Kuliah 4-HYPOTHESIS TESTING.ppt
HYPOTHESIS TESTING
Dr. Jamil Ahmad
HYPOTHESIS
In many cases the purpose of research is to answer a
question or test a prediction, generally stated in the form of
hypotheses -- testable propositions.
Examples:
Question
Hypothesis
Does a training program in driver
safety result in a decline in accident
rate?
People who take a driver safety course
will have a lower accident rate than
those who do not take the course.
Who is better in math, men or
women?
Men are better in math than women.
What is the relationship between age
and cell phone use?
Cell phone use is higher for younger
adults than for older adults.
Is there a relationship between
education and income?
Income increases with years of
education.
Can public education reduce the
occurrence of AIDS?
The number of AIDS cases is inversely
related to the amount of public
education about the disease.
What is a Hypothesis?
A hypothesis is an educated guess about how things work.
Most of the time a hypothesis is written like this:
"If ____[I do this] _____, then _____[this]_____ will happen."
(Fill in the blanks with the appropriate information from your own
experiment.)
What is a Hypothesis?
A hypothesis is a statement about the relationship between two or more
variables. A hypothesis requires at least two variables, one independent
variable and one dependent variable.
Your hypothesis should be something that you can actually test, what's
called a testable hypothesis. In other words, you need to be able to
measure both "what you do" and "what will happen."
What is a Hypothesis?
A hypothesis is an explanation for a phenomenon which can
be tested in some way which ideally either proves or
disproves the hypothesis.
A statement about some population parameter that is to be
tested for its correctness.
A tentative explanation for an observation, phenomenon, or
scientific problem that can be tested by further investigation.
Hypothesis is a formal statement that presents the expected
relationship between an independent and dependent
variable.(Creswell, 1994)
A research question is essentially a hypothesis asked in the
form of a question.”
Nature of Hypothesis
It can be tested
Hypotheses are not moral or ethical questions
It is a prediction of consequences
It is considered valuable even if proven false
Types of Hypotheses
NULL HYPOTHESES
Designated by: Ho
Pronounced as “H oh” or “H-null”
(hipotesis nol, hipotesis kosong, hipotesis tidak beza)
Ho: μ1 = μ2
Ho: μ1 - μ2 = 0
ALTERNATIVE HYPOTHESES
Designated by: H1 or Ha
Ha: μ1 ≠ μ2
ALTERNATIVE HYPOTHESIS
The alternative hypothesis is a statement of what a
hypothesis test is set up to establish.
Opposite of Null Hypothesis.
Only reached if Ho is rejected.
Frequently “alternative” is actual desired
conclusion of the researcher!
The first step of hypothesis testing is to convert the research
question into null and alterative hypotheses.
We start with the null hypothesis (Ho).
The null hypothesis is a claim of “no difference.”
The opposing hypothesis is the alternative hypothesis
(Ha).
The alternative hypothesis is a claim of “a difference in the
population,” and is the hypothesis the researcher often
hopes to bolster.
It is important to keep in mind that the null and alternative
hypotheses reference population values, and not observed
statistics.
Contoh:
Dalam satu kajian bagi mengenal pasti keberkesanan kaedah pengajaran
berbantukan komputer berbanding dengan kaedah tradisional dalam
meningkatkan pencapaian pelajar dalam mata pelajaran sains.
Soalan kajian:
Adakah terdapat perbezaan pencapaian pelajar dalam mata pelajaran sains
antara kumpulan yang diajar dengan kaedah pengajaran berbantukan
komputer berbanding dengan kaedah tradisional?
Hipotesis nol:
Ho: Tidak terdapat perbezaan yang signifikan skor min pencapaian pelajar
dalam mata pelajaran sains antara kumpulan pelajar yang diajar dengan
kaedah berbantukan komputer berbanding dengan kumpulan tradisional.
Ho: μ1 = μ2
Hipotesis alternatif:
Ha: Terdapat perbezaan yang signifikan skor min pencapaian pelajar dalam
mata pelajaran sains antara kumpulan pelajar yang diajar dengan kaedah
berbantukan komputer berbanding dengan kumpulan tradisional.
Ha: μ1 ≠ μ2
(two-Tailed/sided)
Hipotesis alternatif juga boleh ditulis seperti berikut:
Ha: Pencapaian pelajar dalam mata pelajaran sains bagi kumpulan yang
diajar dengan kaedah berbantukan komputer lebih baik berbanding
dengan kumpulan yang diajar dengan kaedah tradisional.
Ha: μ > μ0 (one-Tailed/sided to right)
CONTOH SOALAN KAJIAN
1. Adakah terdapat perbezaan tahap budaya penyelidikan antara
guru sekolah bandar dengan guru sekolah luar bandar?
