# The ANOVA technique is designed to evaluate the null hypothesis that: a) Two populations have equal variance b) The mean of each treatment group is no

The ANOVA technique is designed to evaluate the null hypothesis that: a) Two populations have equal variance b) The mean of each treatment group is no different from the mean of the pooled population c) The mean square error (MSE) of the treatment group is larger than the overall MSE Write down the sum of squares decomposition and explain, briefly, in your own words how the sum of squares decomposition is used to conduct statistical inference in ANOVA.
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The ANOVA technique is designeed to evaluate the null hypotesis that: b) The mean of each treatment group is no different from the mean of the pooled population. Sum of the square decompasition the total sum of square in the response variable is $SST=\sum \left({y}_{i}-\stackrel{―}{y}{\right)}^{2}$ the total SS can be compose in the two main sources, error SS and regression SS. the error SS is $SSE=\sum {e}_{i}^{2}$ the regression SS is $SSR={b}_{1}^{2}\sum \left({x}_{i}-\stackrel{―}{x}{\right)}^{2}$ Statistical inference: ANOVA:- Compare mean from more than two groups Are they so for apart That the difference cannot be attributed to sampling variability (i.e randomness) ${H}_{0}:{\mu }_{1}={\mu }_{2}=...={\mu }_{k}$ Test statistic: ANOVA table:
${R}^{2}=\frac{SSR}{SST}=1-\frac{SSE}{SST}$
${F}_{stat}=\frac{MSR}{MSE}$