The Statistical Inference and Hypothesis Testing Flashcards
What is Statistical Inference?
Process of analyzing data from a sample to infer the true values or true effects in the population
What are the two complementary approaches of statistical inference?
Hypothesis testing and Statistical estimation (confidence intervals)
What are the characteristics of Hypotheses?
- A declarative sentence
- Describes a relationship between two or more variables
- Testable by empirical means
- Provides an indirect method of statistical inference
What is the Null Hypothesis H0?
What the researches are attempting to nullify, main purpose is to disprove a proposed assumption
What is the Alternate Hypothesis HA?
What happens if the null hypothesis is not true, hypothesis that researches are attempting to prove
What are components of the hypothesis testing?
Method focus on testing the null hypothesis only and conclusions are made in terms of rejecting or failing to reject the null hypothesis?
Distribution under H0 has what?
Sample Mean under the null hypothesis, centered on population mean U0
Standard Deviation of the Population Mean is what?
Standard Error
What is the formula for Standard Error of the Mean SEm?
SEm = SD / (square root of n)
Distribution under HA has what?
Sample Mean under the alternative hypothesis, centered on population mean UA, assuming the expected effect or difference
What does SEm represent?
How close the means of repeated samples will come to the population mean, describes the dispersion of means
What is a Type 1 Error?
Reject the null when the null is true, false positive
What is a Type II Error?
Fail to reject the null when the null is false, false negative
How to find the probability of Type 1 error?
Confidence
How to calculate Confidence?
1-a
How to find probability of Type 2 Error?
Power
How to calculate Power?
1-B
Define Power
Power 1-B is the probability of conclusion there is a difference when one actually exists (HA is true), you want statistical power in a study
What does the Z-Score show?
How many standard deviations away from the population mean we are
What is Probability (p)?
The probability of observing the sample data if the null hypothesis is true
What Apriori Alpha (a) level?
Specified in advance the critical value usually 0.05
Compare p to a allows you to reject or accept the H0
p less than a = reject
p greater than a = accept
What are the types of hypothesis testing?
Non-Directional and Directional
Non Directional Tests are?
Two-tailed, look in both pos and neg directions
alpha a is cut into two areas, one at each tail to look a pos/neg critical values
Directional Tests are?
One-tailed, look in only one direction
Test of superiority and non-inferiority
What is the formula to test the difference?
H0 = u1 - u2 = 0
the test is non-directional since the direction of the difference is not specified
Research questions are framed as directional but..
tested using a non-directional test
Rejecting the null says that there is a what?
Difference
Failing to reject the null says that is what?
Insufficient evidence to conclude there is a difference
What is testing for Equivalence?
Tests whether two quantities are within an acceptable range of each other
Equivalence H0 = mean 1 - mean 2 =
greater than or equal to 10%
Equivalence HA = mean 1 - mean 2 =
less than 10%
What does rejecting the null say in testing for equivalence?
The that two are equivalent aka HA is less than 10%
What is testing for Superiority?
Tests whether one quantity is greater than or less than the other
Superiority H0 =
u1 - u2 < 0
Superiority HA =
u1 - u2 > 0
What does rejecting the null say in testing for superiority?
That one group is greater than than the other
What is testing for Non-Inferiority?
Tests whether one quantity is no worse than a second quantity
Non-Inferiority H0 =
Mean 1 - Mean 2 > Confidence Interval
Non-Inferiority HA =
Mean 1 - Mean 2 < Confidence Interval
What does rejecting the null say in testing for non-inferiority?
Says that one group is non-inferior to the other on the variable of interest
How is non-inferiority different from equivalence?
Similar to equivalence but WITHOUT the absolute value because the test is directional
What are the steps in Traditional Approach to performing hypothesis tests?
- Convert the research question into appropriate null and alternate hypothesis
- Select the appropriate statistical test
- Select the desired significance level and the appropriate critical value for the statistical test
- Calculate the test statistic
- Compare the test statistic to the critical value and draw conclusions
How do you calculate Degrees of Freedom?
Sample Size - Number of Groups
How do you calculate the Significance Level?
a / (number of groups)
How do you calculate the Critical Value?
Use degrees of freedom and the significance level, Planas said she would provide it
How to calculate the test statistic?
Planas said it would be provided ONLY on Exam 1
If the test statistic is greater than the critical value what does that mean?
You reject the null hypothesis meaning HA is true
The probability number found is the change of finding a result of this magnitude
Planas said it would be provided ONLY on Exam 1
You want the p value to be less than alpha
Because you want the p value to be less than the alpha 0.05 to reject the null hypothesis
What does Statistically Significant mean?
Null hypothesis is reject after statistical analysis
What does Clinical Significance mean?
Whether the findings are clinically or practically meaningful
Does statistical significance prompt use of new medication?
No cause it does not mean it is clinically significant