Hipotesis nol:
Ho. Tidak terdapat perbezaan yang signifikan tahap budaya
penyelidikan antara guru sekolah bandar dengan guru sekolah luar
bandar.
Hipotesis alternative:
Ha: . Terdapat perbezaan yang signifikan tahap budaya penyelidikan
antara guru sekolah bandar dengan guru sekolah luar bandar.
LEVEL OF SIGNIFICANCE (p value)
The p value is the probability that the samples are from the same
population with regard to the dependent variable (outcome).
Usually, the hypothesis we are testing is that the samples (groups)
differ on the outcome.
The p value is directly related to the null hypothesis.
The p value determines whether or not we reject the null hypothesis.
We use it to estimate whether or not we think the null hypothesis is
true.
LEVEL OF SIGNIFICANCE (p value)
The p value provides an estimate of how often we would get the
obtained result by chance, if in fact the null hypothesis were true.
If the p value is small, reject the null hypothesis and accept that the
samples are truly different with regard to the outcome.
If the p value is large, accept the null hypothesis and conclude that
the treatment or the predictor variable had no effect on the outcome.
??????????
How small is "small?“
What p value should we use as a cutoff?
In the behavioral and social and sciences, a general
pattern is to use either .05 or .01 as the cutoff.
The one chosen is called the level of significance.
If the probability associated with an inferential statistic is
equal to or less than .05, (p≤ .05) then the result is said to
be significant at the .05 level.
If the .01 cutoff is used, then the result is significant at the
.01 level.
Using the .05 level of significance means if the null hypothesis is true,
we would get our result 5 times out of 100 (or 1 out of 20). We take the
risk that our study is not one of those 5 out of 100.
Rejecting or accepting the null hypothesis is a gamble.
There is always a possibility that we are making a mistake in rejecting
the null hypothesis.
This is called a Type I Error - rejecting the null hypothesis when it is
true.
If we use a .01 cutoff, the chance of a Type I Error is 1 out of 100.
With a .05 level of significance, we are taking a bigger gamble. There is
a 1/20 (5 out of 100) chance that we are wrong, and that our treatment
(or predictor variable) doesn't really matter.
Why would we take the bigger gamble of .05 rather than .01 cutoff?
Because we don't want to miss discovering a true difference. There is
a tradeoff between overestimating and underestimating chance effects.
You will often see the probability
value described as p < .05,
meaning that the probability
associated with the inferential
statistic is .05 or less (5 out of
100).
Notation used with p values:
< = less than
> = greater than
< = less than or equal to
> = greater than or equal to
When you use a computer program to calculate an inferential
statistic (such as a t-test, Chi-square, correlation), the results will
show an exact p value (e.g., p = .013).
If you use the formulas for hand calculation, you will need to use a
table of critical values in order to get p.
The Decision Criterion
The Decision Criterion
Alpha Level
The Decision Criterion
Critical Region
A very small
number on either
side
2.5% on either
side
.5% on either
side
The locations of the critical region boundaries for three different
levels of significance: = .05, = .01, and = .001.
Types of error
Type of decision
H0 true
H0 false
Reject H0
Type I error ()
Correct decision (1-)
Accept H0
Correct decision (1-)
Type II error ()
If you reject Ho when it is false, you’ve made a correct decision
(upper-right cell)
However, if you reject Ho when it is true, you’ve made a “Type I error”
(upper left cell)
This error has a particular name, alpha.
On the other hand, if Ho is false and you do not reject Ho, you commit
a Type II error .
The probability of committing a Type II error is called beta.
Nov 2, 2018
22
SUMMARY
CONCEPT
DESCRIPTION
Null Hypothesis
The hypothesis stating that the independent variables has no
effect and that there will be no difference between two groups
Alternative
Hypothesis or
Research
Hypothesis
The hypothesis stating that the independent variables has an
effect and that there will be a difference between two groups
Two-Tailed or
Nondirectional
Test
An alternative hypothesis stating that a difference is expected
between the two groups, but there is no prediction as to which
group will perform better or worse
One-Tailed or
Directional Test
An alternative hypothesis stating that a difference is expected
between the two groups, and it is expected to occur in a
spesific direction.
Type I Error
The error of failing to reject Ho when we should have reject it
Type II Error
The error of rejected Ho when we should have failed to reject it
Statistical
Significance
When the probability of a type I error is low (less than .05)
Nov 2, 2018
23
Steps in Test of Hypothesis
1.
2.
3.
4.
5.
6.
