Math 2 (Basic Statistics)
MW 5:30-7:00pm
Prof. Danilo de Guzman
Instructor
AN OVERVIEW OF
THE HYPOTHESIS
TESTING
Hypothesis Testing: An Overview
Hypothesis
• Hypothesis - An Educated Guess
• Null Hypothesis – empty or resulting to zero
results
• Alternative Hypothesis – an option or choice
• Research – systematic search using various
tools
Hypothesis Testing: An Overview
T-Test
• Testing differences between 2 means
proportion etc., S.D. taken from the
sample
Hypothesis Testing: An Overview
Testing Hypothesis: Step 1
• Formulate a null hypothesis &
alternative null (H0) – there is NO
significant differences between X1-X2
• Alternative (H1) there is significant
differences x1>x2 │x1<x2, x1≠x2
Hypothesis Testing: An Overview
Step 2:
• df = n1 + n2 – 2
Step 3:
• Tabular value
Step 4:
• Computed “ t ”
Hypothesis Testing: An Overview
Step 5
• Conclusion:
T computed > that reject H0
T computed < that accept H0
Hypothesis Testing: An Overview
F-Test
• Analysis of Variance (ANOVA)
─ Testing difference among 3 or more
groups treatments, sample or
population means or proportion.
Hypothesis Testing: An Overview
Formulae:
• SStr = T12 + T22 + T32 – T2
N1 N2 N3 N
where: SStr = sum of squares of treatment
T1,T2,T3 = sum in each column
T = total of all items or entries
N = total number of items
Hypothesis Testing: An Overview
SSt = Σx2 – T2
N
Where: SSt = total sum of squares
Σx2 = x21 + x22 + x23 ....... x2n
Hypothesis Testing: An Overview
SSe = SSt - SStr
Where: SSe = sum of squares of error
Hypothesis Testing: An Overview
Mean Sum of Squares
• Treatment:
MSStr = SStr
K–1
where: MSStr = mean sum of squares of treatment
K = number of column
K – 1 = degrees of freedom of numerator
Hypothesis Testing: An Overview
MSSe = SSe
N–K
where: MSSe = mean sum of squares of error
N – K = difference denominator
Computed value of F
Fc or F ration
Fc = MSStr
MSSe
Hypothesis Testing: An Overview
Some On-Line Resources
• www.mathaid.com/products/HypthsTest
• www.lhs.logan.k12.ut.us/~jsmart/hypothesis.html
• www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html
Hypothesis Testing: An Overview
Powerpoint and Research by:
Karlo Celis A. Bacsafra
On-Line Research by:
Edward Azucenas II
Hypothesis Testing: An Overview