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# Analysis of Variance

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Each year a study is conducted of children's drug, alcohol, and tobacco usage. Children in fourth, eighth, and twelfth grades are asked about their use of cigarettes, chewing tobacco, marijuana, cocaine, ecstasy, (abuse of) prescription drugs, beer, wine, and liquor. For each substance, they are asked about their use during the past 30 days, and during the past twelve months.

The results of the study are reported separately for boys and girls, and are compared with the previous year's results. Typically, media reports of the annual study take the form of, "Marijuana use rises among eighth grade girls."

Explain why it is not possible to know whether the increase in eighth grade girls' use of marijuana is statistically significant.

Explain the role that an analysis of variance could play in establishing whether any of the results of the study are statistically significant, and how you would identify which results of the study might be statistically significant.

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Each year a study is conducted of children's drug, alcohol, and tobacco usage. Children in fourth, eighth, and twelfth grades are asked about their use of cigarettes, chewing tobacco, marijuana, cocaine, ecstasy, (abuse of) prescription drugs, beer, wine, and liquor. For each substance, they are asked about their use during the past 30 days, and during the past twelve months.

The results of the study are reported separately for boys and girls, and are compared with the previous year's results. Typically, media reports of the annual study take the form of, "Marijuana use rises among eighth grade girls."

Explain why it is not possible to know whether the increase in eighth grade girls' use of marijuana is statistically significant.
In term of statistical significance, we are testing it against a hypothesis. In other words, we would need a level of alpha (i.e. 0.05, 0.1 etc...) Then, we use this level of alpha to conduct our test hypothesis. Hopefully, the results will tell us whether or not our data has any "statistical significance." Now, it is impossible to know whether the increase in eighth grade can be statistically significance or not. The reason is that, the data most likely plotting on a regression line. They will show that the regression line has an upward trend, but we do not know whether the analysis has any statistical relevancy. This is why we cannot use the "statistical significance" with these things, because we simply do not know anything other than it has an upward trend!

Explain the role that an analysis of variance could play in establishing whether any of the results of the study are statistically significant, and how you would identify which results of the study might be statistically significant.
ANOVA can be used whether the variance in abuse data for all substances is significance when they are tested for the students, or whether the data have significance variance among children with different types of drug uses. ANOVA can be use to test between two or more factors at a time. This will tell us whether or not there is a result that is statistically significant.

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