Hypothesis Testing.pptx

Mrs. D. Melba Sahaya Sweety RN,RM
PhD Nursing , MSc Nursing (Pediatric Nursing),BSc Nursing
Associate Professor
Department of Pediatric Nursing
Enam Nursing College, Savar,
Bangladesh.
1

INTRODUCTION
• Hypothesis testing is a form of statistical inference that uses data from a
sample to draw conclusions about a population parameter or a
population probability distribution. Hypothesis testing is used to estimate
the relationship between 2 statistical variables. First, a tentative assumption
is made about the parameter or distribution. This assumption is called
the null hypothesis and is denoted by H0. An alternative hypothesis
(denoted Ha), which is the opposite of what is stated in the null hypothesis,
is then defined.
• The hypothesis-testing procedure involves using sample data to determine
whether or not H0 can be rejected. If H0 is rejected, the statistical
conclusion is that the alternative hypothesis Ha is true. 2

PROPOSITION
• A proposition is a tentative and conjectural relationship between
constructs that is stated in a declarative form. An example of a
proposition is: “An increase in student intelligence causes an
increase in their academic achievement.”
• This declarative statement does not have to be true, but must be
empirically testable using data, When a proposition is formulated for
empirical testing, it is called a hypothesis. so that we can judge
whether it is true or false. Propositions are generally derived based
on logic (deduction) or empirical observations (induction).
• A proposition is similar to a hypothesis, but its main purpose is to
suggest a link between two concepts in a situation where the link
cannot be verified by experiment. As a result, it relies heavily on
prior research, reasonable assumptions and existing correlative
evidence. 3

HYPOTHESIS
• INTRODUCTION: Hypothesis is a statement or proposition
that attempts to explain phenomena or facts. Hypotheses are often
tested to see if they are accurate. It includes components like
variables, population and the relation between the variables. A
research hypothesis is a hypothesis that is used to test the
relationship between two or more variables. The researcher's
prediction is usually referred to as the alternative hypothesis, and
any other outcome as the null hypothesis
• DEFINITION OF HYPOTHESIS:
“Hypothesis is a tentative prediction or explanation of the
relationship between two variables’ It implies that there is a
systematic relationship between an independent and dependent
variable”. 4

HYPOTHESIS
CHARACTERISTICS OF HYPOTHESIS:
Hypothesis must possess the following characteristics:
(i) Hypothesis should be clear and precise. If the hypothesis is not clear and precise,
the inferences drawn on its basis cannot be taken as reliable.
(ii) Hypothesis should be capable of being tested.
(iii) Hypothesis should state relationship between variables, if it happens to be a
relational hypothesis.
(iv) Hypothesis should be limited in scope and must be specific. A researcher must
remember that narrower hypotheses are generally more testable and he should develop
such hypotheses.
(v) Hypothesis should be stated as far as possible in most simple terms so that the
same is easily understandable by all concerned. 5

HYPOTHESIS
CHARACTERISTICS OF HYPOTHESIS:
(vi) Hypothesis should be consistent with most known facts i.e., it should be
one which judges accept as being the most likely.
(vii) Hypothesis should be amenable to testing within a reasonable time.
One should not use even an excellent hypothesis, if the same cannot be tested
in reasonable time for one cannot spend a life-time collecting data to test it.
(viii) Hypothesis must explain the facts that gave rise to the need for
explanation. This means that by using the hypothesis plus other known and
accepted generalizations, one should be able to deduce the original problem
condition. Thus hypothesis must actually explain what it claims to explain; it
should have empirical reference. 6

HYPOTHESIS
TESTING
INTRODUCTION:
Hypothesis testing aims to make a statistical conclusion about
accepting or not accepting the hypothesis Is also called significance
testing . The purpose of hypothesis testing is to determine whether
there is enough statistical evidence in favor of a certain belief, or
hypothesis, about a parameter.
DEFINITION
Hypothesis testing is a statistical method that uses sample data to
evaluate the validity of a hypothesis about a population parameter. 7

