Hypothesis Testing
The sole purpose of hypothesis testing is to determine whether or not research that has been collected is proved or disproved; usually allowing up to a 5% error factor. By using this 5% margin of error a researcher can consider the question of research being conducted is proven. There are five steps to be followed in doing hypotheses testing. The steps are: developing the research question, specifying between null and alternative hypotheses, calculating the statistic, computing probability, and stating the conclusions. For our hypotheses testing the issue of post traumatic stress syndrome (PTSD) is the focus. These five steps can be used to determine related illnesses and disorders that can develop along with PTSD. Issues Developed through PTSD

There are many side effects, issues, and disorders that can develop due to post traumatic stress syndrome. Some of these can include: eating disorders, alcoholism, depression, anxiety/panic disorders, acute stress disorder. Each of these disorders can develop in different individual’s who suffer from PTSD. It is not specific as to why they develop in certain individuals but psychologists and psychiatrists are working on research of this area. In doing this they are using the five steps of hypotheses testing.

Using the Five Steps of Hypotheses Testing
Utilizing the first step the process is to come up with the question of how PTSD is linked to other mental and personality disorders. As well as why certain individuals are prone to developing these different disorders. We can use different test groups to analyze and gather data to begin the second step of hypotheses testing.

Next determining the null and alternative hypotheses is done by computing the population of test subjects that are affected by PTSD and develop other disorders (null hypotheses) and those who are not (alternative hypotheses).

After the determination between the null and alternative hypotheses is completed it is time to...

...HYPOTHESISTESTING
WHAT IS THIS HYPOTHESIS????
• In simple words it means a mere assumption or supposition to be proved of disproved.
• But, for a researcher it is a formal question that he intends to resolve.
• Example: I assume that 1) under stress and anxiety a person goes into depression.
2) It leads to aggressive behaviour.
Eg. : Students who get better counselling in a university will show a greater increase in creativity than students who were not counselled.
• So, the hypothesis should be capable of being verified and tested.
CHARACTERISTICS
• Should be clear and precise – inferences not reliable
• Capable of being tested
“ A hypothesis is testable if other deductions can be made from it which, in turn can be confirmed or disproved by observation.”
• Should be limited in scope and must be specific
• Should be stated in simple terms -understandable by all concerned.
• Must explain the facts that gave rise to the need for explanation.
BASIC CONCEPTS: NULL & ALTERNATIVE HYPOTHESIS
• If we are to compare two methods A & B and both are equally good, then this assumption is termed as null hypothesis(H0)
• If it is stated that method A is better than method B-alternative hypothesis(Ha)
LEVEL OF SIGNIFICANCE
• A very important concept in the context of hypothesistesting
• It is represented in a % age...

...Lesson note #
Statistical Inference
Testing of Hypothesis
Type I Error:
Rejection of the null hypothesis when it is true is called a type I error.
Type II Error:
Acceptance of the null hypothesis when it is false is called a type II error.
|Decision of the test for the Null Hypothesis |The Null Hypothesis is |
| |True |False |
|Accept |Correct decision |Incorrect decision |
| | |Type II Error |
|Reject |Incorrect decision |Correct decision |
| |.Type I Error | |
Test Concerning Mean
One and Two tailed Tests:
A test procedure is called a one tailed test procedure if the alternative hypothesis is one sided. The test will be two tailed if the alternative hypothesis is two sided.
Example:
Let a specified value of population mean is 45. Construct the null and alternative hypothesis for the following questions;
a) Do the sample data provide...

...all, the video did a fair job buttressing my understanding of hypothesistesting. The textbook explained the aspects and steps of hypothesistesting in a legible fashion, while the video helped demonstrate a real-life application.
I learned from the text that hypothesistesting is a “Procedure for deciding whether the outcome of a study (results from a sample) supports a particular theory or practical innovation (which is thought to apply to a population)” (Aron A., Aron, E., and Coups, 2011, p. 145). I also learned that hypothesistesting follows a set procedure that appears as follows:
Step 1) Restate the question as a research hypothesis and a null hypothesis about the populations
- Basically, a researcher constructs a hypothesis. Then he/she forms a null hypothesis that opposes the research hypothesis in
polar fashion. To help support one’s research hypothesis, one has to disprove the null hypothesis.
Step 2) Determine the characteristics of the comparison distribution
- When using two or more samples, one must gather information about the distribution of means.
Step 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
- Most researchers...

...A hypothesis is a claim
Population mean
The mean monthly cell phone bill in this city is μ = $42
Population proportion
Example: The proportion of adults in this city with cell phones is π = 0.68
States the claim or assertion to be tested
Is always about a population parameter, not about a sample statistic
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 )
Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove
If the sample mean is close to the stated population mean, the null hypothesis is not rejected.
If the sample mean is far from the stated population mean, the null hypothesis...

