Unit 3

Question 1

What are direct scores?

Answer 1

Data directly provided by the measuring instrument.

Question 2

What are direct scores also known as?

Answer 2

raw data

Question 3

What do direct scores (raw data) offer?

Answer 3

little information

Question 4

can raw data be interpreted on their own?

Answer 4

no
-> a reference is needed

Question 5

Is raw data comparable to each other?

Answer 5

no, unless they come from the same instrument

Question 6

What do we need to do with the direct score x in order to interpret and compare it?

Answer 6

we need to transform it

Question 7

What is the differential score?

Answer 7

a transformed score by subtracting the mean
-> difference between the mean and the direct score

Question 8

What is the formula of differential scores?

Answer 8

x - 𝑥̅ (score - mean)

Question 9

is the sign negative or positive when the score is greater than the mean?

Answer 9

positive sign

Question 10

is the sign negative or positive when the score is less than the mean?

Answer 10

negative sign

Question 11

what does the differential score measure?

Answer 11

Difference between an individual and his or her own reference group.

Question 12

what is a limitation of differential scores?

Answer 12

does not take variability into account

Question 13

What are differential scores usually not used as?

Answer 13

measures

Question 14

What do differential scores serve for?

Answer 14

the calculation of standard scores and typified indexes
-> such as variance or standard deviation

Question 15

what is a standardized score / Z score?

Answer 15

Difference between an individual and its reference group taking into account the dispersion of the data.

Question 16

What is the formula for calculating a Z score?

Answer 16

Z = x - 𝑥̅ : S
x = individual score
𝑥̅ = mean
S = standard deviation

Question 17

What do we do, when we convert a direct score into a typical score?

Answer 17

standardize that distribution/score
-> transform to normal distribution

Question 18

What does ‘typify’ mean in statistics?

Answer 18

refers to the process of converting a direct score into a standardized score (Z-score), allowing for comparison within a distribution.

Question 19

How does standardization help us?

Answer 19

It will help us to compare two or more different distributions, even if they are composed of scores of different nature.

Question 20

What are examples for different nature in standard scores?

Answer 20

different groups
scores from different variables

Question 21

What do standard scores always indicate?

Answer 21

how many standard deviations the score (x) deviates from the mean of its group

Question 22

What does a Z-score of 0 indicate?

Answer 22

A Z-score of 0 indicates that the subject’s score is equal to the mean of the distribution

Question 23

What is the typical range of Z-scores?

Answer 23

Z-scores usually range between -3 and 3 in most standard distributions

Question 24

What do positive and negative Z-scores represent?

Answer 24

• Positive Z-scores indicate scores above the mean
• Negative Z-scores indicate scores below the mean

Question 25

What is the sum/mean of standard Z-scores in a distribution?

Answer 25

The sum or mean of all Z-scores in a distribution is always 0

Question 26

What are the standard deviation and variance of Z-scores?

Answer 26

The standard deviation (SD) and variance of Z-scores are always 1

Question 27

What do we use the Z-score for? (Z = x - 𝑥̅ : s)

Answer 27

• In terms of standard deviation
• Comparison considering dispersion
• Comparison between variables and different groups

Question 28

What do we use the Differential score for? (x - 𝑥̅)

Answer 28

• Absolute distance from the mean
• Comparison within the same group
• Comparison with the mean as a reference

Question 29

What do we use the Direct for? (x)

Answer 29

• Unit
• Comparison only with data from the same variable and group

Question 30

What are the characteristics of a symmetrical distribution?

Answer 30

the mode, median, and mean coincide at the central point (50%)

Question 31

What does the term “asymptotic” refer to in the context of a distribution?

Answer 31

asymptotic distribution extends from negative infinity to positive infinity, never crossing the x-axis.
- in practice typically considered from -3 to 3 standard deviations (Z-scores) and 2 inflection points on each tail

Question 32

What do percentages indicate in the context of a normal distribution?

Answer 32

Percentages indicate the proportion of subjects that are present or expected within a certain interval in a normal or standardized distribution

Question 33

How can percentages be calculated in relation to Z-scores?

Answer 33

can be calculated exactly from a Z-score by using the probabilities and proportion tables of normal distributions which provide the necessary data for interpreting Z-scores

Question 34

What is the interpretation of cumulative probabilities in a normal distribution?

Answer 34

represent the likelihood that a variable or individual will take values equal to or less than a given area (a), denoted as P (Z ≤ a)