HYPOTHESIS
TESTING
B, Level of
Significance
A, Types of
hypothesis
C, Types of Errors
D, Two tail and one
tail test
E, Significance
Probability
BASIC CONCEPTS IN HYPOTHESIS TESTING
8

HYPOTHESIS
TESTING
BASIC CONCEPTS IN HYPOTHESIS TESTING :
A, TYPES OF HYPOTHESIS
NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS
The null hypothesis state that there is no
relationship between independent and
dependent variable.
The alternative hypothesis are statements of
expected relationships between independent
and dependent variables.
It is denoted by (H0) It is denoted by (Ha) or (H1)
Typical phrases used are: No effect, No
difference, No relationship, No change, Does
not increase, Does not decrease
Typical phrases used are: An effect, A
difference, A relationship, A change,
Increases, Decreases
Symbols used are : Equality symbol (=, ≥, or
≤)
Symbols used are : Inequality symbol (≠, <,
or >) 9

HYPOTHESIS
TESTING
TYPES OF HYPOTHESIS:
NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS
It is also known as STATITICAL HYPOTHESIS. It is also known as RESEARCH HYPOTHESIS.
It is what the researcher tries to disprove. It is what the researcher tries to prove.
In this hypothesis, the p-value is smaller than the
significance level.(Rejected)
In this hypothesis, the p-value is greater than the
significance level.(Supported)
If the null hypothesis is accepted researchers
have to make changes in their opinions and
statements.
If the alternative hypothesis gets accepted
researchers do not have to make changes in their
opinions and statements.
Here the testing process is implicit and indirect. Here the testing process is explicit and direct.
10

HYPOTHESIS
TESTING
In hypothesis testing, the level of significance is a measure of
How confident about rejecting the null hypothesis. The level of
significance determines whether the outcome of hypothesis
testing is statistically significant or otherwise. The significance
level is also called as alpha level or (α). Another way of looking
at the level of significance is the value which represents the
likelihood of making a type I error. The level of
significance can take values such as 0.1, 0.05, 0.01. The most
common value of the level of significance is 0.05. The lower the
value of significance level, the lesser is the chance of type I error.
B, LEVEL OF SIGNIFICANCE
11

When testing, we arrive at a conclusion of rejecting the null
hypothesis or failing to reject the null hypothesis. Such conclusions
are sometimes correct and sometimes incorrect (even when we have
followed all the correct procedures). We use incomplete sample data
to reach a conclusion and there is always the possibility of reaching
the wrong conclusion. There are four possible conclusions to reach
from hypothesis testing. Of the four possible outcomes, two are
correct and two are NOT correct.
C, TYPES OF ERRORS
12
HYPOTHESIS
TESTING

A Type I error is rejecting the null hypothesis when it is true. The
symbol α (alpha) is used to represent Type I errors. This is the same
alpha we use as the level of significance. By setting alpha as low as
reasonably possible to control the Type I error through the level of
significance.
A Type II error is fail to reject the null hypothesis when it is false.
The symbol β (beta) is used to represent Type II errors.
C, TYPES OF ERRORS
13
HYPOTHESIS
TESTING

C, TYPES OF ERRORS
14
HYPOTHESIS TESTING
Type I and II Error
Null Hypothesis is.. True False
Rejected Type I error
False positive
Probability = α
Correct Decision
True Positive
Probability= 1 - β
Accepted Correct Decision
True Negative
Probability= 1-α
Type II error
False Negative
Probability= β

• Controlling For Error there is a mathematical relationship between α, β, and n
(sample size).
• As α increases, β decreases
• As α decreases, β increases
• As sample size increases (n), both α and β decrease
More likely to reject the Null Hypothesis at the .05 than the .01 level of significance. This
means more likely to have a Type I Error at the .05 than the .01 level of significance.
Conversely, more likely to have a Type II Error at the .01 than the .05 level of significance, to
decrease the likelihood of making either a Type I or Type II Error, then increase the sample
size.
C, TYPES OF ERRORS
15
HYPOTHESIS
TESTING