Determine the appropriate test
Establish the level of significance:α
Determine whether to use a one tail or two tail test
Calculate the test statistic
Determine the degree of freedom
Compare computed test statistic against a tabled
value
TERIMA KASIH
Nov 2, 2018
25
Dr. Jamil Ahmad
HYPOTHESIS
In many cases the purpose of research is to answer a
question or test a prediction, generally stated in the form of
hypotheses -- testable propositions.
Examples:
Question
Hypothesis
Does a training program in driver
safety result in a decline in accident
rate?
People who take a driver safety course
will have a lower accident rate than
those who do not take the course.
Who is better in math, men or
women?
Men are better in math than women.
What is the relationship between age
and cell phone use?
Cell phone use is higher for younger
adults than for older adults.
Is there a relationship between
education and income?
Income increases with years of
education.
Can public education reduce the
occurrence of AIDS?
The number of AIDS cases is inversely
related to the amount of public
education about the disease.
What is a Hypothesis?
A hypothesis is an educated guess about how things work.
Most of the time a hypothesis is written like this:
"If ____[I do this] _____, then _____[this]_____ will happen."
(Fill in the blanks with the appropriate information from your own
experiment.)
What is a Hypothesis?
A hypothesis is a statement about the relationship between two or more
variables. A hypothesis requires at least two variables, one independent
variable and one dependent variable.
Your hypothesis should be something that you can actually test, what's
called a testable hypothesis. In other words, you need to be able to
measure both "what you do" and "what will happen."
What is a Hypothesis?
A hypothesis is an explanation for a phenomenon which can
be tested in some way which ideally either proves or
disproves the hypothesis.
A statement about some population parameter that is to be
tested for its correctness.
A tentative explanation for an observation, phenomenon, or
scientific problem that can be tested by further investigation.
Hypothesis is a formal statement that presents the expected
relationship between an independent and dependent
variable.(Creswell, 1994)
A research question is essentially a hypothesis asked in the
form of a question.”
Nature of Hypothesis
It can be tested
Hypotheses are not moral or ethical questions
It is a prediction of consequences
It is considered valuable even if proven false
Types of Hypotheses
NULL HYPOTHESES
Designated by: Ho
Pronounced as “H oh” or “H-null”
(hipotesis nol, hipotesis kosong, hipotesis tidak beza)
Ho: μ1 = μ2
Ho: μ1 - μ2 = 0
ALTERNATIVE HYPOTHESES
Designated by: H1 or Ha
Ha: μ1 ≠ μ2
ALTERNATIVE HYPOTHESIS
The alternative hypothesis is a statement of what a
hypothesis test is set up to establish.
Opposite of Null Hypothesis.
Only reached if Ho is rejected.
Frequently “alternative” is actual desired
conclusion of the researcher!
The first step of hypothesis testing is to convert the research
question into null and alterative hypotheses.
We start with the null hypothesis (Ho).
The null hypothesis is a claim of “no difference.”
The opposing hypothesis is the alternative hypothesis
(Ha).
The alternative hypothesis is a claim of “a difference in the
population,” and is the hypothesis the researcher often
hopes to bolster.
It is important to keep in mind that the null and alternative
hypotheses reference population values, and not observed
statistics.
Contoh:
Dalam satu kajian bagi mengenal pasti keberkesanan kaedah pengajaran
berbantukan komputer berbanding dengan kaedah tradisional dalam
meningkatkan pencapaian pelajar dalam mata pelajaran sains.
Soalan kajian:
Adakah terdapat perbezaan pencapaian pelajar dalam mata pelajaran sains
antara kumpulan yang diajar dengan kaedah pengajaran berbantukan
komputer berbanding dengan kaedah tradisional?
Hipotesis nol:
Ho: Tidak terdapat perbezaan yang signifikan skor min pencapaian pelajar
dalam mata pelajaran sains antara kumpulan pelajar yang diajar dengan
kaedah berbantukan komputer berbanding dengan kumpulan tradisional.
Ho: μ1 = μ2
Hipotesis alternatif:
Ha: Terdapat perbezaan yang signifikan skor min pencapaian pelajar dalam
mata pelajaran sains antara kumpulan pelajar yang diajar dengan kaedah
berbantukan komputer berbanding dengan kumpulan tradisional.
Ha: μ1 ≠ μ2
(two-Tailed/sided)
Hipotesis alternatif juga boleh ditulis seperti berikut:
Ha: Pencapaian pelajar dalam mata pelajaran sains bagi kumpulan yang
diajar dengan kaedah berbantukan komputer lebih baik berbanding
dengan kumpulan yang diajar dengan kaedah tradisional.
Ha: μ > μ0 (one-Tailed/sided to right)
CONTOH SOALAN KAJIAN
1. Adakah terdapat perbezaan tahap budaya penyelidikan antara
guru sekolah bandar dengan guru sekolah luar bandar?
