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Hypothesis testing compares
Known population before treatment and unknown population after treatment

Hypothesis testing is usually used in what type of study
research

Hypothesis testing tests the ___ of the treatment
effectiveness

Hypothesis testing compares __ to eachother
means
 compare sample mean to population mean
 or compare two or more sample means to eachother

Differences between M and u are expected by __
This is called __ __ and __ __
 chance
 sampling variability
 sampling error

Goal of hypothesis testing is to rule out __ chance as a plausible explanation for the results of a study
chance

Hypothesis Testing
Statistical method using sample data to evaluate a hypothesis about a population

Difference is statistically significant when


 M is unlikely to have occurred by chance
 M is in the extreme tails of the sampling distribution

"Unlikely" or "Extreme" percentage
 If M would occur 5% or less of the time
 p<0.05

We always assume _ difference between the means, called the __ __
no difference between the means, called the null hypothesis

Null hypothesis
If true, M should be close to _
If M is not close to _, we reject
 u
 if M is not close to u, we reject the null hypothesis

The type of statistics that deals with hypothesis testing
inferential statistics

Hypothesis Testing Steps




 State the hypothesis
 Set the criterion for a decision
 Compute the test statistic
 Make a decision

Step 1:


Ho: Predicts there is no change, difference, or relationship between our treatment and the general population
H1: There is a change in the population after we apply the treatment

H0 and H1 are __ __
mutually exclusive (if one is true, the other cannot be)

Nondirectional hypothesis
 Also known as a twotailed hypothesis
 Direction of difference is not specified

Step 2:
Create a decision rule, find the critical value, put probability, one or twotailed

Critical Value
boundary between likely/unlikely outcomes

Critical Region
area under the curve more extreme than the critical value

Decision Rule
Reject H0 if observed test statistic falls in the critical region (exceeds critical value)

Step 3:
Compute the test statistic
z score formula
standard deviation formula
See paper

Step 4:
Reject or fail to reject H0

When we reject H0
Difference between means is unlikely to be due to __
We call this a __ __ finding
We can never __ or __ H0 or H1
 chance
 statistically significant
 prove or disprove

When we fail to reject H0
Due to __
We call this __ __
We don't accept or prove H0, we just don't find evidence supporting _
 chance
 statistically significant
 H1

We never __ or __ a difference
prove or disprove

Type 1 error
 Rejecting a null hypothesis when it's actually true
 Concluding a treatment has an effect when in reality it doesn't

How do we control Type 1 Error?
 We do this with our alpha level, or p value
 a=0.05 > there's a 5% chance we will falsely reject the null hypothesis
 5% chance of type 1 error
 a=0.01> there's a 1% chance we will falsely reject the null hypothesis

Type 2 Error
 Failing to reject a null hypothesis that is false
 The test failed to detect a real treatment effect

B
probability of making a type II error when H_{o} is false

Minimizing type 2 error is increasing __
Based on __ and __
 power
 effect size and sample size

Power
Power is greater when
1)
2)
 Effect size is bigger because big effects are easy to use
 Sample size is larger because large samples make it easy to detect tiny effects

We increase power (1B) by
1)
2)
3)
4)
 Increase sample size (n) is the best possible way
 Increase treatment effect size
 Choose less stringent alpha level
 Use a onetailed test

Uncertainty and Error
We never know
We try to minimize
We balance the risk of
Three alpha levels researchers use
 The absolute truth
 p (making a mistake)
 Type I and Type II error
 0.05, 0.01 or 0.001

Effect size
Different types of statistics
Descriptive statistic that indicates magnitude of an effect
Cohen's d, r2, etasquared

Cohen's D formula
What does Cohen's D tell us
see paper
difference between means in standard deviation units

Cohen's D
small effect
medium effect
large effect

Twotailed tests (nondirectional) have critical regions in
Onetailed tests (directional) have critical region
 each tail
 in the lower negative tail onlyfor one tailed tests, critical value is smaller

Assumptions of the ztest
1)
2)
3)
4)
 Distribution of sample means is normal
 Individuals were randomly sampled
 Independent observations
 Know that SD does not change with treatment

What do you state when reporting results?
1)
2)
3)
4)
 Two means
 Z score
 probability
 tails

Unimodal Distribution
Distributions with one clear peak

Bimodal DIstributions
Distributions with two clear peaks

Uniform Distribution
 A probability distribution for which all of the values that a random variable can take on or occur with equal probability
 Or the shape of a graph that has no peaks and valleys

Symmetric Distribution
Can be divided at the center so that each half is a mirror image of the other

Standard Normal Distribution
 Occurs when a normal random variable has a mean of zero and a standard deviation of one
 The normal random variable is called a z score

Skewed right
Distributions with fewer observations on the right

Skewed left
Distributions with fewer observations on the left

Normal Distribution
 All normal distributions look like a symmetric, bellshaped curve
 Associates the normal random variable X with a cumulative property

Positive Skewness
The tail on the right side is longer or fatter than the left side

Negative Skewness
Tail on the left side of the distribution is longer or fatter than the left side

Long tail of a distribution
Portion of the distribution having a large number of occurrences far from the "head" or central part of the distribution

Body of a distribution
Middle of the bell curve

1B
 Probability of making a correct decision when H_{o }is false
 Ability to detect a real treatment effect

