research statistics

2. HYPOTHESIS TESTING
Through our experience and survey of
previous researches related to our
problem, we are able to uncover
pertinent information and learn about
the methods used by other
researchers in investigating similar
topics. Because of this, we will be able
to define our hypothesis.

3. OBJECTIVES:
At the end of this chapter, you should be
able to:
1)Apply the steps to be followed in
hypothesis testing;
2)Test a one-sample hypothesis;
3)Do a t-test between two independent
samples;
4)Apply a t-test between two correlated
samples;
5)Apply ANOVA; and
6)Do non-parametric statistical tests.

4. WHAT IS A HYPOTHESIS?

5. WHAT ARE THE KINDS OR
TYPES OF HYPOTHESIS?

6. IS THIS A HYPOTHESIS?
There is no significant difference between
the immune booster from Is-is fruit
extract and the commercial one in terms
of improving the weight of chickens.
Why do you think so? What type of
hypothesis?

7. IS THIS A HYPOTHESIS?
Is-is plant have phytochemical properties
that enables it to be a potential source of
alternative immune booster for chickens.
Why do you think so? What type of
hypothesis?

8. ARRANGE THE FOLLOWING STEPS?
a. CHOOSE THE SAMPLING DISTRIBUTION AND
SPECIFY THE CRITICAL REGION.
b. STATE THE NULL AND ALTERNATIVE
HYPOTHESIS.
c. STATE THE LEVEL OF SIGNIFICANCE AND
SAMPLE SIZE.
d. DECIDE ON WHETHER TO ACCEPT OR
REJECT THE NULL HYPOTHESIS.
e. CHOOSE THE APPROPRIATE TEST STATISTIC
TO BE USED.

10. LESSON OBJECTIVES:
A.Identify the steps used in teting the
hypothesis.
B.Differentiate null from alternative
hypothesis.
C.Enumerate the levels of
measurement.

11. WHAT IS A HYPOTHESIS?
A hypothesis is a prediction based on the
body of knowledge, scientific theory, or
observations.
 After the hypothesis is formulated, it
has to be tested to find out whether it is
true or false.
 In hypothesis testing, we test our
prediction about one or more of the
population parameters (or
characteristics) that will either be
accepted or rejected on the basis of the
information obtained from the sample.

12. WHAT IS A HYPOTHESIS?
A hypothesis is a prediction based on the
body of knowledge, scientific theory, or
observations.
 Sample data provided us with estimates
of population parameters or
characteristics.
 These estimates are used in arriving at a
decision to either accept or reject a
hypothesis.

13. STEPS IN HYPOTHESIS TESTING:
A. STATE THE NULL AND ALTERNATIVE
HYPOTHESIS.
B. CHOOSE THE APPROPRIATE TEST STATISTIC
TO BE USED.
C. STATE THE LEVEL OF SIGNIFICANCE AND
SAMPLE SIZE.
D. CHOOSE THE SAMPLING DISTRIBUTION AND
SPECIFY THE CRITICAL REGION.
E. DECIDE ON WHETHER TO ACCEPT OR
REJECT THE NULL HYPOTHESIS.

15. TWO TYPES OF HYPOTHESIS:
NULL HYPOTHESIS (Ho)
 Indicates the value of the population
parameter to be tested.
 This is the hypothesis of “No DIFFERENCE”
and is usually formulated for the sole
purpose of being REJECTED.
 This is what is called a “TEST of
SIGNIFICANCE”.
A test of significance is a determination of the truth of a
prediction.

16. TWO TYPES OF HYPOTHESIS:
ALTERNATIVE HYPOTHESIS (HA)
 Is the operational statement of the
experimenter’s research hypothesis.
 The null hypothesis is the one being tested
statistically. Once the null hypothesis is
rejected, the alternative hypothesis is TAKEN
TO BE TRUE OR ACCEPTED.
Research hypothesis- is the prediction derived from the
theory being tested.

17. TEST OF SIGNIFICANCE
It is therefore a problem of deciding
between the null and the alternative
hypotheses on the basis of the
information contained in the sample.
> The GOAL is to reject the null hypothesis
in favor of the alternative hypothesis.

18. EXAMPLE 8.1:
Suppose that the standard medication
for influenza is effective in 70% of all
cases. A drug company believes that
its new drug “MEDIFLU”, is more
effective than the old treatment.
Formulate the null and alternative
hypothesis to test if there is statistical
evidence to support the new drug.

19. SOLUTION:
Let X denote the cure rate of the new drug.
Since the drug company believes that
Mediflu is better than the standard
medication, the research hypothesis
should be,
HA: µ > 70%
And the null hypothesis is
HO: µ = 70%
If HO is rejected in this case, then we have to
accept that HA is true. Otherwise the
reverse must be accepted.

21. STATISTICA TEST OR TEST STATISTIC
Is a calculated number that is used to
decide whether to reject or accept the
null hypothesis.
The formula to be used for the test
statistics depends on the variable we are
testing.
The level of measurement of the variable is
the basis for choosing the appropriate
statistics to be used in testing the
hypothesis.

