# Intro to hypothesis testing

### 29 terms by exodus1513

#### Study  only

Flashcards Flashcards

Scatter Scatter

Scatter Scatter

## Create a new folder

### Where we have been

Making predictions about likelihood of true population
mean falling within specific range around sample mean
 Want to know how closely sample statistic approximates
population parameter
 In other words, we interested drawing conclusions about
characteristic of SINGLE VARIABLE (ie. test scores or time
spent studying) from sample data

### Where we are going

Test whether mean value of SINGLE variable is greater
or less than predetermined value
AND
 Test whether mean values of SINGLE variable from
TWO DIFFERENT samples are equivalent

Single variable in relation to specific value OR
 Single variable from one sample in relation to same
variable from another sample

### Two Types of Hypothesis Tests

single means/two means test

### single means test

Test whether population
mean is greater to or lesser than predetermined
value

### two means test

Test whether population
means from two distinct groups actually differ

### single means test example

program increases standardized test scores by

### two means test example

standardized test scores more than Reading
Program Y

### null hypothesis (Ho)

States that in population there is
no association, no change, or no difference between two
variables or conditions. Indicates statistical
INDEPENDENCE

### alternative hypothesis (H1)

States that in population
there is an association, change, or difference between two
variables or conditions. Indicates statistical
DEPENDENCE.

### null hypothesis example

standardized test scores by more than 1.25

### alternative hypothesis example

New 5th
standardized test scores by more than 1.25

### What's up with this null hypothesis nonsense?

Because of basic assumptions about epistemology & philosophy
of science, can only directly test null hypothesis
 Can only REJECT or FAIL TO REJECT null hypothesis. Cannot
prove that alternative hypothesis is true.

### Central principle of inductive reasoning (null)

single study can
never PROVE something to be true. We can only FAIL TO
PROVE that it is false (thanks Karl Popper).
 This is what is meant by "falsifiability" in science. In order for
hypothesis to be testable, it has to be possible to prove it to be
false.
 It is basically science's way of being VERY CONSERVATIVE

### Type I Error

We reject null hypothesis when, in fact, null hypothesis is
really true
 Conclude that treatment had effect when it actually was
not effective (less conservative conclusion)
 Occurs when information from sample is misleading.
Cannot make "correct" estimates about population
parameters from sample statistics
 Probability of making Type I error is alpha

### Type II Error

We fail to reject null hypothesis when, in fact, null
hypothesis is really false
 Conclude that treatment had no effect when it actually
was effective (more conservative conclusion)
 Occurs when hypothesis test fails to detect statistical
dependence
 Probability of making Type II error is beta (b)

### Which Error to Minimize?

Need to carefully examine specific research question
 What if you want to determine if sexual contact is related
to particular viral infection
 Want to use this information to decide whether or not to
Ho: Sexual contact is not related to viral infection (do not
inform patients)
H1: Sexual contact is related to viral infection (inform
patients)

### Which Error to Minimize?

Fail to reject null hypothesis & say that sexual contact is NOT
related to virus when, in fact, it is (Type II error). Therefore, you
do not inform public of risks.
 Implications: jeopardize health of sexually active
individuals
OR
 Reject null hypothesis & conclude that sexual contact IS related
to virus when, in fact, it is not (Type I error). Therefore, you tell
public there are risks which really do not exist.
 Implications: people have safer sex when they don't really
need to, as least as far as this virus is concerned

### What is the point?

Must carefully consider your research question(s) when
deciding what type of error to minimize
 However, we will largely focus on decreasing Type I error
because it is more common in social sciences AND
 Type I error typically can result in potentially serious
consequences

### How to Minimize Errors

increase sample size/replicating study by selecting new sample

### increase sample size

Reduces error because samples are never identical
to population from which drawn

### Replicate study by selecting new sample

Reduces error because samples are never identical
to one another

### Steps to follow

1. State null & alternative hypotheses
2. Set significance level
3. Determine critical region
4. Collect data & compute test statistic(s)
5. Make decision to either reject null hypothesis or fail
to reject null hypothesis

### Take Home Message (of example)

By doubling sample size, we can now reject null hypothesis
and conclude, with 99% certainty, that the Cooper gets
less than 35 miles to the gallon...
 Even though sample mean & population SD did not change
given population so...
 Our sample statistics will more accurately approximate
population parameters

### Two Tailed Single Means Test

Tests whether population mean is equal to or not
equal to predetermined value
 Previously (with one-tailed test) we were testing
whether population mean was greater than or less
than predetermined value

### Error in TwoTailed Test

Alpha level that we choose (probability of Type I error) is
now distributed in BOTH tails of distribution (rather than
in just one tail)
 You can make a Type I error in two ways:
(a) by rejecting H0 because you think μ is greater than
value of interest when it is not OR
(b) by rejecting H0 because you think μ is less than value
of interest when it is not

### Relationship between One & Two Tailed Critical Value

For a given a, one-tailed CV will be smaller than
two-tailed CV (ie. closer to zero)
 For a = 0.05, one-tailed CV is 1.65 while two-tailed
CV is 1.96
 This is because we are dividing alpha by two

### Interpret Results

Based on our findings, we reject null hypothesis &
conclude that educational attainment was significantly
different in 2007 than in 2000

### A Reminder

We expect sample mean to approximate population mean
 Standard error provides simple measure of degree to which
sample mean differs from population mean
 Based on mean & SD we can calculate Z-score
 This Z-score indicates whether observed difference is
significantly greater than would be expected by
chance alone

Example: