unit 3 Flashcards
What are direct scores?
Direct scores are the raw data directly provided by the measuring instrument.
What is a limitation of direct scores?
Direct scores offer little information, cannot be interpreted on their own, and require a reference for comparison.
Are direct scores comparable?
Direct scores are not comparable unless they come from the same instrument.
What is a differential score?
A differential score is a transformed score calculated by subtracting the mean from the direct score.
How do you calculate a differential score?
A differential score is calculated by the formula: x - ̅ (direct score minus the mean).
What does a positive differential score indicate?
A positive differential score indicates that the direct score is greater than the mean.
What does a negative differential score indicate?
A negative differential score indicates that the direct score is less than the mean.
What is the main purpose of differential scores?
Differential scores serve as a basis for calculating standard scores and typified indexes.
Do differential scores take variability into account?
Differential scores do not take variability into account.
What is a standard score (z-score)?
A standard score (z-score) is a transformed score that represents the difference between an individual score and its reference group, considering the dispersion of the data.
What is the formula for calculating a standard score?
The formula for a standard score is: (x - ̅) / s (direct score minus the mean, divided by the standard deviation).
What is standardization or typification in the context of scores?
Standardization or typification refers to the process of converting a direct score into a typical score, which standardizes the distribution.
What does standardizing a distribution achieve?
Standardizing a distribution helps in comparing two or more different distributions, even if they are composed of scores of different natures.
What are the mean and standard deviation of a standardized distribution?
When a distribution is standardized, the mean is always 0, and the standard deviation is always 1.
What does a standard score indicate?
A standard score indicates how many standard deviations a score deviates from the mean of its group.
What is the standard score if a subject’s score is equal to the mean?
If a subject has a score equal to the mean, the standard score (Z) will be equal to 0.
What range do standard scores typically fall within?
Standard scores usually take values between -3 and 3.
What is the sign of a standard score for scores above the mean?
Scores above the mean have a positive sign for their standard score.
What is the sign of a standard score for scores below the mean?
Scores below the mean have a negative sign for their standard score.
What is the sum/mean of the standard scores always?
The sum/mean of the standard scores is always 0.
What are the standard deviation and variance of the standard scores always?
The standard deviation and variance of the standard scores are always 1.
What are the characteristics of a normal distribution?
A normal distribution is symmetrical, with the mode, median, and mean matching at the central point, and is asymptotic, never crossing the x-axis.
What do the percentages in a normal distribution indicate?
The percentages in a normal distribution indicate the proportion of subjects that are expected in a certain interval.
How are cumulative probabilities interpreted in a normal distribution?
Cumulative probabilities are interpreted as the probability that the variable/individual takes values equal to or less than a given area.
What is the probability of obtaining a score above a Z score of 1 in a normal distribution?
The probability of obtaining a score above a Z score of 1 is 15.9%.
What is the probability of obtaining a score between Z = -1 and Z = 1?
The probability of obtaining a score between Z = -1 and Z = 1 is 68.3%.
What is the probability of obtaining a score between Z = -1.96 and Z = 1.96?
The probability of obtaining a score between Z = -1.96 and Z = 1.96 is 95%.
In the nursing home example, how do you calculate the probability of finding a person younger than 65 years old, given a mean age of 80 and standard deviation of 14?
You’d calculate the Z score using the formula Z = (65-80)/14 = -1.07 and then find the corresponding probability, which is 14.23%.
How do you calculate the probability of finding a person older than 95 in the nursing home example where the mean age is 80 and standard deviation is 14?
You would calculate Z = (95 - 80) / 14 = 1.07 and then find the probability of Z > 1.07 which is 1 - 0.8577 = 14.23%.
In the IQ study, how do you calculate the probability of a participant having an IQ score equal to or lower than 80, given a mean of 115 and standard deviation of 20?
You calculate Z = (80-115)/20 = -1.75, and the probability of a score equal to or lower than this is 4.01%.
