Week 8 - Hypothesis testing and t-tests Flashcards
What is the goal in hypothesis testing?
To make an inference about the population parameter.
We want to infer the true value of the unknown population parameter using data from the study sample.
It allows us to make comparisons in data
What is a hypothesis?
The untested statement about relationships or associations between factors
Hypotheses can be tested using significance tests.
Ex. Null hypothesis, alternative hypothesis, and null distribution
What is a null hypothesis (H0)?
There is no difference between groups
What is an alternative hypothesis (HA)?
There is a difference between the two groups
What is a null distribution?
The sampling distribution from a(n imaginary statistical) population where the null hypothesis is true (there is no difference)
Ex. all the things that help you find the t-crit, x2, etc.
How does hypothesis testing relate to statistical significance?
Statistical significance: The conclusion that a set of data are unlikely to come from the null hypothesis
P-value: The probability under the null assumption of getting a result/finding that is equal or more extreme than what was observed
What are the two possible outcomes of hypothesis testing?
Fail to reject the null hypothesis (H0): The data is likely to fall under the null hypothesis
Reject the null hypothesis (HA): The data is unlikely to fall under the null hypothesis
What is a type one error rate?
The probability of rejecting the null hypothesis when it is true.
The rejection region is the decision point where the data is sufficiently far from the null hypothesis that it should be rejected.
The value is arbitrary but is usually set as a=0.05.
How is the p-value determined and what does it mean?
It is the probability of seeing your result, or something more extreme, under the null hypothesis. It is determined by the data.
What does the type one error rate to p-value represent?
p-value < a : reject the null hypothesis
p-value =/> a : fail to reject the null hypothesis
What are the types of error rates?
Type one error rate: probability of rejecting the null hypothesis when it is true (false positive)
Type two error rate: probability of failing to reject the null hypothesis when it is false (false negative)
What are the types of t-tests?
Single-sample t-test
Independent samples t-test
Paired-samples t-test (dependent)
Describe a single sample t-test
Evaluates whether your sample mean of a numerical variable is different from a reference value (ex. known population mean or mew) - the null distribution is a t-distribution.
H0: there is no difference between the mean of the variable and the mean of the reference value
HA: there is a difference
Df = n-1
tcrit (2-tailed, a = 0.05, df) = found on the t-distribution table
t0 = |x bar - mew|/ SE
Assumptions: outcome variable is scale numeric and data is normally distributed
T0 </= tcrit : fail to reject the null hypothesis
T0 > tcrit : reject the null hypothesis
What are the assumptions for single-sample t-test?
The outcome variable is scale numeric
Data is normally distributed
Describe an independent t-test
Evaluates whether the mean of a numerical variable for one group is different from the mean of another group
Assess the significance between a continuous outcome and a categoric predictor that has mutually exclusive categories
The groups are independent (do not affect one another)
Null hypothesis: there is no difference in the means of both groups
Alternative hypothesis: there is a difference in the means of both groups
df = n1 + n2 - 2
tcrit (2-tailed, a = 0?.05, df) = ________
t0 = |m1 - m2| /SE
Assumptions: outcome variable is interval or ratio, independence, normal distribution, and homogeneity of variance
t0 </= tcrit : fail to reject the null
t0 > tcrit : reject the null
