1.2

Question 1

Population

Answer 1

The collection of units to which we want to generalize a set of findings or a statistical model.

(i.e. people, plankton, plants, cities, suicidal authors, etc.)

Question 2

Sample

Answer 2

A smaller (but hopefully representative) collection of units from a population used to determine truths about that population.

Question 3

The mean is a model of

Answer 3

what happens in the real world: the typical score.

It is not a perfect representation of the data.

Question 4

A deviation is…

Answer 4

the difference between the mean and an actual data point.

Question 5

Sum of Squared Errors

Answer 5

• We could add the deviations to find out the total error.
• Deviations cancel out because some are positive and others negative.
• Therefore, we square each deviation.
• If we add these squared deviations we get the sum of squared errors (SS).

Question 6

Variance

Answer 6

• The sum of squares is a good measure of overall variability, but is dependent on the number of scores.
• We calculate the average variability by dividing by the number of scores minus 1 (which is called the degrees of freedom).
• This value is called the variance (s^2).

SS / (N-1)

Question 7

The variance has one problem:

Answer 7

It is measured in units squared. So difficult to interpret.

Question 8

The standard deviation

Answer 8

Since the variance is measured in units squared. We take the square root to make it a meaningful metric.

Question 9

The sum of squares, variance, and standard deviation represent the same thing:

Answer 9

• The ‘fit’ of the mean to the data
• The variability in the data
• How well the mean represents the observed data
• Error

Question 10

Central Limit Theorem

Answer 10

The distribution of the sample means will be approximately normally distributed

Question 11

Central Limit Theorem

How can we measure the accuracy of this average?

Answer 11

• We can use the standard deviation of the sample means.
• In fact, we could collect a very large number of samples, and calculate the standard deviation of the sample means from the population mean.
• Because this is tedious and almost impossible, statisticians have found an approximation.

—> approximation = standard error

Question 12

Test Statistics

Answer 12

• A statistic for which the frequency of particular values is known.
• Observed values can be used to test hypotheses.

Question 13

Type I error

Answer 13

• occurs when we believe that there is a genuine effect in our population when, in fact, there isn’t
• The probability is the α-level (usually .05)

Question 14

Type II error

Answer 14

• occurs when we believe that there is no effect in the population when, in reality, there is.
• Or, put differently: when we use tests, do not find an effect, but there really is one.
• The probability is the β-level (often .2)

Question 15

Examples type 1/2 error

Answer 15

Type 1: we believe pregnancy is there, but it’s actually not there
Type 2: we believe pregnancy is not there, but there’s actually a pregnancy present

Type 1: covid test, you think you have it, but you don’t
Type 2: covid test, you think you don’t have it, but you do

Question 16

What Does Statistical Significance Tell Us?

The importance of an effect?

Answer 16

No, significance depends on sample size. When doing tests, you should always aim at interpreting the effect size as well.

Question 17

What Does Statistical Significance Tell Us?

That the null hypothesis is false?

Answer 17

No, it is always false.

Question 18

What Does Statistical Significance Tell Us?

That the null hypothesis is true?

Answer 18

No, it is never true.

Question 19

Assessing Normality

Answer 19

We don’t have access to the sampling distribution so we usually test the observed data

Question 20

Shapiro-Wilk Test

Answer 20

• Tests if data differ from a normal distribution
• Significant = non-normal data
• Non-significant = normal data

Shapiro-Wilk test for exam and numeracy for whole sample