How Statistics Work
What is a discrete variable and give an example
separate values; cannot have any values between the established ones
your decision to reject the null rests on...
the p-value
What is the important question a z test is asking? (I will guide you if needed as this question is vague)
Is the difference I am observing due to my treatment or just from error?
Name the three types of t-test and define the situations when we would use which
single sample ttest - 1 sample, unkown pop SD
indep. ttest - 2 samples of different people
dependant ttest - 1 sample over 2 time periods
explain the process for finding SD
calc mean, subtract scores from mean, square these and sum them, divide by n, this gets you variance, now sq root for SD
Create an example of an experiment. Then identify the dependent and independent variables for this experiment
[Provide valid example]
Define what sampling error is and provide an example of it
The amount of error between the sample and the population it represents. Ex. Sampling students only in EA and posing them as representative of MRU as a whole would create a larger sampling error than if we were to be in the main building. These are mostly arts students, and most of the science/nursing/etc students would not be in EA very often.
what is a type 2 error and give an example
false negative
How can we go about accounting for different sample sizes in two samples that are undergoing a t-test? [Bonus marks for formula]
Spooled (pooling variance).
what is the formula for the z statistic for both single score and single sample
Z=X-M/SD ; Z=M-u/SDm
I have created a survey that asks participants to rank ice cream flavours from 1-5, 1 being least preferred and 5 being most preferred. What type of scale is this, and explain why?
Ordinal (rank-order). This is because there is a direction of difference (the higher the more preferred), but it cannot measure an exact difference, like height can for example.
Explain the central limit theorem and give an example to show why it makes sense.
It is the idea that the more scores we have in a distribution the closer it gets to a normal distribution. For example, flipping coins you might get more heads at first than tails, but if you do 1000 coin flips it will look normal
1 sample that we are comparing against the population and the population SD is KNOWN
State 1 advantage and 1 disadvantage of each type of t test
ss - need little info to get going, not good if sample is small
it - allows us to see if two different groups differ, more potential for var between groups
dt - no var issues, sensitive to interference effects
what is the formula for independant t statistic
(m1-m2)/S difference
How do we know if the mean is representative of the data? Why and how would we interpret the height of this value?
SD/Var. Higher SD/Var = more variation between scores, lower means vice versa.
Identify the 3 different types of distributions and explain what each of them consists of.
Original population of scores, sample, distribution of sample means. First and second self-explanatory. Distribution of sample means is the mean of several different samples from the population. (Bonus marks: what do we do with it??)
name 3 ways we can increase power in a z test
lower alpha, higher sample size, less error
Explain why the t test sample variance estimate is bias and the problem with it. How do we account for it? What is different about the t distribution in comparison to z?
The var in a small # of scores (sample) will always be bigger than in the pop. account with df. t distrib changes with df, more spread out, and has heavier tails.
how do you calculate estimated population variance (and in what test is this used)
used in T-test: S2 = sum of X-M2 / n-1
Define central tendency. Provide the 3 types of central tendency measure. Provide the 2 ways we look for it (terms) and explain the difference between them.
Set of measures that reflect where on the scale the distribution is centered. Mode, median, mean. Sufficiency - does statistic make use of all data in sample? Robustness - is the statistic easily influenced by outliers?
You did a one tailed z-test for whether texting and driving had an effect or not on hitting pedestrians (unethical? perhaps...). There was a group that was texting and driving and long term population data of people not texting and driving. Z=2.75, p<.01, d=.69, m=13.8, u=10.5. Write up an APA conclusion.
texting while driving had a significant effect on the number of people hit by participants, zscore, pval, dval. texting while driving negatively influenced participants driving performance as participants hit more people when texting (m=13.8) compared to a population not texting (u=10.5).
What is cohen's d? how is it calculated? what is it NOT effected by? give an example of a large and a small cohen's d in a study.
Measure of effect size. mean difference/population SD. sample size doesnt effect cohen's d. .20 small, .80 large
The independent t-test has _ population distributions, _ distributions of means, distribution of _____ between means, and if the null is true, the distribution of ____ between ____ has a mean of ____
2, 2, differences, differences, means, zero
write the formula for the test statistic of a dependent t test
t = sum of (difference - mean difference)2 / n-1
In this case, difference is after-before