Chapter 7: Tests of Significance
Statistical Significance
Inference
The act of drawing conclusions about a population of interest based on characteristics of a sample
Key Things
Quality of the sample (is it random?)
Size of the sample (bigger is better)
Population Standard Deviation (smaller is better)
How do we know if a difference is significant
An observed relationship between an ind var and dep var really exists in the population and is unlikely the product of chance
What do we compare it to
The null hypothesis
No relationship between IV & DV
Any relationship that does appear is the product of chance
Ha: Alternative Hypo: There is a difference
Ho: Null Hypo
Errors
Type I
Theres a relationship in our sample
But not in our population
Type II
Theres no relationship in our sample
But there is in our population
Miss a relationship
Mistakenly see a relationship (just like my ex)
This is why we check with null hypo
How to reject the Null
Be 95% sure that the null hypothesis is wrong
Example
Ho: In comparing individuals, women & men are equal to be democrats
Ha: In comparing individuals, women are more likely to be democrats then men
If our sample shows that more women are democrats, is it random chance?
Women
Mean: 60.5
N: 625
SE: 1.00
Men
Mean: 55.9
N: 553
SE: .98
Hypothesis Testing
Confidence Interval Method: If the potential mean upper and lower bounds touch then you cant deny the null
Find the upper and lower bounds
Women
Upper: Mean(60.5) + 2 * Standard Error(1)
Lower: Mean(60.5) - 2 * Standard Error(1)
58.5
Men
Lower: Mean(60.5) - 2 * Standard Error(1)
53.94
Upper: Mean(55.9) + 2 * Standard Error(.98)
Ay 58.5(Lower for Women) doesnt touch 57.9(Upper for Men)
Difference unlikely to be 0
57.9
62.5
P-Value: Find the probability of getting the observed sample difference. If its less than .05 then you can reject the null
Eyeball test: Is sample difference twice as big than the null
Square Each Mean's SE
Male: .98 ^ 2 = .96
Add that Jaunt
Square that Jaunt
1 + .96 = 1.96
sq(1.96) = 1.4
Sample Difference:
Women(60.5) - Men (58.5) = 2
Women: 1^2 = 1
It isnt
Cannot reject the null
Tail stuff
Two Tailed: Looking at both sides of the distrubution
One-Tailed: Only look at the tail you care about
Directional hypothesis
Non-Directional Hypothesis (no increase/decrease)
Example
Ha: In a comparison of individuals, gender is related to political opinions on gun control
Ho: No Relationship between gender & gun control options
Confidence Range is split between the two tails: 0.025 on each side
Example
Ha: In a comparison of individuals, females love big guns
more than men
Ho: Females are just as likely as men to love big guns
Confidence Range either hits left or right depending on the hypo
Left side: Negative Rel
0.05 aint split boy
Right side: Positive Rel
How many units of Z lie between the sample statistic and population parameter implied by the null hypothesis
Some weird chart
Need
Difference by Ha
Difference by Ho
Standard error of difference
Difference: 4
❓
Comparing Sample Proportions
p1q1/n1 + p2q2/n2
Measures of Association
x2 (ki-square)
Is the observed dispersion of cases differ significantly from the expected dispersion of cases
Ho: Distribution of cases in each column should be the same as total distribution in all cases in the sample
If a category gets stacked then its significant
This wild ass formula I have no idea
Theres a damn chart you have to use
Just hope on god its .05 or below
Strength of relationship between IV & DV
Two Qualities
PRE
Assymetrical > Symmetrical
How much could you figure out just by looking at the DV
Choosing the lower likely option is your prediction error
Lamba
male lower option + female lower option = 584
prediction error with looking at the IV
(pred error w IV) / (pred error no IV)
Jaunt is 17%
Stages
Weak = Less or Equal to .1
Moderate= Between .1 & .2
Moderately Strong = Between 2 & 3
Strong = Greater than .3
Kinda trash
Somers' dyx
Use with ordinal data
Tells you whether the direction of the difference between cases on the IV helps predict direction of the difference on the DV
This jaunt is for direction
Pairs
Concordant: Positive Relationship
Discordant: Negative Relationship
Tied: Depends on the Dep Var
Yo I got no idea how to interpret ❓