Misc.
What is the formula for calculating a z-test?
z = score - mean / standard deviation
Which type of t-test has the following degrees of freedom df = n1 + n2 – 2?
Two Sample Mean T-test (aka Independent Sample Mean Test)
What type of variables are appropriate for a chi-squared test?
Nominal and/or ordinal. This is a non-interval party.
A sociologist is interested in seeing if there is a significant difference between the average number of dates that a undergrad at the University of Michigan and a undergrad at The Ohio State University go in a month. The researcher suspects that OSU students go on more dates than Michigan students. They collect data from 150 Michigan undergrads and 156 OSU undergrads and find that the average number of dates that Michigan undergrads go on is .45 and 1.56 for OSU undergrads. The standard error of the difference of means is 0.0276.
What information do we have?
We have: Two samples from OSU and Michigan, and nothing about the population.
The researchers should use a one tailed two mean t-test
What is a type I error?
A type I error is when we reject the null hypothesis, when in fact we should not have.
Which piece of information is known in a z-test but is estimated in a t-test?
Population standard deviation.
Let’s say we have an example of:
We have a random sample of 25 fifth grade pupils who can do 15 pushups on the average, with a standard deviation of 9, after completing a special physical education program. We find out that the average for all 5th graders is 17. We’re interested in if the number of pushups by our 5th graders differs significantly from all 5th graders at the .05 alpha level.
What would be the t-critical value for this test?
How can we find this? We need two pieces of information:
a. What tailed test? This is a two tailed test because we’re looking at differences
b. Degrees of freedom:
n-1 : 25-1 = 24 degrees of freedom.
Thus, the tcritical value is +/- 2.064
What is a chi-squared test testing? (i.e. with no interval level data we can't compare and contrast means to one another.)
It's looking for an association between two categorical variables. It compares observed frequencies to expected frequency. If observed differs significantly from expected we will likely reject the null hypothesis and say that we think we have evidence that suggests that our independent variable is associated with (i.e. influences) our dependent variable.
A researcher finds that the average age of a sample of 426 Norton residents when they first begin to smoke is 16 years old. She wants to know if this age is significantly different from the population that has a mean of 17.5 and a standard deviation of 1.2. What test should she use?
What information do we have?
We have: One sample of age of first smoke with a mean of 16; population Mean of 17.5, population Standard Deviation of 1.2,
The researchers should use a two tailed z-test
Why? Oh why do we do n-1 when calculating the variance/standard deviation of sample data?
This is to deal with the known issue of sample level data - we know, thanks to the central limit theorem and probability theory, that samples tend to underestimate population level variation. We subtract one from the sample to help create an unbiased statistic.
A researcher wants to know if university students sleep more or less than the recommended 8 hours of the general population. She takes a random sample of 15 university students and records how much they’ve slept on average for the past week. Outline the null and alternative hypotheses for this research.
H0: u students = u population
H1: u students ≠u population
What is the chi-squared critical statistic if you have 10 degrees of freedom and you want to be 95% confident in your result?
To find a chi-squared critical value, you need two pieces of information:
a. Degrees of freedom - derived by picking whichever is smaller between columns -1 or rows - 1.
b. Your alpha level (1 - your confidence level converted into a proportion)
So in this case you have 10 degrees of freedom and an alpha of .05.
Your critical stat is 18.037
A sociologist is interested in determining whether college graduates spend more hours per week at their jobs than people who have high school degrees. The research knows that high school graduates work, on average, 43.76 hours per week. This researcher takes a sample of 150 college graduates and finds that they work 45.6 hours with a standard deviation of 5.6.
Which test should they use?
What do we have? We have:
1 sample: college grads with a mean and standard deviations.
1 predetermined value: mean hours worked by high school graduates.
The sociologist should do a one tailed single mean t-test
What does statistical significance mean? What is its relationship to meaningful significance?
Statistical significance is our way to note that we think (after running our hypothesis test) that we have evidence that suggests that our sample is _______ (different than, more than, less than, associated with) to whatever we are testing it against. Most importantly this means that we are implying that we think that something else is at play beyond the chance that we drew the sample that we did. Borrowing from Tom Redman, "When a finding is significant, it simply means you can feel confident that’s it [the result] real, not that you just got lucky (or unlucky) in choosing the sample."
Let's say that you are interested in running a two tailed z-test where you are 99% confident in your result. What is the z-critical score that you should use?
You need two pieces of information:
a. Number of tails - in this case it's a two tail test
b. Covert % to proportion and look for that number in Column C of your z-table. For a two-tailed test you need to divide your proportion in half. (1-tailed test - no need to do anything)
So in this case: +/- 2.58
Cramér’s V - What's this all about?
This is a post-estimate test that examines how the strength of a statistically significant association. Remember that one should calculate this if you find a statistically significant result.
A researcher is interested in seeing if there is an association between age range (18-35, 35-55. 56 and above) and one's attitude towards if there are aliens living among us (yes, maybe, no). The research takes a sample of 150 people in the United States and looks into if there is an association between age range and aliens living among us.
What do we have? We have:
2 categorical variables - age ranges, attitude towards aliens living among us.
"association"
We should run a chi-squared test