Hypothesis testing involves proposing and testing hypotheses, or predictions, about relationships between variables. There are four main types of hypotheses: null, alternative, directional, and non-directional. The null hypothesis proposes no relationship between variables, while the alternative hypothesis contradicts the null. Directional hypotheses predict the nature of a relationship, while non-directional hypotheses do not. Common statistical tests used for hypothesis testing include the z-test, t-test, chi-square test, and F-test. Hypothesis testing is a crucial part of the scientific method for assessing theories through empirical observation.
INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
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Chapter 12: Analysis of Variance
12.2: Two-Way ANOVA
Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
THIS POWERPOINT EXPLAINS ABOUT HYPOTHESIS AND ITS TYPES, ROLE OF HYPOTHESIS,TEST OF SIGNIFICANCE AND PROCEDURE FOR TESTING A HYPOTHESIS, TYPE I AND TYPE ii ERROR
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
Please Subscribe to this Channel for more solutions and lectures
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Chapter 12: Analysis of Variance
12.2: Two-Way ANOVA
Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
THIS POWERPOINT EXPLAINS ABOUT HYPOTHESIS AND ITS TYPES, ROLE OF HYPOTHESIS,TEST OF SIGNIFICANCE AND PROCEDURE FOR TESTING A HYPOTHESIS, TYPE I AND TYPE ii ERROR
hypothesis-Meaning need for hypothesis qualities of good hypothesis type of hypothesis null and alternative hypothesis sources of hypothesis formulation of hypothesis, hypothesis testing
Hypothesis Testing. Inferential Statistics pt. 2John Labrador
A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis.
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Explain the 8 Steps in hypothesis testing.
1. State null hypothesis- this is the opposite of the expected results, the importance of stating the null hypothesis is because according to Karl Popper’s principle or Falsifiabilty, it not possible to exclusively confirm a hypothesis but it is possible to conclusively negate a hypothesis.
2. Alternative hypothesis- this is indication of what the experiment expects. It is stated as not all equal, because despite the fact that it is possible to have not all equal variables it is only one of the many chances. For instance, when comparing effect of infectious disease of the colour of urine the alternative hypothesis can state that disease 1 results in tinting of the colour of urine to yellow but disease 2, 3… and normal un-infected persons do not differ in the colour of urine.
3. Set α- this is the level of significance. This is the probability or chance of committing the ‘grievous’ error type one denoted by α
There are two types of errors;
Reality
decision
H0 is correct
H0 in incorrect
Accept H0
OK
Type 2 error which is the β equal to possibility of type 2 error.
H0 rejected
Type 1 error
α=possibility of type 1 error
OK
4. Data collection- it’s important to use valid data collection techniques possibly for this case use observational or experimental methods
5. Stating and calculating the statistics for the study- this are the statistic values tested which include the mean, population, sample proportion and the difference in mean and sample proportions.
mean
61.82
median
61.50
mode
69.50
Mid-range
58
range
41
variance
79.64
Standard deviation
8.3
6. Decide on the test to be used- there are basically two types of tests; one tailed and two tailed. The decision is reached depending on the spread of error; two tailed is used when error spread is on two extremes side while one tailed test is used when error is spread on one side in the distribution.
7. Create accept and reject regions- a critical F value is established, you can establish the study F value from the statistical tables it is also called the Fα. It represent the minimum value for the study test statistics which determine which values should be rejected. With the value of F you locate it in the F distribution which form the location for boundary for acceptance and rejection.
8. Standardize the test statistics to draw a conclusion- using step 5 and 6 you can make some inference on the study, but to make more specific conclusion computation of z-test will help decide on the whether to reject or accept the hypothesis. In such cases p-value lower then α, then null hypothesis H0 is conclusively negated and therefore should accept the alternative hypothesis HA.
In testing a hypothesis using the above eight steps I prefer using critical value.
This method include the coming up with the unlik ...
