Unit 7b: Standard Scores and Data Transformations Flashcards
standardized score/z score
A standard score indicates how many standard deviations a data point is above or below the population/sample mean. It is derived by subtracting the population/sample mean from an individual raw score and then dividing the difference by the population/sample standard deviation
2 Major types of standard scores
- z-scores
- T-scores
- Both tell you how many standard deviations a particular raw score lies
above or below the group mean
difference between sd and variance
Standard deviation measures how far apart numbers are in a data set. Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean. Standard deviation is the square root of the variance and is expressed in the same units as the data set.
Standard Normal Distribution Curve
All normal distributions, like the standard normal distribution, are unimodal and symmetrically distributed with a bell-shaped curve. However, a normal distribution can take on any value as its mean and standard deviation. In the standard normal distribution, the mean and standard deviation are always fixed
solving for z score
Z = (raw score – mean) / SD
estimating percentages with tabled values of the normal
outliers for z score
the general rule of thumb is z = 3 (or -3) (too high/low)
outliers with box plots
answer that is 1.5*IQR is an outlier
Which of the following is a benefit of standardized scores?
It facilitates comparison of individual points when the scales are not the same.
It helps correct for different rating preferences.
It helps us compare individual items that otherwise would have different units.
Which of the following is NOT a benefit of standardized scores?
It allows you to compare two groups to see if the groups are different from one another
Notice how in the exercises from lecture video and class activity, we have been comparing individual points. For example, we compared Harry’s scores from Draco’s scores. We did not compare Gryffindors with Slytherins. z-scores are individual data points.
You will learn about this later, but if we are comparing groups, we will need to use t-test or ANOVA or regression
Which of the following combination of statistics will be enough to help you calculate the z-score of an item?
The item’s original raw score, the standard deviation of its group, and the mean of its group
standard score
mean is 0 and the SD is 1.
when is the null rejected z test?
if the value of z is greater than 1.96 or less than -1.96, the null is rejected
how to find number of observations in a sample
degrees of freedom + 2
how to find degrees of freedom
n-1
number of groups - 1
