8.3 Data Analysis: Inferential Statistics

Question 1

Inferential Statistics

Answer 1

• 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.

Question 2

Hypothesis Testing

Answer 2

Null Hypothesis
- Hypothesis that states there is no relationship between the variables

Research Hypothesis
- Hypothesis that states there is a relationship between variables

Question 3

Statistical Probability and Sampling Error

Answer 3

• 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

Question 4

Type 1 Error

Answer 4

• 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

Question 5

Type 2 Error

Answer 5

• 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

Question 6

Questions

Answer 6

• In practice type 1 errors are more serious

Question 7

Levels of Significance and Effect Size

Question 8

Power Analysis

Answer 8

• 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.

Question 9

Example

Answer 9

• 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)

Question 10

Signifiance

Answer 10

• 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.

Question 11

Categories of Inferential Statistics

Answer 11

• 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

Question 12

General Facts

Answer 12

• 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