Power is the probability of making a correct decision (to reject the
null hypothesis) when the null hypothesis is false. Or power is the
probability of not making a Type II error Mathematically, power is
1 – beta (1- β). The power of a hypothesis test is between 0 and 1; if
the power is close to 1, the hypothesis test is very good at detecting a
false null hypothesis.
Beta is commonly set at 0.2, but may be set by the researchers to be
smaller that is 0.8.
C, TYPES OF ERRORS
16
HYPOTHESIS
TESTING

One and Two-Tailed Tests are ways to identify the relationship
between the statistical variables.
Two-Tailed Test : A two-tailed test is also called a nondirectional
hypothesis. For checking whether the sample is greater or less than a
range of values, we use the two-tailed. It is used for null hypothesis
testing. Symbolically, the two tailed test is appropriate when we have
H0: µ = µH0 and Ha: µ ≠ µH0 which may mean µ > µH0 or µ < µH0
Thus, in a two-tailed test, there are two rejection regions, one on each
tail of the curve which can be illustrated as under:
D, TWO TAILED TEST AND ONETAILED TEST
17
HYPOTHESIS
TESTING

18
0.475 of
area
0.475 of
area
Both are taken together
equal 0.95 or 95% of area
Z = - 1.96 Z = 1.96
0.025 of
area
0.025 of
area
H0
Rejection Region
Rejection Region
Acceptance region (Accept H0
if the sample mean ( X ) falls in
this region)
Acceptance and rejection
regions in case of a two-tailed
test (with 5% significance level)
Reject H0 if the sample mean
( X ) falls in either of these two regions
HYPOTHESIS
TESTING

One-Tailed Test
• A one-tailed test is based on a uni-directional hypothesis where the area of rejection is on
only one side of the sampling distribution. It determines whether a particular population
parameter is larger or smaller than the predefined parameter. It uses one single critical value
to test the data.
Left – tail Test
• For instance, if our H0: µ = µH0 and Ha: µ < µH0 then we are interested in what is known as
left-tailed test (wherein there is one rejection region only on the left tail) For a left-tailed
test, the null hypothesis is rejected if the test statistic is too small. Thus, the rejection
region for such a test consists of one part, which is left from the center.
19
HYPOTHESIS
TESTING

20
0.475 of
area
0.50 of
area
Z = - 1.96
0.05 of
area
H0
Rejection Region
this region)
Acceptance and rejection regions in case
of one -tailed test (left tail) with 5%
significance level)
( X ) falls these regions
Mathematically we can state:
Acceptance Region A: Z > - 1.96
Rejection Region R : Z ≤ -1.96
HYPOTHESIS
TESTING
Left – tail Test

Right Tail test
• For instance, if our H0: µ = µH0 and Ha: µ > µH0 then we are
interested in what is known as Right -tailed test (wherein there is one
rejection region only on the Right tail) For a right-tailed test, the null
hypothesis is rejected if the test statistic is too large. Thus, the
rejection region for such a test consists of one part, which is right
from the center. which can be illustrated as below:
21
HYPOTHESIS
TESTING

22
0.50 of
area
0.475 of
area
Z = 1.96
0.05 of
area
H0
Rejection Region
this region)
Acceptance and rejection regions in case
of one -tailed test ( Right tail) with 5%
significance level)
( X ) falls these regions
Mathematically we can state:
Acceptance Region A : Z ≤ 1.96
Rejection Region A: Z > 1.96
HYPOTHESIS
TESTING
Right – tail Test

• The significance probability is denoted as p value, or probability
value, It is defined as the probability of getting a result that is either
the same or more extreme than the actual observations. It does this
by calculating the likelihood of test statistic, which is the number
calculated by a statistical test using the observed data.
23
HYPOTHESIS
TESTING
A, SIGNIFICANCE PROBABILITY

24
HYPOTHESIS
TESTING
A, SIGNIFICANCE PROBABILITY
The P-value table shows the hypothesis interpretations:
P-value Decision
P-value >
0.05
The result is not statistically significant and hence don’t reject the
null hypothesis.
P-value <
0.05
The result is statistically significant. Generally, reject the null
hypothesis in favor of the alternative hypothesis.
P-value <
0.01
The result is highly statistically significant, and thus rejects the null
hypothesis in favor of the alternative hypothesis.

