How Statistics Work
Hyp Testing and Statistical Jargon
Z tests/terms in stats tests
T tests
The maths
100

What is a discrete variable and give an example

separate values; cannot have any values between the established ones

100

your decision to reject the null rests on...

the p-value

100

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?

100

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

100

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

200

Create an example of an experiment. Then identify the dependent and independent variables for this experiment

[Provide valid example]

200

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.

200

what is a type 2 error and give an example

false negative

200

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). 

200

what is the formula for the z statistic for both single score and single sample

Z=X-M/SD ; Z=M-u/SDm

300

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.

300

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

300
What has to be the case for us to choose a z-test over a t-test?

1 sample that we are comparing against the population and the population SD is KNOWN

300

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

300

what is the formula for independant t statistic

(m1-m2)/S difference

400

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.

400

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??)

400

name 3 ways we can increase power in a z test

lower alpha, higher sample size, less error

400

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.

400

how do you calculate estimated population variance (and in what test is this used)

used in T-test: S= sum of X-M2 / n-1

500

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?

500

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).

500

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

500

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

500

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