Faculty of Business & Economic Sciences
BED3332/ECO3022 LECTURE 5:RECAP OF HYPOTHESIS TESTING
DR QABHOBHO
Outline of the lecture
 This
lecture will provide a recap of hypothesis testing
 Take
note that hypothesis testing can be done using
three ways:
1.
2.
3.
T-test
P-value approach
Confidence interval approach
Introduction
 Hypothesis
testing is used to test whether a result is
in accordance with the expectation of a particular
theory
Introduction
 Recall
1.
2.
3.
4.
5.
6.
the following:
Type I error
Type II error
Null hypothesis
Alternative hypothesis
One tail test
Two-tail test
Test of significance
 The
hypothesis that is tested in empirical economic
research is the test of significance
 In
other words, is there a relationship between the
dependent and the independent variable(s)?
Test of significance
A
test of significance can be specified as follows:
𝐻0 : 𝛽𝑘 = 0
𝐻1 : 𝛽𝑘 ≠ 0
 The null hypothesis states that there is no relationship
between the variables
 The
alternative hypothesis states that there is a
relationship between the variables
Test of significance
 If
a variable has a t-statistic that is greater than 1.96
in absolute value and the degrees of freedom are
greater than 20 then its significant at 5%
The p-value
 The
p-value is known as the exact level of
significance or the exact probability of committing
type ɪ error
 Most
computer software packages used in statistical
analysis produce the p-value (prob)
The p-value
 The
p-value is compared to the chosen level of
significance
 The
p-values that is reported by computer software
such as Eviews are two-sided
The p-value
 The
p-value rule for a two-sided test is:
 Reject
the null hypothesis when the p-value is
less than or equal to the level of significance 𝜶
𝒑 ≤ 𝜶 𝐭𝐡𝐞𝐧 𝐫𝐞𝐣𝐞𝐜𝐭 𝑯𝟎
𝒑 > 𝜶 𝐭𝐡𝐞𝐧 𝐝𝐨 𝐧𝐨𝐭 𝐫𝐞𝐣𝐞𝐜𝐭 𝑯𝟎
The p-value
 Rejecting
the null hypothesis means that the
variables are related and the relationship is
statistically significant
 Not
rejecting the null hypothesis means that the
relationship is not statistically significant or its
insignificant
The p-value
 If
the p-value is less than 0.01 then the variable is
significant at 1% level of significance
 If the p-value is greater than 0.01 but less than 0.05
then the variable is significant at 5% level of
significance
 If the p-value is greater than 0.05 but less than 0.1
then the variable is significant at 10% level is
significance
 If the p-value is greater than 0.1 then the variable is
insignificant
The p-value
𝑝
𝑣𝑎𝑙𝑢𝑒=0.001 (Significant at 1%)
𝑝
𝑣𝑎𝑙𝑢𝑒=0.02 (Significant at 5%)
𝑝
𝑣𝑎𝑙𝑢𝑒=0.07 (Significant at 10%)
Example
 We
will conduct the following test of significance
𝐻0 : 𝛽1 = 0
𝐻1 : 𝛽1 ≠ 0
 In
other words does income have a statistically
significant impact on food expenditure? And if so at
what level of significance?
Example 1
Dependent Variable: WEEKLY_FOOD_EXPENDITURE
Method: Least Squares
Date: 07/11/16 Time: 11:25
Sample: 1973 2012
Included observations: 40
Variable
Coefficient
Std. Error
t-Statistic
Prob.
WEEKLY_INCOME
C
10.20964
83.41600
0.020933
43.41016
4.877381
1.921578
0.0000
0.0622
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.385002
0.368818
89.51700
304505.2
-235.5088
23.78884
0.000019
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
283.5735
112.6752
11.87544
11.95988
11.90597
1.893880
Example
 Another
way in which a question can be asked is as
follows:
 Test
the following hypothesis at 1% level of
significance
𝐻0 : 𝛽1 = 0
𝐻1 : 𝛽1 ≠ 0
Example 2
Dependent Variable: INVESTMENT
Method: Least Squares
Date: 07/31/16 Time: 00:37
Sample: 1985 2012
Included observations: 28
Variable
Coefficient
Std. Error
t-Statistic
Prob.
REAL_INTEREST_RATE
C
-0.236778
18.88577
0.126821
0.757203
-1.867015
24.94150
0.0732
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.118218
0.084303
2.337967
142.1183
-62.47265
3.485745
0.073215
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
17.73769
2.443220
4.605189
4.700347
4.634280
0.597497
Example 2
 Based
on the regression output on the previous slide,
test the following hypothesis:
𝐻0 : 𝛽1 = 0
𝐻1 : 𝛽1 ≠ 0
 In
other words does the real interest rate have a
statistically significant impact on investment? And if
so at what level of significance?
Example 2
 Another
way in which a question can be asked is as
follows:
 Test
the following hypothesis at 5% level of
significance
𝐻0 : 𝛽1 = 0
𝐻1 : 𝛽1 ≠ 0
Example 3
Dependent Variable: GDP
Method: Least Squares
Date: 07/10/16 Time: 23:01
Sample: 1985 2012
Included observations: 28
Variable
Coefficient
Std. Error
t-Statistic
Prob.
INVESTMENT
C
-0.169750
5.408087
0.171730
3.073840
-0.988465
1.759391
0.3320
0.0903
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.036218
-0.000850
2.180177
123.5825
-60.51614
0.977063
0.332035
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
2.397122
2.179251
4.465439
4.560596
4.494529
0.882228
Example 3
 Test
the following hypothesis
𝐻0 : 𝛽1 = 0
𝐻1 : 𝛽1 ≠ 0
 In
other words, does Investment have a statistically
significant impact on GDP? And if so at what level of
significance?