22. APPROPRIATE STATISTICS FOR THE DIFFERENT
SCALES OF MEASUREMENT
Scale of
measuremen
t
Relations
being
defined
Appropriate
statistical
test to be
used
Examples of
statistics
that can be
used
NOMINAL EQUIVALENC
E
NON
PARAMETRI
C TEST
Mode,
Frequency,
Chi Square
test
ORDINAL EQUIVALENC
E, GREATER
THAN, LESS
THAN
NON
PARAMETRI
C
TEST
Median,
Spearman
rank,
Friedmann’s
test, Kendall’s
tau percentile

23. APPROPRIATE STATISTICS FOR THE DIFFERENT
SCALES OF MEASUREMENT
Scale of
measurement
Relations being
defined
Appropriate
statistical test
to be used
Examples of
statistics that
can be used
INTERVAL EQUIVALENC
E, GREATER
THAN, LESS
THAN,
KNOWN
RATIO OF ANY
TWO
INTERVALS
NON
PARAMETRIC
AND
PARAMETRIC
TEST
Mean,
statndard
deviation, z-
test, t-test,
ANOVA,
Pearson’s r
Ratio Equivalence,
greater than,
less than,
known ratio of
any two ratios
Non parametric
and parametric
Mean, standard
deviation,
coefficient of
variation,
Pearson’s r, z

24. Qualitative (Nominal & Ordinal Scale)
- Cannot make use of PARAMETRIC statistial tests.
Only uses NONPARAMETRIC statistica tests.
Quantitative (Interval & Ratio Scale)
- Can make use of both PARAMETRIC &
NONPARAMETRIC statistical tests.
Note: Interval & ratio measurements can be reduced
to nominal & ordinal measurements, while nominal &
ordinal measured cannot be upgraded to interval or
ratio measures.

26. STATE THE LEVEL OF SIGNIFICANCE & SAMPLE SIZE
In stating the level of significance (α) , the
researcher sets up the rejection & acceptance
region for the null hypothesis.
REJECTION REGION- is called the critical region.
ACCEPTANCE REGION- is the remaining region.
α greek small letter alpha.

27. TYPES OF TESTS
a. Two tailes test – rejection regions on the left
and on the right of the distribution curve.
b. One-tailed test- rejection region on the left side
of the curve.
c. One –tailed test- rejection region on the right
side of the curve.
Rejection regions contain teh critical value.

28. REJECTION REGION FOR DIFFERENT TYPES OF
SYMBOLS FOR ALTERNATIVE HYPOTHESIS.
Type of
symbol used
in the
alternative
hypothesis.
<
(less than)
≠
(not equal)
>
(greater
than)
Example of
HA
HA: µ < µ0 HA: µ ≠ µ0 HA: µ > µ0
Location of
the rejection
region to be
used
One region
on the left
side
Two regions,
one on each
side
One region
on the right
side
Type of test One-tailed
test
Two-tailed
test
One-tailed
test

29. LEVEL OF SIGNIFICANCE
 It is the probability that the test statistic falls
within the rejection region.
 The most commonly used level of significance (α)
are 0.05 and 0.01. These are the risks taken in
rejecting a TRUE HYPOTHESIS.
 When a null hypothesis is rejected or accepted,
there is a risk of making an error. There are two
types of possible errors that can be made at this
point. The TYPE I ERROR or TYPE II ERROR.

30. LEVEL OF SIGNIFICANCE
 TYPE I ERROR: When we reject a true null
hypothesis when we should accept it.
 TYPE II ERROR: When we accept a false null
hypothesis when infact we should reject it.
 The probability of making a type I error is equal to
the level of significance which is either 0.05 or
0.01 level. This is denoted by the greek letter alpha
(α).
 The probability of making a correct decision is 1 -
α.

32. SAMPLING DISTRIBUTION
 It is the theoretical distribution associated with the
test statistic applied.
Example:
When we are testing a hypothesis concerning
means, we may either use the standard normal
distribution table (z-table) or the table for t-values or
the student’s t distribution table.

34. REJECT OR ACCEPT?
 We say the value of the computed statistic is
significant when it falls within the rejection region.
Otherwise, we have to accept the null hypothesis.
 There are 4 possible decisions a researcher can
make in a test of hypothesis.
 Therefore: In any decision that we make, there is
always a risk of making an error.
Null Hypothesis
(Ho)
Decision
Reject Ho Accept Ho
True Type I error Correct Decision
False Correct Decision Type II error

35. Common statistical tests
used in experimental
research

36. PARAMETRIC TESTS
 One sample hypothesis test of means
A. Z-test
B. T-test (When the sample size is small)
 Two sample hypothesis tests of means
A. T-test (two independent sample means)
B. T-test (two dependent samples/Matched-pair
design experiments)
 Three or More Sample Hypothesis Tests of
Means
A. ANOVA (Analysis of Variance)

37. NONPARAMETRIC TESTS
 Chi- Square test (One way)
 Chi-Square test (two way)
 The Sign test
 Wilcoxon Signed Rank test
 Kruskal-wallis H test
 Friedman test