Module 2: Normal Distributions and Z-scores

Question 1

Mean (average)

Answer 1

-sum of all values, divided by the number of values

Question 2

Median

Answer 2

-middle value in an ordered data set

Question 3

Mode

Answer 3

-most frequently occurring value

Question 4

Range

Answer 4

-difference btwn highest and lowest values

Question 5

Variance

Answer 5

-average of squared differences from mean
-how far a value (or set) is from the mean

Question 6

Standard deviation

Answer 6

-square root of variance
-small: data is tightly grouped around the mean

Question 7

Characteristics of a normal distribution

Answer 7

-symmetrical, bell-shaped curve
-approximately 68% of data falls within -/+ 1 SD from the mean

Question 8

What does the Law of Large Numbers state

Answer 8

-statistical properties become reliable with large sample sizes (n>30)

Question 9

Def: z-score

Answer 9

-measures how many standard deviations a raw score is from the mean (z= (x-u)/o)
-mean of 0, SD of 1

Question 10

x =

Answer 10

individual score

Question 11

u =

Answer 11

population mean

Question 12

o =

Answer 12

population standard deviation

Question 13

Purpose of z-score

Answer 13

-allows comparison of scores from different distributions
-compare different measures/tests
-compare performance across different variables/populations

Question 14

z = 0

Answer 14

-value is the same as the mean

Question 15

z = + (>0)

Answer 15

-value is above the mean

Question 16

z= - (<0)

Answer 16

-value is below the mean

Question 17

Assumptions necessary for z-score

Answer 17

-requires interval/ratio data
-population mean and variance must be known
-data from normally distributed population
-not suitable from small sample sizes

Question 18

Def: statistical significance

Answer 18

-determine if observed differences are likely not due to chance

Question 19

a = 0.05 (p<0.05)

Answer 19

likelihood of occurrence is less than 1/20

Question 20

a = 0.01 (p<0.01)

Answer 20

likelihood of occurrence is less than 1/100

Question 21

a = 0.001 (p<0.001)

Answer 21

likelihood of occurrence is less than 1/1000

Question 22

T-scores

Answer 22

-similar to z-scores but used for groups

Question 23

Requirements for comparison:

Answer 23

1) mean
2) standard deviation