Tutorial 1

Question 1

How to measure the mean?

Question 2

How to measure the deviations?

Question 3

How to measure sample variance?

Question 4

How to measure variance?

Question 5

How to measure standard deviation?

Question 6

What does an 𝑆𝑆 tell us about a set of data?

Answer 6

The value of the SS indicates the spread of the data in terms of how far observations are located away from the mean. However, it is not an incredibly useful measure since it is
unlimited and, depending on the amount of observations can approach infinity. (Each added
observation will add to the SS as long as its score is not exactly equal to the mean).
So, it does relate to variance, the standard deviation and is a measure of how far people tend to be away from the mean, but it is not interpretable without knowing the number of
observations, and tends not to be considered in research output.

Question 7

Under what circumstances will the value of 𝑆𝑆 equals 0?

Answer 7

The distance between each observation and the mean must equal 0. If it does not equal the
mean, even by a little, the square of the distance is also not zero.
That means that if all scores must be equal to the mean, all scores must also be equal to each
other. I.e. if all scores are identical, since that would then be the mean, and all scores would have a distance to the mean of 0.

Question 8

Can SS ever be negative?

Answer 8

No

Question 9

What is a sampling distribution?

Answer 9

The sampling distribution of a statistic (such as the mean, or a certain test statistic) is the
(theoretical) distribution of a set of samples that we draw from the population.
E.g. if we were to measure average length in thousands (or infinitely many) samples by drawing
a sample, measuring everybody, computing the average, drawing a new sample, again
compute the average, draw a new sample, etc. it would be a distribution that shows how likely
it is to get a particular average sample value. Thus, it describes how the mean, the value of 𝑀
varies across samples of size 𝑁.

Question 10

What do we know about the shape and characteristics of the sampling distribution for 𝑀, the sample mean?

Answer 10

We know the distribution for the sample mean to be approximately normally distributed in
reasonably large samples. This is related to what we call the central limit theorem, which
roughly implies that the distribution of the sample mean becomes a normal distribution if we
look at enough large samples, regardless of what the population distribution of the individual
observations looks like. (In small samples, the variable itself needs to be normally distributed
for this to be true). It is centred (the peak is at) the population mean and has a standard deviation equal to the 𝜎/√𝑁, which is called the Standard Error when talking about the sampling distribution.

Question 11

What is 𝑆𝐸𝑀?

Answer 11

It is the Sampling Error of the Mean. This Sampling Error is related to the size of the sample 𝑁 and the variance of individual scores 𝜎.

Question 12

What does the value of 𝑆𝐸𝑀 tell you about the typical magnitude of sampling error?

Question 13

As 𝑠 increases, how does the size of 𝑆𝐸𝑀 change (assuming 𝑁 stays the same)?

Answer 13

As the variance increases there is more ‘room’ to have sample means that differ a lot from the population mean. So, the sampling error becomes larger.
In the formula 𝑆𝐸𝑀 = 𝑠 / √𝑁 this is also clear to see: If we keep N the same and s becomes
larger as we divide a larger number by an equal number.

Question 14

As 𝑁 increases, how does the size of 𝑆𝐸𝑀 change (assuming 𝑠 stays the same)?

Answer 14

As the number of observations increases it becomes less likely that we accidentally sample predominantly extreme values, and more likely that we sample people
equally from above and below the mean score. (Imagine sampling, by accident, the 10 tallest people from a population. Our mean then is way too high. If we instead sample 11 people, the added person must be shorter than the other 10 as those were the 10 tallest, so the mean will
become lower and closer to the population mean. Moreover, it becomes increasingly unlikely that we sample only very tall or small people if our sample would be of size 40).
In the formula 𝑆𝐸𝑀 = 𝑠 / √𝑁 this is also clear to see: If we increase N and keep s the same, we divide by a larger number and the sampling error becomes smaller.

Question 15

What research decisions influence the magnitude of risk of Type I error?

Question 16

What factors influence the magnitude of risk of Type II error?

Question 17

How are the risk of Type II error and statistical power related?

Question 18

In your own words (not a direct quote): What does it mean to say that 𝑝 < 0.05?

Question 19

Describe at least two problems with Null-Hypothesis Significance Testing (NHST)

Question 20

What are a null hypothesis and an alternative hypothesis?

Question 21

What is an alpha level, and what determines the value of α?

Question 22

What is an exact p-value?

Question 23

What is statistical power?

Question 24

What information is needed to decide what sample size is required to obtain some desired level of power (such as 80%)?

Question 25

What conclusions can be drawn from a study with a null result?

Question 26

What conclusions can be drawn from a study with a statistically significant result?

Question 27

Suppose a researcher writes in a journal article that the obtained p was 𝑝 = .32. Thus, there is a 3.2% chance that the null hypothesis is correct. Is this a correct or incorrect statement?