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2. Introduction
A specific, testable and precise prediction about what the researcher assumes to
happen in his/her study
Hypothesis is usually considered as the principal instrument in research
Involves proposing a possible relationship between two variables i.e. the
dependent and independent variable
A complete hypothesis must include three components i.e. the variables, the
population and the relationship between the variables
2
3. Characteristics of Hypothesis
Should be clear and precise
Should be capable of being tested
Should state relationship between variables (if relational hypothesis)
Should be limited in scope and must be specific
Should be stated as far as possible in most simple terms
Should be consistent with most known facts
3
4. Contd…
Should be amenable to testing within a reasonable time
Must explain the facts that gave rise to the need for explanation
4
5. Types of Research Hypothesis
Generally, there are four types of research hypothesis which are:
1. Null Hypothesis
2. Alternate Hypothesis
3. Directional Hypothesis
4. Non-directional Hypothesis
5
6. Purpose of Hypothesis Testing
A statistical process of testing an assumption regarding a phenomenon or
population parameter
It is a critical and crucial part of the scientific method
Is a systematic approach to assessing theories through observations and
determining the probability that a stated statement is true or false
For an analyst who makes predictions, hypothesis testing is a difficult way of
backing up his prediction with statistical analysis
Also helps to determine whether there is sufficient statistical evidences that
support a certain hypothesis about the population parameter or not
6
7. Null Hypothesis
Null hypothesis is normally referred to as hypothesis of no difference and it is
denoted by Ho
Assumes that there is no difference between the hypothetical population and
the one, from which the sample under study has been drawn
A/c to this hypothesis, “there is no difference between the effects of two
treatments or there is no association between two attributes”
7
8. Contd…
It declares that there is no true difference in the sample statistic and
population parameter under consideration,
Hence it is called ‘null’ which means invalid, void, or a mounting to nothing
and the difference found is accidental, arising out of instabilities of sampling
Rejecting a null hypothesis does not necessarily mean that the experiment did
not produce the required results, but it sets the situation for further
experimentation
8
9. Contd…
For example, the hypothesis may be set in a form “maize variety A will give the
same yield per hectare as that of the variety B or there is no difference between
the average yields of maize varieties A and B”
Symbolically, Ho: μ1=μ2
Thus, these hypothesis form a basis to work with and such a working
hypothesis is known as null hypothesis.
It is called null hypothesis because if nullifies the original hypothesis i.e. variety
A will give more/less yield than variety B
9
10. States of Nature and Decisions on Null Hypothesis
Decision on Null
Hypothesis
States of Nature
Null Hypothesis True Null Hypothesis False
Accept Correct Decision
Probability=1 − 𝛼
Type II error committed
Probability=𝛽
Reject Type I error committed
Probability=𝛼
(𝛼 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑐𝑒 𝑙𝑒𝑣𝑒𝑙)
Correct Decision
Probability=1 − 𝛽
(1 − 𝛽 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑎 𝑡𝑒𝑠𝑡)
Note. Adapted from “Formulating and Testing Hypothesis” by Muhammad, K. S. (2016). Basic Guideline for Research. pp.
51-71.
10
11. Contd…
In the choice of null hypothesis, the following considerations are usually kept in
view:
A. Alternative hypothesis is usually the one which one wishes to prove and the
null hypothesis is the one which one wishes to disprove. Thus, a null
hypothesis represents the hypothesis we are trying to reject, and alternative
hypothesis represents all other possibilities.
B. If the rejection of a certain hypothesis when it is actually true involves great
risk, it is taken as null hypothesis because the probability of rejecting it when
it is true is 𝜶 which is chosen very small.
C. Null hypothesis should always be specific hypothesis i.e., it should not state
about or approximately a certain value.
11
12. Alternative Hypothesis
Hypothesis that contradicts the null hypothesis i.e. rejecting the null hypothesis
is known as alternative hypothesis
In other words, the set of alternatives to the null hypothesis is referred to as the
alternative hypothesis.