HYPOTHESIS
TESTING
25
PROCEDURE OF HYPOTHESIS TESTING :
State H0 as well as Ha
Specify the level of
significance (or the α value)
Decide the correct
Sampling Distribution
Selecting a random sample and
computing an appropriate value
Calculation of
the probability
Comparing the
probability
Yes No
Reject H0 Accept H0

HYPOTHESIS TESTING
26
Hypothesis testing for
Population Mean
Single Population Mean
Where σ 𝑖𝑠 𝐾𝑛𝑜𝑤𝑛
Single Population Mean
Where σ 𝑖𝑠 𝑈𝑛𝐾𝑛𝑜𝑤𝑛
Two Population Mean
Where σ 𝑖𝑠 𝐾𝑛𝑜𝑤𝑛
Population Proportion
Hypothesis testing for single
population Proportion
Hypothesis testing for double
population proportion
Single Variance
double Variance

HYPOTHESIS
TESTING
Hypothesis Testing Type of test and formula
n > 30 n ≤ 30
Population Mean Where σ
is Known.
Z test
Hypothesis testing for Single
Population Mean Where σ is
Unknown.
Z test
Hypothesis testing for Two
Population Mean Where σ is equal
Variance 27
Hypothesis testing for Population Mean
One
Sample
t Test
One
Sample
t Test
Independent
t Test

HYPOTHESIS
TESTING
Hypothesis Testing Type of test and formula
Hypothesis testing for Two
Population Mean Where σ is
unknown or unequal
n >30
Z test
n < 30
Independent
t test
Hypothesis Tests for two
population mean where σ is
unknown but considered to be
equal
Hypothesis Testing for two
population mean but Related
Samples 28
Independent
t Test
Paired t Test

HYPOTHESIS
TESTING
Hypothesis Testing
(Large sample)
Type of test and
formula
Hypothesis
Testing
Type of test and
formula
population proportion Where
Proportion is Known.
Hypothesis testing
for Single
Variance
Hypothesis testing for two
population proportion Where
P and Q are not Known
Hypothesis testing
for double
Variance
Hypothesis testing for two
population proportion or
difference in Proportion 29

Statistical test Null hypothesis (H0) Alternative hypothesis (Ha)
Two-sample t test
or
One-way
ANOVA with two
groups
The mean dependent
variable does not differ
between group 1 (µ1)
and group 2 (µ2) in the
population; µ1 = µ2.
The mean dependent
variable differs
between group 1 (µ1), group
2 (µ2) in the population; µ1 ≠
µ2.
One-way
ANOVA with three
groups
The mean dependent
variable does not differ
between group 1 (µ1), group
2 (µ2), and group 3 (µ3) in the
population; µ1 = µ2 = µ3.
The mean dependent
variable of group
1 (µ1), group 2 (µ2),
and group 3 (µ3) are not all
equal in the population.
Pearson correlation There is no correlation
between independent
variable and dependent
variable in the population; ρ =
0.
There is a correlation
between independent
variable in the population; ρ
≠ 0.
HYPOTHESIS TESTING
STATISTICAL TEST AND
HYPOTHESIS FORMULATION
30

Statistical test Null hypothesis (H0) Alternative
hypothesis (Ha)
Simple linear
regression
There is no
relationship
between independent
variable in the
population; β1 = 0.
There is a relationship
between independent
variable in the
population; β1 ≠ 0.
Two-proportions z test The dependent
variable expressed as a
proportion does not
differ between group
1 (p1) and group 2 (p2)
in the
population; p1 = p2.
The dependent
variable expressed as a
proportion differs
between group 1 (p1)
and group 2 (p2) in the
population; p1 ≠ p2.
STATISTICAL TEST AND
HYPOTHESIS FORMULATION
HYPOTHESIS TESTING
31

Hypothesis Testing.pptx

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