13. STATISTICAL HYPOTHESIS TESTING Flashcards
- What two aspects are assessing when we look at the associations between variables?
- the presence of an association
(this is the most important part) - the magnitude of the association
- What is very important with regards to research?
- being able to state whether an association exists or not
in the source population - this is based on sample estimates
- this has to be stated with high certainty
- How many possibilities are there for any given association between two variables?
- 2
- What are the 2 possibilities available for any given association between two variables?
ONE:
- the association does not exist in the population
- this means that the 2 variables are not linked
TWO:
- the association exists in the population
- the two variables are linked
- What is the Null Hypothesis (H₀)?
- it is a hypothesis
- it always states that there is no association between
the two variables in the population
- What is the Alternative Hypothesis (H𝝖)?
- this is a hypothesis
- it always states that there is an association between
the two variables in the population
- What do we do first when we conduct a Research Study?
- we formulate the Null and Alternative Hypotheses
- we then use statistical analysis to decide whether we
have enough evidence to reject the Null Hypothesis
- In which group does all the research take place?
- it takes place in the Samples
- we also make sure to quantify the inherent error
present in our samples estimates
(the Random Error)
- List the first 4 steps to testing a Hypothesis?
STEP ONE:
- define the Null Hypothesis (H₀)
- define the Alternative Hypothesis (H𝝖)
STEP TWO:
- start this process by assuming that NO association
exists in the population
- this means that you start with a Null Hypothesis (H₀)
STEP THREE:
- define the sufficient evidence against the Null
Hypothesis (H₀)
STEP FOUR:
- collect some sample data from the population
- this data has to be greater than the sufficient evidence
- List the next 5 steps to testing a Hypothesis?
STEP FIVE:
- assess whether the sample estimate provides
sufficient evidence against the Null Hypothesis (H₀)
STEP SIX:
- assess whether the sample estimate can be explained
by random error alone
- this assesses whether the results are consistent with
the expected sampling variation that exists when there
is no association in the population
STEP SEVEN:
- calculate the value of the test statistics
- you do this using samples
STEP EIGHT:
- derive a probability that quantifies our belief against
the Null Hypothesis (H₀)
- you do this using test statistics
- this is known as the p-value
STEP NINE:
- we interpret the p-value
- this is often in the context of the significance level
- EG: is my p-value smaller than the given significance
level
- What is the p-value?
- this is the probability of obtaining an association that is
as strong or stronger - than the value observed in our sample
- What does a lower p-value mean?
- there is a lesser chance that we have obtained an
association as strong or stronger in our sample - this applies if there is no true association that exists in
the population
- How does a lower p-value relate to the Null Hypothesis?
- the lower the p-value
- the higher the chance of rejecting the Null Hypothesis
- the higher the chance of favouring the Alternative
Hypothesis
- What results in a lower p-value?
- a stronger association
- a larger value of the test statistics
- What is the purpose of a Binary Cutoff?
- it is used to say what is sufficient evidence
- it is used to indicate how low the p-value should be
- What values represent Statistical Significance?
- a significance level of 5%
- this means that the p-value is less than 0.05
- What kind of evidence does the p-value provide?
- it is used as evidence for rejecting or not rejecting the
Null Hypothesis - a rejection of the Null Hypothesis favours the
Alternative Hypothesis
- What is deduced when we have a p-value of less than 0.05?
- the Null Hypothesis is rejected
- there is no association in the population
- What is decided when we have a p-value that is equal to or greater than 0.05?
- the Null hypothesis cannot be rejected
- there is an association in the population
- What can be said about the rejection or acceptance of the Null Hypothesis when it comes to Hypothesis testing?
- there is either enough evidence to reject the H₀
- or there is not enough evidence to reject it
- we can only ever reject the H₀
- or fail to reject the H₀
- we cannot confirm whether H𝝖 or H₀ are true
- What principles is the calculation of the p-value based on?
- the same principles as the 95% Confidence Intervals
- both make use of the Standard Error
- What values affect the p-value?
THE SAMPLE SIZE:
- the larger the sample size
- the smaller the p-value
THE MAGNITUDE OF THE ASSOCIATION
- the larger the magnitude
- the smaller the p-values
- What other measurement can we use to deduce whether or not we can reject the Null Hypothesis?
- the 95% Confidence Intervals
- this decision depends on the measure of association
- What can be said about the Mean Difference and the 95% Confidence Interval?
IF THE 95% CONFIDENCE INTERVAL INCLUDES 0:
- the Null Hypothesis cannot be rejected
THIS IS BECAUSE:
- Zero is a likely value in the source population
- it means that there is no difference between the two
means
- What can be said about the Regression Coefficient or Correlation Coefficient and the 95% Confidence Interval?
IF THE 95% CONFIDENCE INTERVAL INCLUDES 0:
- the Null Hypothesis cannot be rejected
THIS IS BECAUSE:
- Zero is a likely value in the source population
- it means that there is no difference between the two
means
- What can be said about the Odds, Rate or Risk ratio and the 95% Confidence Interval?
IF THE 95% CONFIDENCE INTERVAL INCLUDES 1:
- the Null Hypothesis cannot be rejected
THIS IS BECAUSE:
- one is a likely value in the source population
- it means that there is an equal risk, rate or odd
between the 2 groups
- Which cases are considered not statistically significant?
- THE P-VALUE OF AN ESTIMATE
- is equal to or greater than 0.05 - THE 95% CONFIDENCE INTERVALS
- include zero - THE MEAN DIFFERENCE, REGRESSION COEFFICIENT
OR CORRELATION COEFFICIENT
- include zero - THE ODDS RATIO, RATE RATIO OR RISK RATIO
- include 1
NB:
- these cases have study findings that are not conclusive
- Which cases are considered statistically significant?
- THE P-VALUE OF AN ESTIMATE
- is less than 0.05 - THE 95% CONFIDENCE INTERVALS
- do not include zero - THE MEAN DIFFERENCE, REGRESSION COEFFICIENT
OR CORRELATION COEFFICIENT
- do not include zero - THE ODDS RATIO, RATE RATIO OR RISK RATIO
- do not include 1
NB:
- these cases are study findings that are conclusive
