The document discusses hypothesis testing and statistical techniques including parametric and non-parametric tests. It provides examples of one-sample t-tests, independent sample t-tests, and paired sample t-tests. It explains the concepts of null and alternative hypotheses and how statistical tests are used to reject or fail to reject the null hypothesis based on comparing calculated and critical t, Z, or F values and p-values. Examples are provided for each type of t-test.
10. Hypothesis Testing
• Likert Scale data
• Research Hypothesis & Statistical Hypothesis
• Check Normality of Data
• Choose Parametric /Non Parametric test
• Check p value for Ho or Ha depending on
confidence interval
11. Hypothesis Testing
Null and Alternative Hypotheses
Both Ho and Ha are statements about population
parameters, not sample statistics.
A decision to retain the null hypothesis implies a lackof
support for the alternative hypothesis.
A decision to reject the null hypothesis implies supportfor the
alternative hypothesis.
13. Types of Tests
Parametric Test
The statistical test which makes assumptions
about the distribution of population
parameters are known as parametric tests.
Non Parametric Test
The alternative which makes no assumptions
about the distribution of population
parameters are known as non parametric
tests.
15. 2 Groups > 2 Groups
Mann
Whitney U
test
Wilcoxon
Rank Test
1 Sample
Sign Test
Kruskal-
Wallis H test
Friedman
Test
Rank Order
Correlation
Contingency
Coefficient
Phi
Correlation
Tetrachoric
Correlation
Point Biserial
Correlation
Biserial
Correlation
Goodness of
fit
Test for
independence
Statistical
Techniques
Parametric
Statistics
Non Parametric
Statistics
Comparative Relationship Others
Chi Square
16. P value
• The level in which we are allowed to
reject the null hypothesis when it is
true or Type 1 Error
• A rule of thumb is if p-value < 0.05
(5% level of significance) we reject
null hypothesis
• if p-value > 0.05 (5% level of
significance) we fail to reject null
hypothesis.
17.
18. Tcal and Ttab to decide Hypothesis
• Tcal < Ttab – Fail to Reject Null Hypothesis
• Tcal>Ttab – Reject Null Hypothesis
Tcal , Zcal ,Fcal will be obtained from formulae
Ttab ,Ztab,Ftab will be obtained from Tables
All Software give Tcal,Fcal along with p values
20. Various types of T Test
One sample T Test
Independent sample T Test
Dependent sample T Test
21. T Test
In t-test, independent variable is
in nominal scale and
dependent variable
is in ratio scale.
22. One Sample T Test
• Null hypothesis: There is no significance
differences between the population mean and
the sample mean.
• In one sample T Test, a sample mean is compared
with the known population mean
Sample
23. Independent Sample T Test
• In Independent sample T Test, means of two
groups are compared.
• Null hypothesis: There is no significant difference
in means of two groups
24. Dependent Sample T Test
• In dependent sample T Test, means of same
group is compared before and after the
treatment.
• Null hypothesis: There is no significant difference
in means before and after treatment.
25. One Way ANOVA
• In Independent sample T Test, means of more
than three groups are compared.
• Null hypothesis: There is no significance
differences in marks of more than two groups
32. Hypothesis Testing Examples
Example : A normal white blood count is assumed to be approximately 8
thousand cells per cc of blood. A random sample of 15 employees of a nuclear
plant yielded a mean white count of 7.81 with a standard deviation of 0.872 (in
thousands).Is there significant evidence that the mean white count is lower for
plant employees using a=0.05?
Example : A pill is supposed to contain 20 mg of Phenobarbital. A random sample
of 29 pills yielded a mean of 20.5 mg and a standard deviation of 1.5 mg. Test
using a=0.10 whether the true mean amount per pill is 20 mg
Example: When a process producing ball bearings is operating correctly the
weights of the ball bearings have a normal distribution with mean 5 ounces and
standard deviation 0.1 ounce .An adjustment has been made to the process and
the plant manager suspects that this has raised the mean weight of ball bearings
produced leaving the standard deviation unchanged . A random sample of sixteen
ball bearings is taken, and their mean weight is found to be 5.038 ounces. Test at
significance levels .05 and .10 (that is, at 5% and 10% levels) that the adjustment
has not increased the mean weights of the ball bearings
33. 6) When a process producing ball bearings is operating
correctly the weights of the ball bearings have a
normal distribution with mean 5 ounces and standard
deviation 0.1 ounce .An adjustment has been made to
the process and the plant manager suspects that this
has raised the mean weight of ball bearings produced
leaving the standard deviation unchanged . A random
sample of sixteen ball bearings is taken, and their
mean weight is found to be 5.038 ounces. Test at
significance levels .05 and .10 (that is, at 5% and 10%
levels) that the adjustment has not increased the mean
weights of the ball bearings
44. Example
Proble
m Systolic Blood Pressure Before and After Exercise
Null Hypothesis : There is no difference in Systolic Blood Pressure Before and After Exercise
Alternative Hypothesis : There is a significance difference in Systolic Blood Pressure Before and After Exercise
Statistical Test : Dependent Sample t test /Paired 2 Sample for Means (Excel)
Before Exercise After Exercise
116 126
126 132
128 146
132 144
134 148
136 134
138 144
138 146
140 136
142 152
144 150
148 152
150 162
154 156
162 162
170 174
45. Solution
t-Test: Paired Two Sample for Means
Before
Exercise After Exercise
Mean 141.125 147.75
Variance 185.5833333 152.4666667
Observations 16 16
Pearson Correlation 0.899063955
Hypothesized Mean
Difference 0
df 15
t Stat -4.442450112
P(T<=t) one-tail 0.00023741
t Critical one-tail 1.753050356
P(T<=t) two-tail 0.000474821
t Critical two-tail 2.131449546