An alternative hypothesis and a null hypothesis are mutually exclusive, which
implies that only one of the two hypotheses can be true
A/c to this hypothesis, there is a relationship between the two variables being
studied (one variable has an effect on the other) and the results are not due to
chance
In simple words, null hypothesis means there is no effect while alternate
hypothesis means there is an effect
12
13. Contd…
Usually represented by Ha/H1
For example: “There is a significant difference between the yields of two maize
varieties”
Symbolically, H1: μ1≠μ2 (two tailed or non-direction alternative)
If the statement is that A gives significantly less yield than B or A gives
significantly more yield than B. Such statement is known as alternate hypothesis
Symbolically, H1: μ1 < μ2 (left tailed) H1: μ1 > μ2 (right tailed)
13
14. Directional Hypothesis
Directional hypothesis is also known as one-tailed hypothesis which predicts
the nature of the effect of the independent variable on the dependent variable
States which way you think the results are going to go
For example: “Mansuli variety of rice will have more yield than that of Basmati
variety”; the hypothesis compares the two groups and states which one will have
more/less, be faster/slower and so on
14
15. Contd…
Under correlational study, the directional hypothesis would state whether a
positive or a negative correlation is expected, stating how the two variables will
be related to each other
E.g.: There will be a positive correlation between the number of tillers and
yield of rice, number of irrigation and plant growth etc.
The directional hypothesis can also specify a negative correlation
E.g.: the higher the inflation rate in the country, lower the purchasing power of
the people.
15
16. Contd…
Here the researcher is intellectually committed to a particular outcome and
the anticipated direction of the relationship between variables is also specified
i.e. the investigator predicts not only the existence of a relationship but also its
nature
Such type of hypothesis is generally use by scientific journal
If the normal or t-distribution is used, one side or one tailed test only is
employed to estimate the required probabilities
16
17. Contd…
Figure 1. Directional/One-tailed Test
To reject H0: μ1 ≤ μ2 and accept H1: μ1 > μ2 0, using the normal distribution,
a normal deviate greater than +1.64 (i.e. right tailed) is required for significant
at the 0.05 level.
17
18. Contd…
Likewise, to reject H0: μ1 ≥ μ2 and accept H1: μ1 < μ2, the corresponding
normal curve is less than -1.64 (i.e. left tailed)
The choice between a non-directional or directional alternative hypothesis
should be determined by the rationale that gives rise to the study and should be
made before the data are gathered.
The major advantage of a directional alternative hypothesis is that it takes less
of a deviation from expectation to reject the null hypothesis
18
20. Non-directional Hypothesis
States that “The independent variable will have an influence on the dependent
variable, but the direction of the outcome is not specified”
For e.g.: “There will be a difference in the yield of two varieties of rice namely,
Basmati and Mansuli being cultivated”
A non-directional hypothesis only states that there exists a difference between
the two group/items but does not specify which will be greater/smaller,
positive/negative, faster/slower etc.
Similarly, in case of correlational study, we simply state that variables will be
correlated but do not state whether the relationship will be positive or negative,
e.g. there will be a significant correlation between variable X and variable Y
20
21. Contd…
We may wish to test the null hypothesis H0:μ1− μ2 = 0 against the alternative
H1:μ1− μ2 ≠ 0. This means that if H0 is rejected, the decision is that a difference
exists between the two means.
No confirmation about the direction of the difference is made. Such test is a
non-directional test.
Sometime called a two-tailed or two-sided test, because if the normal
distribution or t-distribution is used, the two tails of the distribution are employed
in the estimation of probabilities
21
22. Contd…
Figure 2. Non-directional/Two-tailed Test
Consider a 5% significance level. If the sampling distribution is normal, 2.5%
of the area of the curve falls to the right of 1.96 standard deviation units above
the mean, and 2.5% lies to the left of 1.96 standard deviation units lower the
mean.
