STATS Module 10 Summary

Question 1

Correlation Study purpose

Answer 1

Evaluates the association between two numerical variables

Question 2

Key characteristics of association are..

Answer 2

• Must have variation
• Not used for predictions
• Strength of the correlation is used using Pearson correlation coefficient.

r= sample correlation coefficient
p= population correlation coefficient

+1 values indicate a strong positive relationship: values -1 indicate a strong negative relationship.

Question 3

Null and Alternative hypothesis for correlation test?

Answer 3

Ho: p=0
Ha: pcannot=o

Question 4

T-distribution test for correlation is given as

Answer 4

to=r-p/SE

SE = sqrt(1-r^2/df)

df = n-2

Question 5

Statistical test for correlation

Answer 5

Compare To to Tc.

Question 6

Scientific conclusion

Answer 6

• Non-directional hypothesis:
  Reject the Ho: Evidence of an association
  Fail to reject the Ho: No evidence of an assoication
• With directionality:
  Reject the Ho: Evidence of a positive/negative association
  Rejetc the Ha: No evidence of a positive/negative association

Reporting: include r, df, To, and P-value.

Question 7

Linear regression purpose?

Answer 7

Predict relationships between two variables

• Predictor variable (x): Independent variable
• Response variable (y): dependent variable

Question 8

Linear regression equation?

Answer 8

slope (b): Change in y for one unit in x

Intercept (a): value of y when x=0

EQ: y= a+ bx

Question 9

Linear regression statistical model?

Answer 9

Systamatic component: Linear equation

Random component: Assumes normal distribution for smapling error

Link function: Connects the systamtic and random components

Question 10

Hypothesis testing in linear regression?

Answer 10

Intercept (a) tests if the response variable equals a referenc evalue when x=0

slope (b): Tests how much y changes for a unit change in x

Question 11

Linear regression null distribution?

Answer 11

Null distribution as a t-distribution

Intercept: To= a-Ba/SE, df=n-2

Slope: To= b-Bb/SE, df=n-2

Question 12

Conduct the statistical test for linear regression

Answer 12

Compare the To vs. the Tc score or Type 1 error rate vs the P-value.

Question 13

Draw scientific conclusions/reporting

Answer 13

Reject the Ho: Evidence that intercept or slope is different from the reference value

Fail to reject the Ho: Evidenc that intercept or slope is not different from the reference value.

Reporting: test paramater, t-score, df, and p-value

Question 14

Linear regression Assumptions:

Answer 14

1) Linearity: Relationships is Linear
2) Independence: Residuals are independent, check random sampling
3) Normality: Residuals are normally distributed
4) Homoscedasticity: Residual variance is consistent across predictor values.