Name those Variables
Do fourth graders tend to be taller than third graders?
The researcher wants to use grade level to explain differences in height. The explanatory variable is grade level. The response variable is height.
In R what type of test does binom.test default too.
(Bonus 100 if you do this without a hint)
Two-tailed/significance test
Justin organizes a fight night in Erickson Hall. We assume that all the participants fighting in fight night are in the same weight class and have the same level of fighting experience (we are assuming they are all the same essentially). Looking back at the statistics of fight night, we found that there were a total of 32 fight nights. One competitor named Anh had a suspicious amount of wins and Justin was worried she lied about her fighting experience or was cheating. Justin expected each fighter to win about 50 percent of the fights but and won 28 out of the 32 fights.
State the Null hypothesis, Alternative Hypothesis, and calculate a P Value. (Bonus 100 for explaining what the p value means in regards to this observation)
Null Hypothesis: Anh wins about 50 percent
Alternate Hypothesis: Anh wins more than 50 percent
P value: 9.651e-06
Reject the null
What is the statistic of a study.
successes/total trials
Finish the sentence. If the P is Low ________________
Reject the HO
A group of middle school students wants to know if they can use height to predict age. They take a random sample of 50 people at their school, both students and teachers, and record each individual's height and age. This is an observational study.
The students want to use height to predict age so the explanatory variable is height and the response variable is age.
(Bonus 100 if you can explain why)
No sample size can not be biased
Yes the sample can be biased
Justin organizes a fight night in Erickson Hall. We assume that all the participants fighting in fight night are in the same weight class and have the same level of fighting experience (we are assuming they are all the same essentially). Looking back at the statistics of fight night, we found that there were a total of 32 fight nights. One competitor named Anh had a suspicious amount of wins and Justin was worried she lied about her fighting experience or was cheating. Justin expected each fighter to win about 50 percent of the fights but and won 28 out of the 32 fights.
Calculate the 90% Confidence Interval for Anh Using a Two Sided Binomial Test and explain what this interval means.
90% Confidence interval (0.74,0.96)
This is Anh's expected probability of success interval. We are 90 percent sure if we did this again she would be somewhere between 74% and 96% win rate.
What does the Null Hypothesis mean and what is the Alternative Hypothesis.
Null Hypothesis: is the expected hypothesis (always predicts no effect)
Alternative Hypothesis: is the hypothesis you are testing or what you may believe to be trueWhat are the major things to focus on for homework and tests that will get you docked points
Explanation. Everything you say explain why. If you can make a good point or show that you understand you will usually get it right. You can not just say the right answer.
A researcher believes that the origin of the beans used to make a cup of coffee affects hyperactivity. He wants to compare coffee from three different regions: Africa, South America, and Mexico.
(Bonus 100 if you can determine what the levels of the explanatory variables is)
The explanatory variable is the origin of coffee bean; this has three levels: Africa, South America, and Mexico. The response variable is hyperactivity level
Why can a study that shows statistical significance be so wrong?
Bias.
Justin organizes a fight night in Erickson Hall. We assume that all the participants fighting in fight night are in the same weight class and have the same level of fighting experience (we are assuming they are all the same essentially). Looking back at the statistics of fight night, we found that there were a total of 32 fight nights. One competitor named Anh had a suspicious amount of wins and Justin was worried she lied about her fighting experience or was cheating. Justin expected each fighter to win about 50 percent of the fights but and won 28 out of the 32 fights.
How would you determine the sample size that would be needed to estimate the population parameter to within 0.025 with 95% confidence. (Double points for coding an example in R)
What is the difference between a parameter and a statistic.
the sample that is summarizing the population (numbers that summarize data for an entire population)
the statistic is a number describing the sample
Example: A researcher wants to estimate the average height of women aged 20 years or older. From a simple random sample of 45 women, the researcher obtains a sample mean height of 63.9 inches.
The parameter is the average height of all women aged 20 years or older.
The statistic is the average height of 63.9 inches from the sample of 45 women.
Tell me about parameter, statistics, population and sample. For example, what are they, how are they different, etc.
A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).
Population: A population is the entire group that you want to draw conclusions about. A sample is the specific group that you will collect data from.
A public speaking teacher has developed a new lesson that she believes decreases student anxiety in public speaking situations more than the old lesson. She designs an experiment to test if her new lesson works better than the old lesson. Public speaking students are randomly assigned to receive either the new or old lesson; their anxiety levels during a variety of public speaking experiences are measured.
This experiment has one explanatory variable: the lesson received. The response variable is anxiety level.
How do you interpret the P value.
(Bonus 100 if you state what value we compare our p value to)
The P value is the probability this event would occur by chance.
We usually compare it to .05
Justin organizes a fight night in Erickson Hall. We assume that all the participants fighting in fight night are in the same weight class and have the same level of fighting experience (we are assuming they are all the same essentially). Looking back at the statistics of fight night, we found that there were a total of 32 fight nights. One competitor named Anh had a suspicious amount of wins and Justin was worried she lied about her fighting experience or was cheating. Justin expected each fighter to win about 50 percent of the fights but and won 28 out of the 32 fights.
Calculate a significance test, and give another name for this test. (Bonus 100 if you explain the difference between a significance test and one tailed test and say which to use for this example)
binom.test(28,32,.5, "two.sided", conf.level = .9)
What is a confidence interval.
Does the confidence interval get wider or tighter when we go from 95% to 90% and why?
the probability that a parameter will fall between a pair of values around the mean
tighter because you can make predictions without being as confident.
is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters.
different types: sampling bias, omitted variables, assignment bias (where two or more groups are treated differently and then compared, it’s important that there aren’t pre-existing differences between groups )
A team of veterinarians wants to compare the effectiveness of two fertility treatments for pandas in captivity. The two treatments are in-vitro fertilization and male fertility medications.
This experiment has one explanatory variable: type of fertility treatment. The response variable is a measure of fertility rate.
Suppose you have a binomial test that looks like the following: binom.test(10,15,p=.5)
What does the 10, 15, and p=.5 represent.
(Bonus 200 if you can explain what happens to the P value if you change 10 to 20, and 20 to 30. Why?)
10 represents successes, 15 represents total trials, p=.5 represents the expected probability.
The P value would decrease because of the increase in sample size. (if the statistic matches the expected probability then it would stay the same)
Justin organizes a fight night in Erickson Hall. We assume that all the participants fighting in fight night are in the same weight class and have the same level of fighting experience (we are assuming they are all the same essentially). Looking back at the statistics of fight night, we found that there were a total of 32 fight nights. One competitor named Anh had a suspicious amount of wins and Justin was worried she lied about her fighting experience or was cheating. Justin expected each fighter to win about 50 percent of the fights but and won 28 out of the 32 fights.
Lets say our stats keeper wrote down a 28 instead of 18. Does our conclusion change? Show work.
Yes the P value is 0.2983, so we can not reject the null. I still might suspect Anh has weighted gloves thought...
Convince me you know about P values. For example, what they mean for the hypothesis, what they may suggest, what to be cautious of, what the P value actually means. Just pour your heart out.
points range from 100-500
Justin's judgement