Hypothesis
a statement about a population parameter or sample variable that you expect to be true based on available evidence.
hypothesis testing
involves comparing a mean value from a specific group or condition (experimental) to the mean value of either the population, another group (control group), or another condition (placebo).
Null Hypothesis (Ho)
A statement that there is "no difference" between your hypothesized group mean value and the population, control, or placebo value.
Ho is usually expressed as ...
both means being equal
group = population
Alternative Hypothesis (H1 or HA)
A statement that disagrees with the null hypothesis and states what you expect to be true.
The HA must be true if the Ho is false.
The HA is usually expressed as ...
the hypothesized group value is either not equal to, greater than, or less than the population, control, or placebo value
group mean ? population mean
group mean > population mean
group mean < population mean
Steps for Hypothesis Testing
1. Determine your Alternative Hypothesis (HA), what you expect to be true based on existing evidence.
2. State your HA as a Null Hypothesis (Ho).
3. Perform statistical analysis to determine if you:
Reject the Ho and thus Accept the HA
or
Accept the Ho an
statistical analysis example
may compare mean blood glucose levels (ml/dl) between a healthy group vs. a diabetic group, determining if these group means are statistically different.
Reject the Ho
Healthy blood glucose ? Diabetic blood glucose
or
Healthy blood glucose < Diabetic blood glucose
Accept the Ho.
Healthy blood glucose = Diabetic blood glucose
Critical (reject) region
all the possible mean values that would cause you to Reject the Ho (a difference exists between means).
Accept region
all the possible mean values that would cause you to Accept the Ho (no difference between means).
Critical value
a value that separates the Critical region and Accept region.
Significance Level (?)
the probability that a mean value will fall in the critical region (causing you to reject the Ho) when the Ho is actual true and should have been accepted.
In other words..
- The probability of saying there is a difference between groups or conditions whe
Determining the Critical (reject) Region
Most statistical tests use a Standardized Distribution to determine the Critical Region for a variable.
By converting the means for the groups or conditions being compared to a Standardized Distribution, the statistical analysis can determine if the means
Two tailed tests
HA states that there is a difference between means (unequal) without further specification. For example:
group mean ? population mean
One tailed tests
HA states that the group mean will be either greater or less than the other. For example:
group mean > population mean
group mean < population mean
Type I Error
Rejecting a Ho when it is true.
"Saying there is a difference between values when there is actual no difference".
Alpha (?) represents the probability of a type I error.
Similar to a False-Positive test. "Saying a patient has a disease when in fact they d
Type II Error
Accepting a Ho when it is false.
"Saying there is no difference between values when there is actual a difference".
Beta (?) represents the probability of a type II error.
Similar to a False-Negative test. "Saying a patient does not have a disease when in
Sensitivity
- Ability to identify patients who actually have a condition.
- A test has High Sensitivity if it has a Low False-negative rate.
Specificity
- Ability to identify patients who do not have a condition.
- A test has High Specificity if it has a Low False-positive rate.
Differential Statistics
- Compares groups or conditions (treatments) to determine if there are differences in a single variable.
- Use hypothesis testing principles.
Dependent Variable
The variable that is measured or observed in a study and determines the outcome of the study.
The values of the Dependent Variable are those analyzed by statistical tests.
Independent Variable
A factor that is thought to influence the Dependent Variable. The Independent variable is often manipulated by the investigator. Independent variables are sometimes called Factors.
Probability Value (P-value)
The probability of getting a mean value for a group or condition based on the mean and standard deviation of a comparison group or condition.
- P-values are related to Significance Level (?). P-values are usually calculated by the statistical analysis and
One Group with 2 conditions (treatments)
Often referred to as;
- Within groups
- Paired
- Repeated measures
Example research question:
Is there a difference in Height (inches) for a group of adults after taking growth hormone compared to the same group after taking a placebo?
Ho: placebo height
Differential Statistics: One Group with 2 conditions
1. For a numeric variable at the interval or ratio measurement level.
(Provided the sample data is approximately normally distributed - parametric)
Recommended Statistical Procedure: Parametric
Paired T-test
*Uses the Student t-distribution
Paired T-test
t-distribution
- Similar to a normal distribution except with a larger standard deviation.
- As n increases the t-distribution approaches the normal distribution.
- Values are distributed around zero (contains positive and negative values).
- Used for sma
Means (median for rank order data)
As the difference between means increases, the likelihood of the means being statistically different increases.
Standard Deviation (SD)
As the SD of the means increases, the likelihood of the means being statistically different decreases.
Subject number (n)
As n increases, the likelihood of the means being statistically different increases.
Differential Statistics: One Group with 2 conditions
2. For a rank order variable at the ordinal measurement level.
(Or if interval/ratio variables are not normally distributed - nonparametric or distribution free)
Recommended Statistical Procedure: Nonparametric
Wilcoxon Signed Rank Test
Differential Statistics: One Group with 2 conditions
3. for proportion or # of observations at the nominal measurement level.
Recommended Statistical Procedure: Nonparametric
McNemar's Test
* Applied to pre (before) and post (after) designs with a square contingency table (example, 2x2 or 3x3).