...4 Hypothesistesting in the multiple regression model
Ezequiel Uriel
Universidad de Valencia
Version: 09-2013
4.1 Hypothesistesting: an overview
4.1.1 Formulation of the null hypothesis and the alternative hypothesis
4.1.2 Test statistic
4.1.3 Decision rule
4.2 Testing hypotheses using the t test
4.2.1 Test of a single parameter
4.2.2 Confidence intervals
4.2.3 Testinghypothesis about a single linear combination of the parameters
4.2.4 Economic importance versus statistical significance
4.3 Testing multiple linear restrictions using the F test.
4.3.1 Exclusion restrictions
4.3.2 Model significance
4.3.3 Testing other linear restrictions
4.3.4 Relation between F and t statistics
4.4 Testing without normality
4.5 Prediction
4.5.1 Point prediction
4.5.2 Interval prediction
4.5.3 Predicting y in a ln(y) model
4.5.4 Forecast evaluation and dynamic prediction
Exercises
1
2
2
3
5
5
16
17
21
21
22
26
27
28
29
30
30
30
34
34
36
4.1 Hypothesistesting: an overview
Before testing hypotheses in the multiple regression model, we are going to offer
a general overview on hypothesistesting.
Hypothesistesting allows us to carry out inferences about population parameters
using data from a sample. In order to test a...

...Hypothesistesting
Use of hypothesistesting can be very useful during decision-making connected with statistical data. A hypothesis is a statement made about a population parameter e.g. a mean and variance of a population. Hypothesistesting is a statistical process, which gives ideas or theories and then determine whether these ideas are true or false. The conclusions inhypothesistesting never 100%, therefore all tested ideas can be only probably true or probably false.
One of the most important concepts in hypothesistesting is sampling distribution.
Sampling distribution is a probability distribution of sample statistics based on all possible random samples. We have to choose randomly some amount of samples to conduct testing. The more samples size we take the better our sample curve looks normally distributed. Difference between the sample mean and population mean is a sampling error. The less this error the better result of testing. Usually we take 30 samples, which are enough to draw normally distributed curve.
Typical use scenario below will make clear the real life situation when we may use Hypothesistesting:
A bottled water manufacturer states on the product label that each of bottle contains 500 ml of water. We work for the government agency...

...HypothesisTesting I
Pat Obi
What is a “Hypothesis?”
A statement or claim about the value of a
population parameter: μ, σ2, p
Pat Obi, Purdue University Calumet
2
Decision Rule
1.
x 0
Z
s
n
Compare calculated Z value to Z value from
Table (critical Z value)
Reject H0 if calculated Z value lies in the
rejection/significance region (i.e. region)
ALTERNATIVELY:
2.
Compare p-value to
Reject H0 if p-value <
Pat Obi, Purdue University Calumet
3
Two-Tail Test
Ex: H0: 0 = 50; H1: 0 ≠ 50. Test at α = 0.05
Reject H0 if calculated Z is either less than ZCV
on the left tail or greater than ZCV on the right
0
Rejection region: /2 = 0.025
Rejection region: /2 = 0.025
0
ZCV = -1.96
ZCV = 1.96
Pat Obi, Purdue University Calumet
4
One-Tail Test: Right/Upper Tail
Ex: H0: 0 ≤ 55; H1: 0 > 55. Test at α = 0.05
Reject H0 if calculated Z > Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = 1.645
Pat Obi, Purdue University Calumet
5
One-Tail Test: Left/Lower Tail
Ex: H0: 0 ≥ 12; H1: 0 < 12. Test at α = 0.05
Reject H0 if calculated Z < Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = -1.645
Pat Obi, Purdue University Calumet
6
Z Table (critical Z values)
Significance
Level
Zcv
One-Tail Test
Zcv
Two-Tail Test
0.10
1.285
1.645
0.05
1.645
1.960
0.01
2.326
2.576
Pat Obi, Purdue University Calumet
7
Rules Governing the Statement of
Hypothesis
In...

...CHAPTER
8
Introduction to
HypothesisTesting
8.1
Inferential Statistics
and HypothesisTesting
LEARNING OBJECTIVES
8.2 Four Steps to
HypothesisTesting
After reading this chapter, you should be able to:
8.3
HypothesisTesting and
Sampling Distributions
8.4
Making a Decision:
Types of Error
8.5
Testing a ResearchHypothesis: Examples
Using the z Test
8.6
Research in Focus:
Directional Versus
Nondirectional Tests
8.7
Measuring the Size of
an Effect: Cohen’s d
8.8
Effect Size, Power, and
Sample Size
8.9
Additional Factors That
Increase Power
1 Identify the four steps of hypothesistesting.
2 Define null hypothesis, alternative hypothesis,
level of significance, test statistic, p value, and
statistical significance.
3 Define Type I error and Type II error, and identify the
type of error that researchers control.
4 Calculate the one-independent sample z test and
interpret the results.
5 Distinguish between a one-tailed and two-tailed test,
and explain why a Type III error is possible only with
one-tailed tests.
6 Explain what effect size measures and compute a
Cohen’s d for the one-independent sample z test.
7 Define power and identify six factors that influence power....