Module 2: Normal Distributions and Z-scores Flashcards
Mean (average)
-sum of all values, divided by the number of values
Median
-middle value in an ordered data set
Mode
-most frequently occurring value
Range
-difference btwn highest and lowest values
Variance
-average of squared differences from mean
-how far a value (or set) is from the mean
Standard deviation
-square root of variance
-small: data is tightly grouped around the mean
Characteristics of a normal distribution
-symmetrical, bell-shaped curve
-approximately 68% of data falls within -/+ 1 SD from the mean
What does the Law of Large Numbers state
-statistical properties become reliable with large sample sizes (n>30)
Def: z-score
-measures how many standard deviations a raw score is from the mean (z= (x-u)/o)
-mean of 0, SD of 1
x =
individual score
u =
population mean
o =
population standard deviation
Purpose of z-score
-allows comparison of scores from different distributions
-compare different measures/tests
-compare performance across different variables/populations
z = 0
-value is the same as the mean
z = + (>0)
-value is above the mean
z= - (<0)
-value is below the mean
Assumptions necessary for z-score
-requires interval/ratio data
-population mean and variance must be known
-data from normally distributed population
-not suitable from small sample sizes
Def: statistical significance
-determine if observed differences are likely not due to chance
a = 0.05 (p<0.05)
likelihood of occurrence is less than 1/20
a = 0.01 (p<0.01)
likelihood of occurrence is less than 1/100
a = 0.001 (p<0.001)
likelihood of occurrence is less than 1/1000
T-scores
-similar to z-scores but used for groups
Requirements for comparison:
1) mean
2) standard deviation
