8.3 Data Analysis: Inferential Statistics Flashcards
Inferential Statistics
- Help researchers estimate how well their data can predict and generalize findings
Research
- First samples are analyzed using descriptive statistics
- If appropriate, then inferential statistics are used to see if decisions can be made about the population based on statistics, or test a hypothesis.
Descriptive Statistics
- Can be used alone if the purpose of the paper is just to describe something
Inferential Statistics
- Used when we are seeking relationships and correlations between variables.
Hypothesis Testing
Null Hypothesis
- Hypothesis that states there is no relationship between the variables
Research Hypothesis
- Hypothesis that states there is a relationship between variables
Statistical Probability and Sampling Error
- To test hypothesis, repeated trials are done to see if the same results come many times under the same conditions
- Inferential statistics is based on random sampling but there is always a chance of sampling error
- Statistical Probability is based on the concept of sampling error
Type 1 Error
- Rejecting the null hypothesis when the null hypothesis is actually true (false alarm)
- Accepted the research hypothesis when there is actually no difference
- Researchers discovered a difference when there is no difference
Type 2 Error
- Not rejection null when null is false (missed opportunity)
- Rejected the research hypothesis even though there is a difference
- Researchers fail to detect a difference when there is in fact a difference
Questions
- In practice type 1 errors are more serious
Levels of Significance and Effect Size
Power Analysis
- Statistical method used to determine sample size
2 Factors must be established
- Significance level (Alpha)
Established prior to the study.
P=0.05 (if the study were done 100 times the null hypothesis would be wrong 5/100 times) P = alpha level
Decision Rule - Reject null hypothesis if statistic being tested falls at or beyond a critical region (acceptance region) which correlates with significance of improbable null hypothesis.
- Effect size
The magnitude of the relationship between 2 variables or difference between 2 groups. - This impacts sample size
- If the effect of an intervention is large, fewer subjects are needed to determine a difference
- If the effect of an intervention is small, larger sample size will be needed to demonstrate effectiveness.
Example
- Study to measure mean attitude of bariatric surgery in obese patients ranging from 0 (extremely negative) to 10 (extremely positive)
- We want to determine if the mean attitude is different from 5.0
Null hypothesis - Mean attitude is 5.0
Alternate hypothesis - Mean is not 5.0 (there is a difference)
Signifiance
- P=0.05
- Greater than 0.05 is insignificant (could have happened by chance)
- Less than 0.05 is significant (most likely did not happen by chance)
- Significance does not mean importance or clinically relevant, it just means they are not attributed to chance or due to sample error.
Categories of Inferential Statistics
- Test of Differences
- Test of Relationships
- Inferential statistics is all about testing hypothesis using data obtained from probability samples.
Purpose
- Estimate probability that the sample accurately reflects the population parameter
- Tests a hypothesis about a population
General Facts
- Statistical procedures are used to test if there is a difference between groups, not what the difference is.
- Level of measurement of variables dictates which statistical procedure can be used
- Inferential statistics must be selected using probable samples
Most Common Tests for Differences
- T-Test
- ANOVA (Analysis of Variance)
- Chi-Square
Most Common Tests for Relationships
- Correlation
- Pearson’s R
- Spearman’s Rho
