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Hypothesis testing compares
Known population before treatment and unknown population after treatment
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Hypothesis testing is usually used in what type of study
research
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Hypothesis testing tests the ___ of the treatment
effectiveness
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Hypothesis testing compares __ to eachother
means
- compare sample mean to population mean
- or compare two or more sample means to eachother
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Differences between M and u are expected by __
This is called __ __ and __ __
- chance
- sampling variability
- sampling error
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Goal of hypothesis testing is to rule out __ chance as a plausible explanation for the results of a study
chance
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Hypothesis Testing
Statistical method using sample data to evaluate a hypothesis about a population
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Difference is statistically significant when
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- -M is unlikely to have occurred by chance
- -M is in the extreme tails of the sampling distribution
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"Unlikely" or "Extreme" percentage
- -If M would occur 5% or less of the time
- -p<0.05
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We always assume _ difference between the means, called the __ __
no difference between the means, called the null hypothesis
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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
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The type of statistics that deals with hypothesis testing
inferential statistics
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Hypothesis Testing Steps
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- -State the hypothesis
- -Set the criterion for a decision
- -Compute the test statistic
- -Make a decision
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Step 1:
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-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
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H0 and H1 are __ __
mutually exclusive (if one is true, the other cannot be)
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Non-directional hypothesis
- -Also known as a two-tailed hypothesis
- -Direction of difference is not specified
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Step 2:
Create a decision rule, find the critical value, put probability, one or two-tailed
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Critical Value
boundary between likely/unlikely outcomes
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Critical Region
area under the curve more extreme than the critical value
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Decision Rule
Reject H0 if observed test statistic falls in the critical region (exceeds critical value)
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Step 3:
Compute the test statistic
-z score formula
-standard deviation formula
See paper
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Step 4:
Reject or fail to reject H0
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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
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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
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We never __ or __ a difference
-prove or disprove
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Type 1 error
- -Rejecting a null hypothesis when it's actually true
- -Concluding a treatment has an effect when in reality it doesn't
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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
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Type 2 Error
- -Failing to reject a null hypothesis that is false
- -The test failed to detect a real treatment effect
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B
-probability of making a type II error when Ho is false
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Minimizing type 2 error is increasing __
Based on __ and __
- -power
- -effect size and sample size
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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
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We increase power (1-B) 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 one-tailed test
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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
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Effect size
Different types of statistics
Descriptive statistic that indicates magnitude of an effect
Cohen's d, r2, eta-squared
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Cohen's D formula
What does Cohen's D tell us
see paper
-difference between means in standard deviation units
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Cohen's D
-small effect
-medium effect
-large effect
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Two-tailed tests (non-directional) have critical regions in
One-tailed tests (directional) have critical region
- -each tail
- -in the lower negative tail only-for one tailed tests, critical value is smaller
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Assumptions of the z-test
1)
2)
3)
4)
- Distribution of sample means is normal
- Individuals were randomly sampled
- Independent observations
- Know that SD does not change with treatment
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What do you state when reporting results?
1)
2)
3)
4)
- -Two means
- -Z score
- -probability
- -tails
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Unimodal Distribution
Distributions with one clear peak
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Bimodal DIstributions
Distributions with two clear peaks
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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
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Symmetric Distribution
Can be divided at the center so that each half is a mirror image of the other
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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
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Skewed right
Distributions with fewer observations on the right
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Skewed left
Distributions with fewer observations on the left
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Normal Distribution
- All normal distributions look like a symmetric, bell-shaped curve
- Associates the normal random variable X with a cumulative property
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Positive Skewness
The tail on the right side is longer or fatter than the left side
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Negative Skewness
Tail on the left side of the distribution is longer or fatter than the left side
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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
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Body of a distribution
Middle of the bell curve
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1-B
- -Probability of making a correct decision when Ho is false
- -Ability to detect a real treatment effect
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