Hipotesis nol:
Ho. Tidak terdapat perbezaan yang signifikan tahap budaya
penyelidikan antara guru sekolah bandar dengan guru sekolah luar
bandar.
Hipotesis alternative:
Ha: . Terdapat perbezaan yang signifikan tahap budaya penyelidikan
antara guru sekolah bandar dengan guru sekolah luar bandar.
LEVEL OF SIGNIFICANCE (p value)
The p value is the probability that the samples are from the same
population with regard to the dependent variable (outcome).
Usually, the hypothesis we are testing is that the samples (groups)
differ on the outcome.
The p value is directly related to the null hypothesis.
The p value determines whether or not we reject the null hypothesis.
We use it to estimate whether or not we think the null hypothesis is
true.
LEVEL OF SIGNIFICANCE (p value)
The p value provides an estimate of how often we would get the
obtained result by chance, if in fact the null hypothesis were true.
If the p value is small, reject the null hypothesis and accept that the
samples are truly different with regard to the outcome.
If the p value is large, accept the null hypothesis and conclude that
the treatment or the predictor variable had no effect on the outcome.
??????????
How small is "small?“
What p value should we use as a cutoff?
In the behavioral and social and sciences, a general
pattern is to use either .05 or .01 as the cutoff.
The one chosen is called the level of significance.
If the probability associated with an inferential statistic is
equal to or less than .05, (p≤ .05) then the result is said to
be significant at the .05 level.
If the .01 cutoff is used, then the result is significant at the
.01 level.
Using the .05 level of significance means if the null hypothesis is true,
we would get our result 5 times out of 100 (or 1 out of 20). We take the
risk that our study is not one of those 5 out of 100.
Rejecting or accepting the null hypothesis is a gamble.
There is always a possibility that we are making a mistake in rejecting
the null hypothesis.
This is called a Type I Error - rejecting the null hypothesis when it is
true.
If we use a .01 cutoff, the chance of a Type I Error is 1 out of 100.
With a .05 level of significance, we are taking a bigger gamble. There is
a 1/20 (5 out of 100) chance that we are wrong, and that our treatment
(or predictor variable) doesn't really matter.
Why would we take the bigger gamble of .05 rather than .01 cutoff?
Because we don't want to miss discovering a true difference. There is
a tradeoff between overestimating and underestimating chance effects.
You will often see the probability
value described as p < .05,
meaning that the probability
associated with the inferential
statistic is .05 or less (5 out of
100).
Notation used with p values:
< = less than
> = greater than
< = less than or equal to
> = greater than or equal to
When you use a computer program to calculate an inferential
statistic (such as a t-test, Chi-square, correlation), the results will
show an exact p value (e.g., p = .013).
If you use the formulas for hand calculation, you will need to use a
table of critical values in order to get p.
The Decision Criterion
The Decision Criterion
Alpha Level
The Decision Criterion
Critical Region
A very small
number on either
side
2.5% on either
side
.5% on either
side
The locations of the critical region boundaries for three different
levels of significance: = .05, = .01, and = .001.
Types of error
Type of decision
H0 true
H0 false
Reject H0
Type I error ()
Correct decision (1-)
Accept H0
Correct decision (1-)
Type II error ()
If you reject Ho when it is false, you’ve made a correct decision
(upper-right cell)
However, if you reject Ho when it is true, you’ve made a “Type I error”
(upper left cell)
This error has a particular name, alpha.
On the other hand, if Ho is false and you do not reject Ho, you commit
a Type II error .
The probability of committing a Type II error is called beta.
Nov 2, 2018
22
SUMMARY
CONCEPT
DESCRIPTION
Null Hypothesis
The hypothesis stating that the independent variables has no
effect and that there will be no difference between two groups
Alternative
Hypothesis or
Research
Hypothesis
The hypothesis stating that the independent variables has an
effect and that there will be a difference between two groups
Two-Tailed or
Nondirectional
Test
An alternative hypothesis stating that a difference is expected
between the two groups, but there is no prediction as to which
group will perform better or worse
One-Tailed or
Directional Test
An alternative hypothesis stating that a difference is expected
between the two groups, and it is expected to occur in a
spesific direction.
Type I Error
The error of failing to reject Ho when we should have reject it
Type II Error
The error of rejected Ho when we should have failed to reject it
Statistical
Significance
When the probability of a type I error is low (less than .05)
Nov 2, 2018
23
Steps in Test of Hypothesis
1.
2.
3.
4.
5.
6.
Determine the appropriate test
Establish the level of significance:α
Determine whether to use a one tail or two tail test
Calculate the test statistic
Determine the degree of freedom
Compare computed test statistic against a tabled
value
TERIMA KASIH
Nov 2, 2018
25