22
23. Procedure For Hypothesis Testing
1. Making a formal statement
2. Selecting a significance level
3. Deciding the distribution to use
4. Selecting a random sample and computing an appropriate value
5. Calculation of the probability
6. Comparing the probability
23
24. Tests of Hypotheses
IMPORTANT PARAMETRIC TESTS
The important parametric tests are:
(1) z-test
(2) t-test
(3) Chi-Square-test, and
(4) F-test
(All these tests are based on the assumption of normality i.e., the source of data
is considered to be normally distributed)
24
25. z-test
Based on the normal probability (z) distribution and is used for judging the
significance of several statistical measures, particularly the mean
z-test is generally used for comparing the mean of a sample to some
hypothesized mean for the population in case of large sample (>30)
Besides, this test may be used for judging the significance of median, mode,
coefficient of correlation and several other measures
25
26. t-test
t-test is based on t-distribution and is considered an appropriate test for judging
the significance of a sample mean or for judging the significance of difference
between the means of two samples in case of small sample(<30)
In case two samples are related, we use paired t-test (aka. difference test) for
judging the significance of the mean of difference between the two related
samples.
It can also be used for judging the significance of the coefficients of simple and
partial correlations
26
27. Contd…
t-statistic is calculated from the sample data and then compared with its
probable value based on t-distribution (to be read from the table that gives
probable values of t for different levels of significance for different degrees of
freedom) at a specified level of significance for concerning degrees of freedom
for accepting or rejecting the null hypothesis
27
28. Chi-Square-test
Chi-Square-test is based on chi-square distribution and as a parametric test is
used for comparing a sample variance to a theoretical population variance
It can also be used to make comparisons between theoretical populations and
actual data when categories are used.
Thus, the chi-square test is applicable in large number of problems.
The test is, in fact, a technique through the use of which it is possible for all
researchers to:
(i) test the goodness of fit
(ii) test the significance of association between two attributes,
(iii) test the homogeneity or the significance of population variance.
28
29. F-test
F-test is based on F-distribution and is used to compare the variance of the
two-independent samples.
This test is also used in the context of analysis of variance (ANOVA) for
judging the significance of more than two sample means at one and the same
time.
It is also used for judging the significance of multiple correlation coefficients
F-statistic is calculated and compared with its probable value (to be seen in the
F-ratio tables for different degrees of freedom for greater and smaller variances at
specified level of significance) for accepting or rejecting the null hypothesis
29
30. Conclusion
Research hypothesis is a specific, testable and precise prediction about what the
researcher assumes to happen in their study
There are four types of research hypothesis (null, alternate, directional and non-
directional hypothesis)
Hypothesis testing is done to determine whether there is sufficient statistical
evidence that supports a certain hypothesis about the population parameter or not
Null hypothesis is the hypothesis of no difference i.e. same
30
31. Contd…
Directional hypothesis predicts the nature of the effect of the independent
variable on the dependent variable i.e. direction of outcome is specified
Non directional hypothesis predicts the influence of independent variable on
the dependent variable, but the direction of the outcome is not specified
Test for hypotheses testing: t-test, z-test, chi-square test, F-test
31
32. References
Agresti, A., & Finlay, B. (1997). Statistical Methods for the Social Sciences (3rd ed.). Prentice
Hall.
CFI. (2020). Null Hypothesis. Retrieved from Corporate Finance Institute:
https://corporatefinanceinstitute.com/resources/knowledge/other/null-hypothesis-2/
Development of the Research Hypothesis and Types of Hypothesis. (2018). Retrieved from
THEINTACTONE: https://theintactone.com/2018/02/26/br-u1-topic-3-development-of-the-
research-hypothesis-and-types-of-hypothesis/
McLeod, S. (2018, August 10). What is a hypothesis. Retrieved from Simply Psychology:
https://www.simplypsychology.org/what-is-a-hypotheses.html
Muhammad, K. S. (2016). Formulating and Testing Hypothesis. In Basic Guideline for Research
(pp. 51-71).
32