# Inferential Statistics II

• Allen M. Khakshooy
• Francesco Chiappelli
Chapter

## Abstract

In the previous chapter, we discussed the basic principles of inferential statistics and emphasized the difference between descriptive and inferential statistics. The latter allows the researcher to make inferences about the population based on the observations collected. Through analytical tools, inferential statistics help researchers decide whether the difference between groups is statistically significant enough to support our hypothesis that the difference exists in the population.

## Keywords

Data analysis Critical values Nondirectional/two-tailed tests Directional/one-tailed tests z test Sampling distribution of z One-sample t test Sampling distribution of t Degrees of freedom (df) Independent sample t test Sampling distribution of the mean difference Estimated standard error Pooled variance Dependent sample t test Paired measures Repeated measures Mean difference Standard error of the mean difference ANOVA Mean square (MS) MS between MS within Independent variable Dependent/outcome variable Post hoc analyses Correlation Correlation coefficient (rStrength Direction Regression Linear regression line Simple linear regression Residuals Regression coefficient (bMultiple linear regression Coefficient of determination (R2

## Supplementary material

Video 4

One-sample t-test. Reprint courtesy of International Business Machines Corporation, © International Business Machines Corporation (MOV 98583 kb)

Video 5

Independent sample t-test. Reprint courtesy of International Business Machines Corporation, © International Business Machines Corporation (MOV 113138 kb)

Video 6

Dependent-sample t test. Reprint courtesy of International Business Machines Corporation, © International Business Machines Corporation (MOV 63979 kb)

Video 7

Video 8

Video 9

## Bibliography

1. Chiappelli F. Comparing two groups: T tests family (13,14,15) [PowerPoint slides]; n.d.Google Scholar

1. Banerjee A, Chitnis UB, Jadhav SL, Bhawalkar JS, Chaudhury S. Hypothesis testing, type I and type II errors. Ind Psychiatry J. 2009;18(2):127–31. .
2. Chiappelli F. Fundamentals of evidence-based health care and translational science. Heidelberg: Springer; 2014.
3. McHugh ML. Multiple comparison analysis testing in ANOVA. Biochem Med (Zagreb). 2011;21(3):203–9.
4. Furr RM. Testing the statistical significance of a correlation. Winston-Salem, NC: Wake Forrest University; n.d.Google Scholar
5. Bewick V, Cheek L, Ball J. Statistics review 7: correlation and regression. Crit Care. 2003; 7(6), 451–459. Print.

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• Allen M. Khakshooy
• 1
• Francesco Chiappelli
• 2
1. 1.Rappaport Faculty of MedicineTechnion-Israel Institute of TechnologyHaifaIsrael
2. 2.UCLA School of DentistryLos AngelesUSA