## Question 597:

1

1. ANOVA is used when we want to know if more than two population means are equal.
TRUE: key phrase is more than 2, if it were just 2 we'd use the t-test

2. The sum of the squares error measures the variability in the measurements within the groups.
TRUE: SSError is within groups, SSTreatment is between the groups and SSTotal is across all values regardless of group

3. Equal replication means that the same number of objects being observed are randomly selected from each population.

TRUE(but this one is worded oddly so don't think about it too hard--this is an example of a bad question which only confuses students trying to learn stats). Equal replication in ANOVA usually refers to all values being represented (also called balanced). We assume the values are randomly drawn from the population—so this appears to mix both replication and representation.

4. A Factor is a variable that can be used to differentiate one group or population from another.
TRUE: Factor, variable, treatment are synonymous

5. A response variable is the qualitative variable that you are measuring or observing.
FALSE (wording is also tricky here--mixing both qualitative and response variable). I don't like the use of "qualitative" which makes this one false--it should be a quantitative variable. In ANOVA for example, the response variable has to be quantitative (numeric not categorical) but it is what you measure—also called the dependent variable.

6. A uniform distribution means that each outcome is equally likely to occur.
TRUE: each value has the same chance of occurrence—this distribution is rarely used in real life and is instead used for other statistical tests

7. Observed frequencies are the actual number of observations that fall into each class in a frequency distribution or histogram.

TRUE: Not much to say other than that appears to be an accurate description in general. With respect to Chi-Square observed frequencies are half the equation of (Observed-Expected)^2 / Expected^2

8. The Chi Square Goodness-of-Fit Test determines how well a set of data fits the model for a particular probability distribution.

TRUE: There are basically two uses for the chi-square. One is to tests for associations between two variables (Test of Independence) and the other is to see how well one set of categories fits an expected, often a distribution and this is the Goodness of Fit.

9. The expected frequencies are the number of observations that should fall into each class in a frequency distribution.
TRUE: This is the other half of Chi-Square, the expected counts, which are based on the row and column totals of a contingency table.

10. When we accept the Null Hypothesis we are certain that the Null Hypothesis is correct.

FALSE: This is a subtlety in the wording. When we fail to reject the null hypothesis, we are basically accepting it for lack of sufficient evidence to reject it (see how that's different than say we are certain it's correct?)  For this reason, many statisticians don't use the term "accept the null" and instead say "fail to reject the null" so we are constantly reminded that we don't have solid proof.