Identifying Variables
What are the two most broad categories of variables, what are the differences?
Quantitative and Qualitative (Categorical); Qualitative are defined by their numeric values and Categorical are not quantitative but are categories or groups
What is the purpose of a confidence interval?
A confidence interval is generated from a sample to infer upon the population. For example if we know the mean of a sample, we do not KNOW the mean of the population BUT we may want to take a guess using the CI.
The null hypothesis always states what?
There are no differences between group; There is no effect of the IV on the DV
When do we use an ANOVA?
When comparing a quantitative variable across three or more levels of a categorical variable.
Effect size, Cohne's d
an explanatory variable (Independent) is what we hypothesize changes, or accounts for change, in the response variable. The response variable is a variable which changes subsequent to changes in the explanatory variable. Additionally, the independent variable is the variable we can, or choose to, manipulate in an experiment.
What are the three major components of a CI calculation
Point estimate, Z critical, and standard error/deviation
Alternative hypotheses come in two different varieties (typically) and correspond to the number of tails you include in your analysis, what are they?
Non-directional and directional. A directional hypothesis is one tailed, as you are testing the direction of a difference. A non-directional is two tailed, because whether one mean is more or less is irrelevant.
What does the F-statistic represent?
The ratio of the average variability within groups, to the average variability within the groups.
You want to know why ice-cream sales increase as number of sunburn related hospital visits increase. The likelihood that either of these variables effects the other is very low, what would we call a third variable which may cause an increase in sunburns that we did not account for?
A confound.
What is the difference between the calculation for a CI for proportion and mean?
The standard error for means and proportions differ in formula.
For an ANOVA, because there are more than two groups, and many directions for the difference between groups, how is the alternative hypothesis formatted?
An ANOVA alternative hypothesis is written out, and stated as "at least one of the groups is different"
Why would you conduct a single ANOVA instead of multiple t-tests to compare more than 2 groups?
When you conduct a T-Test, there is a chance that you will run into a Type 1 error and the chance of running into this error compounds with each T-test you run. So, you run a single ANOVA to reduce this chance.
A quantitative variable has two subtypes. What are they and how would you define them?
Continuous and discrete. Continuous can take on any number within a range, a hypothetically infinite number. Discrete typically takes on whole values, or predetermined values.
What Z-critical values correspond to 90%, 95%, and 99% confidence levels?
1.645, 1.96, and 2.575, respectively
If the p-value is greater than the alpha level, do you reject or fail to reject the null hypothesis?
Fail to reject
If the F-statistic is lower than the F-critical, what does this mean for the null hypothesis? Why?
We DO NOT reject the null hypothesis as there is not sufficient evidence that the group means are truly different.
What is the difference between ratio and interval quantitative variables.
Ratio data is a quantitative variable where "0" genuinely means the absence of the variable and interval does not. For example, 0 as a number of siblings genuinely means the absence of any siblings, but 0 degrees does not mean an absence of temperature.
Interpret a 99% confidence interval with a lower limit of 6.95 feet and an upper limit of 8.21 feet.
We are 99% confident the true population mean of X is between 6.95 feet and 8.21 feet.
BONUS: If your P-value is less than .05, interpret what this means in relation to probability and the null hypothesis.
"There is a less than 5% chance that the results from the analysis are by chance"