Unit 3 Flashcards
Types of scores and variables transformation
What are direct scores?
Data directly provided by the measuring instrument.
What are direct scores also known as?
raw data
What do direct scores (raw data) offer?
little information
can raw data be interpreted on their own?
no
-> a reference is needed
Is raw data comparable to each other?
no, unless they come from the same instrument
What do we need to do with the direct score x in order to interpret and compare it?
we need to transform it
What is the differential score?
a transformed score by subtracting the mean
-> difference between the mean and the direct score
What is the formula of differential scores?
x - 𝑥̅ (score - mean)
is the sign negative or positive when the score is greater than the mean?
positive sign
is the sign negative or positive when the score is less than the mean?
negative sign
what does the differential score measure?
Difference between an individual and his or her own reference group.
what is a limitation of differential scores?
does not take variability into account
What are differential scores usually not used as?
measures
What do differential scores serve for?
the calculation of standard scores and typified indexes
-> such as variance or standard deviation
what is a standardized score / Z score?
Difference between an individual and its reference group taking into account the dispersion of the data.
What is the formula for calculating a Z score?
Z = x - 𝑥̅ : S
x = individual score
𝑥̅ = mean
S = standard deviation
What do we do, when we convert a direct score into a typical score?
standardize that distribution/score
-> transform to normal distribution
What does ‘typify’ mean in statistics?
refers to the process of converting a direct score into a standardized score (Z-score), allowing for comparison within a distribution.
How does standardization help us?
It will help us to compare two or more different distributions, even if they are composed of scores of different nature.
What are examples for different nature in standard scores?
different groups
scores from different variables
What do standard scores always indicate?
how many standard deviations the score (x) deviates from the mean of its group
What does a Z-score of 0 indicate?
A Z-score of 0 indicates that the subject’s score is equal to the mean of the distribution
What is the typical range of Z-scores?
Z-scores usually range between -3 and 3 in most standard distributions
What do positive and negative Z-scores represent?
- Positive Z-scores indicate scores above the mean
- Negative Z-scores indicate scores below the mean
What is the sum/mean of standard Z-scores in a distribution?
The sum or mean of all Z-scores in a distribution is always 0
What are the standard deviation and variance of Z-scores?
The standard deviation (SD) and variance of Z-scores are always 1
What do we use the Z-score for? (Z = x - 𝑥̅ : s)
- In terms of standard deviation
- Comparison considering dispersion
- Comparison between variables and different groups
What do we use the Differential score for? (x - 𝑥̅)
- Absolute distance from the mean
- Comparison within the same group
- Comparison with the mean as a reference
What do we use the Direct for? (x)
- Unit
- Comparison only with data from the same variable and group
What are the characteristics of a symmetrical distribution?
the mode, median, and mean coincide at the central point (50%)
What does the term “asymptotic” refer to in the context of a distribution?
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
What do percentages indicate in the context of a normal distribution?
Percentages indicate the proportion of subjects that are present or expected within a certain interval in a normal or standardized distribution
How can percentages be calculated in relation to Z-scores?
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
What is the interpretation of cumulative probabilities in a normal distribution?
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)
