Inferential procedures allow us to…
generalize from a sample to a population
Inferential procedures are based on what two things?
- Probability
- Sampling Error
Probability definition
- likelihood that any one event will occur, given all the possible outcomes
- likely to be representative to the population differences or if they could have occurred by chance.
Sampling Error
- Likeliness that sample characteristics will be different from population characteristics
Central Limit Theorem
- If one was able to infinitely sample a population and plot the means they would take the shape of the normal curve.
If the population is bigger this means…
the SD is smaller
Standard Error
- The standard deviation of the sampling distribution of means is called the standard error of the mean.
Based on sample size (more is better) and sampling error (accuracy of population characteristics)
Hypothesis testing
- Inference also used to answer questions concerning comparisons or relationships
- Way to decide if an observed effect reflects chance only or if we can argue with confidence that these are real effects
Examples:
* Is treatment A more effective than B?
* Is there a relationship between the length of time a treatment A is applied and the amount of change in variable X?
In hypothesis testing, why do we still expact change wven if the treatment is not effective?
Due to chance differences in subject characteristics
Paired t-test
Sample people tested twice
Independent t-test
Different groups of people tested
Ex: Compare two groups
Null Hypothesis
- Observed differences due to chance as a result of sampling error (aka no difference, means are equal)
- Goal is to reject the goal in research. P-value <0.05.
- Rejecting the null means that it is unlikely that chance is involved – there is a significant effect
independent variable
The thing we manipulate
Ex: BFR, No BFR
Dependent Variable
Values measured
Ex: Knee Extension Strength (Nm)
We want the ____ hypothesis, as it shows a difference has been found.
alternative
Decision to reject or not reject the null are based on ____
the results of objective statistical procedures
This does not guarantee that a correct decision has been made
Alpha
- Probability of chance occuring
- Often 0.05 or 0.02
- This is used to control type 1 error
Type 1 Error
- Rejecting the null when it is true
- Conclude a true difference exists when differences were due to chance
Levels of Significance
- Significant or Not
- Significant = <0.05
Thus is why we say may as there is always a possibility of chance
Type II Error
- Conclude differences were due to chance when they were true differences
- Find no difference but a real difference exists.
- This is when effect size is crucial as there could be a different but was just not seen in the statistical tests; likely due to a small sample size
Standard for rejecting the null hypothesis is called…
the level of significance
How do we choose Alpha?
- Generally 0.05
- Although, the smaller the alpha means less likely Type 1 error to occur (Alpha = 0.01)
Power
- 1-beta
- Is like sensitivity; The more power the better chance of seeing a difference.
- Should be .8, some say higher .9
What influences Statistical Power?
- Lower Alpha makes it harder to find differences
- Variance
– Less variance, increases power
– less variance with repeated measures - Sample size
– Larger sample, greater power - Effect Size (difference between groups)
– Greater effect size = greate group differences
