13. STATISTICAL HYPOTHESIS TESTING Flashcards

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1
Q
  1. What two aspects are assessing when we look at the associations between variables?
A
  • the presence of an association
    (this is the most important part)
  • the magnitude of the association
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2
Q
  1. What is very important with regards to research?
A
  • 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
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3
Q
  1. How many possibilities are there for any given association between two variables?
A
  • 2
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4
Q
  1. What are the 2 possibilities available for any given association between two variables?
A

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

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5
Q
  1. What is the Null Hypothesis (H₀)?
A
  • it is a hypothesis
  • it always states that there is no association between
    the two variables in the population
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6
Q
  1. What is the Alternative Hypothesis (H𝝖)?
A
  • this is a hypothesis
  • it always states that there is an association between
    the two variables in the population
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7
Q
  1. What do we do first when we conduct a Research Study?
A
  • we formulate the Null and Alternative Hypotheses
  • we then use statistical analysis to decide whether we
    have enough evidence to reject the Null Hypothesis
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8
Q
  1. In which group does all the research take place?
A
  • it takes place in the Samples
  • we also make sure to quantify the inherent error
    present in our samples estimates
    (the Random Error)
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9
Q
  1. List the first 4 steps to testing a Hypothesis?
A

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

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10
Q
  1. List the next 5 steps to testing a Hypothesis?
A

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

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11
Q
  1. What is the p-value?
A
  • this is the probability of obtaining an association that is
    as strong or stronger
  • than the value observed in our sample
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12
Q
  1. What does a lower p-value mean?
A
  • 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
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13
Q
  1. How does a lower p-value relate to the Null Hypothesis?
A
  • the lower the p-value
  • the higher the chance of rejecting the Null Hypothesis
  • the higher the chance of favouring the Alternative
    Hypothesis
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14
Q
  1. What results in a lower p-value?
A
  • a stronger association
  • a larger value of the test statistics
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15
Q
  1. What is the purpose of a Binary Cutoff?
A
  • it is used to say what is sufficient evidence
  • it is used to indicate how low the p-value should be
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16
Q
  1. What values represent Statistical Significance?
A
  • a significance level of 5%
  • this means that the p-value is less than 0.05
17
Q
  1. What kind of evidence does the p-value provide?
A
  • it is used as evidence for rejecting or not rejecting the
    Null Hypothesis
  • a rejection of the Null Hypothesis favours the
    Alternative Hypothesis
18
Q
  1. What is deduced when we have a p-value of less than 0.05?
A
  • the Null Hypothesis is rejected
  • there is no association in the population
19
Q
  1. What is decided when we have a p-value that is equal to or greater than 0.05?
A
  • the Null hypothesis cannot be rejected
  • there is an association in the population
20
Q
  1. What can be said about the rejection or acceptance of the Null Hypothesis when it comes to Hypothesis testing?
A
  • 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
21
Q
  1. What principles is the calculation of the p-value based on?
A
  • the same principles as the 95% Confidence Intervals
  • both make use of the Standard Error
22
Q
  1. What values affect the p-value?
A

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

23
Q
  1. What other measurement can we use to deduce whether or not we can reject the Null Hypothesis?
A
  • the 95% Confidence Intervals
  • this decision depends on the measure of association
24
Q
  1. What can be said about the Mean Difference and the 95% Confidence Interval?
A

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

25
Q
  1. What can be said about the Regression Coefficient or Correlation Coefficient and the 95% Confidence Interval?
A

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

26
Q
  1. What can be said about the Odds, Rate or Risk ratio and the 95% Confidence Interval?
A

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

27
Q
  1. Which cases are considered not statistically significant?
A
  1. THE P-VALUE OF AN ESTIMATE
    - is equal to or greater than 0.05
  2. THE 95% CONFIDENCE INTERVALS
    - include zero
  3. THE MEAN DIFFERENCE, REGRESSION COEFFICIENT
    OR CORRELATION COEFFICIENT
    - include zero
  4. THE ODDS RATIO, RATE RATIO OR RISK RATIO
    • include 1

NB:
- these cases have study findings that are not conclusive

28
Q
  1. Which cases are considered statistically significant?
A
  1. THE P-VALUE OF AN ESTIMATE
    - is less than 0.05
  2. THE 95% CONFIDENCE INTERVALS
    - do not include zero
  3. THE MEAN DIFFERENCE, REGRESSION COEFFICIENT
    OR CORRELATION COEFFICIENT
    - do not include zero
  4. THE ODDS RATIO, RATE RATIO OR RISK RATIO
    • do not include 1

NB:
- these cases are study findings that are conclusive