13.28005 17.93995
Deg. of Freedom 1 23

Residual standard error: 0.8831748
Estimated effects may be unbalanced
> summary(b)
Df Sum Sq Mean Sq F value Pr(>F)   
levels 1 13.28 13.28 17.03 0.000411 ***
Residuals 23 17.94 0.78
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here p value =0.000411 < 0.05

thus we reject null hypothesis (H0) at 5% level of significance.

And conclude that steel produced in all four plant is not same.

  

here we heve to test steel produced in all four plants is same .

by using t test we can test equality in steel produced in two plants ,

thus to test   steel produced in all four plants is same or not , we have to conduct six individual t tests.

if we do this then calculations are too lengthy.

to avoid this we use ANOVA

by using ANOVA we can simultaneously test  steel produced in all four plants is same or not

also if null hypothesis is rejected then ANOVA gives which treatment are significantly differ by using

tukey test.