week 6: inferential statistics

Question 1

Inferential statistics

Answer 1

We infer with inferential statistics

Inferential statistics help us make decisions (test hunches, make conclusions

Question 2

Finding percentages using a normal curve (Z) table

Answer 2

rarely are scores exactly 1 or 2 SDs from the mean
can calculate the exact percentage by using a normal curve table
first need to calculate the Z score based on the corresponding raw score
using a normal curve table (Table A-1 p. 671-674), find the area between the score and the mean

Question 3

Tips for using a normal curve table

Answer 3

for each Z score, the “%age to Mean” value and the “%age in Tail” sum to 50.00%

• if looking for scores above the z score you use the tail
• if looking for scores from z score to mean use to the mean

Question 4

example:

What percentage of IQ scores are greater than 92.5?

Answer 4

Z score = -.5
area between Z = -.5 and the mean is 19.15%
but 50% of scores are greater than Z = 0
50% + 19.15% = 69.15%

Question 5

example:

In a distribution of IQ scores, what percentage of the distribution lies between 85 and 122.5?

Answer 5

find the Z scores for IQ = 85 and IQ = 122.5
draw a curve and mark these scores on it
look up the percentages associated with the first Z score
shade in the area that is associated with this percentage
look up the percentages associated with the second Z score
shade in the area that is associated with this percentage
read the question again and answer it
add the two percentages together

IQ Scores: M = 100, SD = 15
IQ Score = 85, Z Score = -1
IQ Score = 122.5, Z Score = 1.5
percentages
for Z = -1, % to mean = 34.13%
for Z = 1.5, % to mean = 43.32%
refer back to the question:
total % between IQ of 85 and IQ of 122.5 =    
	34.13% + 43.32% = 77.45%

Question 6

Finding raw scores from percentages

Answer 6

draw the normal curve and shade the area you want to identify
look up the % column in the table and find the Z score associated with%
use this Z score and your knowledge of IQ scores to calculate the raw score

Question 7

example:

What IQ score cuts off the top 10% of IQ scores?

Answer 7

draw the normal curve and shade the area you want to identify
look up the % column in the table and find the Z score associated with 40%
Z = 1.29
use this Z score and your knowledge of IQ scores to calculate the raw score
if Z = 1.29, M = 100, SD = 15
x=(z)(sd)+m
X =1.29 x 15 + 100 = 119.35

Question 8

Probability

Answer 8

based on the likelihood of outcomes (expected frequency)

Question 9

Calculating probability

Answer 9

probabilities are calculated as the proportion of successful outcomes

Question 10

probability example

Answer 10

If tossing a coin, heads are likely to occur half the time

Number of possible head outcomes = 1
Number of possible outcomes = 2

So, the probability is 1/2 or p (probability) = .5

p = .5 is what we call a 50/50 chance (50% chance of it occurring)

Question 11

Expected relative frequency

Answer 11

The relative frequency is the number of times something actually happens relative to the number of times it could have happened

Question 12

Z scores and probability

Answer 12

can use our knowledge of the percentages under the curve to represent a probability
need to think of the total area under the curve as 100% or p = 1

Question 12

Z scores and probability

Answer 12

can use our knowledge of the percentages under the curve to represent a probability
need to think of the total area under the curve as 100% or p = 1

Question 13

Z scores and probability example

Answer 13

What is the probability that a score is between the mean and a Z score of +1 (1 SD above the mean)?
p = .34 (34%)
e.g., What is the probability that a person’s IQ score will be greater than 100?
p = .5 or 50%

Question 14

Methods of sampling

Answer 14

random sampling (equal chance of being in study)
non-random sampling
random sampling is optimal

Question 15

types of non-random sampling

Answer 15

haphazard selection (e.g., person sitting next to you)
convenience sample (e.g., family and friends)
snowball sample (e.g., friends pass on to their friends)

Question 16

Population parameters and sample statistics

Answer 16

need to distinguish between the characteristics of a sample (M, SD, Variance) and those of a population
in a sample, these are called statistics, in a population the same quantities are called parameters
often don’t know the population mean or SD…
estimated from the sample
in a population, they are denoted by Greek letters