3. TEST OF HYPOTHESIS
• Curious mind fuels investigations, learnings, and discoveries. A
human mind is always full of queries and tends to seek answers
through research. Despite the many findings and discoveries, there
is still a lot to be investigated and re-investigated since change is
endless. For instance, one might want to know if spraying people
with disinfectant lowers the spread of COVID-19, or what
supplements to take to have better protection against the disease.
Filipinos nowadays were also eager to know which among the
available COVID-19 vaccines will be purchased, if they will decide to
take one. To arrive at a decision, research requires a process known
as the test of hypothesis.
4. TEST OF HYPOTHESIS
• In conducting a test of hypothesis, we usually use sample data to
estimate what is taking place in a larger population, to which we
have no access. Research questions or statements of the problem
were formulated.
• Then, we come up with a set of testable predictions known as a
hypothesis.
• A hypothesis is defined as a proposed explanation (may or may not
be true) for a phenomenon that can be used as a basis for further
verification or investigation.
5. NULL HYPOTHESIS VS. ALTERNATIVE HYPOTHESIS
• There are two opposing hypotheses for each phenomenon: the null
hypothesis and the alternative hypothesis.
• The null hypothesis, represented by H0, states that there is no
difference between a parameter and a statistic, or that there is no
difference between two parameters.
• On the other hand, the alternative hypothesis, represented by Ha,
states the existence of a difference between a parameter and a
statistic or states that there is a difference between two
parameters.
6. NULL HYPOTHESIS VS. ALTERNATIVE HYPOTHESIS
• A decision rule to resolve which of these two opposing hypotheses is
more likely to be true will be followed. The null hypothesis will be
rejected in favor of the alternative hypothesis if the sample evidence
strongly suggests that it is false. In the same manner, if we favor the
null hypothesis, we reject the alternative hypothesis.
7. TWO TYPES OF TESTS
1. A type of test used for directional hypothesis is known
as a one-tailed test.
– A directional (or one-tailed hypothesis) states which way you
think the results are going to go, for example in an experimental
study we might say…”Participants who have been deprived of
sleep for 24 hours will have more cold symptoms the week after
exposure to a virus than participants who have not been sleep
deprived”; the hypothesis compares the two groups/conditions
and states which one will ….have more/less, be quicker/slower,
etc.
8. TWO TYPES OF TESTS
2. The one used for a non-directional hypothesis is known
as a two-tailed test.
– A non-directional (or two tailed hypothesis) simply states that
there will be a difference between the two groups/conditions but
does not say which will be greater/smaller, quicker/slower etc.
Using our example above we would say “There will be a
difference between the number of cold symptoms experienced
in the following week after exposure to a virus for those
participants who have been sleep deprived for 24 hours
compared with those who have not been sleep deprived for 24
hours.”
9. RIGHT TAILED TEST VS. LEFT TAILED TEST
• . A one-tailed test can only be right-tailed or left-tailed,
which leans in the direction of the inequality of the
alternative hypothesis.
• To state the hypotheses, we must translate the words into
mathematical symbols. The basic symbols used are as
follows:
11. WHEN CAN WE USE ONE TAILED OR TWO TAILED TEST?
15. Level of Significance
• When one has formulated the hypothesis, the next
step is to make a research design. The researcher
decides on the right statistical test and selects a
fitting level of significance. For example, in
Scenario 1, a sample of patients who will be given
the vaccine will be chosen. After letting an
appropriate period for the vaccine to be absorbed,
the researcher will take each patient’s temperature.
16. Level of Significance
• The level of significance, usually designated by the alpha
(α) symbol pertains to the degree of confidence we require
in order to reject the null hypothesis in favor of the
alternative hypothesis. It is the highest probability of
committing a Type I error. The significance testing that we
currently use is a combination of the Ronald Fisher’s idea
of utilizing the probability value pass an index of the weight
of evidence against a null hypothesis, and Jerzy Neyman
and Egron Pearson’s notion of testing a null hypothesis
against an alternative hypothesis.
17. Level of Significance
• Fisher proposed that 95% is a useful threshold of
confidence for only when we are 95% positive that a result
is accurate should we accept it as true.
• In other words, if there is only a 5% chance (α= 0.05) of
committing an error, then we say that it is a statistically
significant finding.
18. Rejection Region
• In testing a hypothesis, the researcher decides the level of
significance to be used. The gravity of the type I error will be
the basis for the level to be used. Selecting a critical value
from a table, given the appropriate test, will then follow.
• The critical value determines the critical and non-critical
regions. The symbol for critical value is C.V. Critical values
had to be computed by remarkably brilliant people like Fisher.
His tables for particular probability values (.05, .02 and .01)
led to a trend that state test statistics as being significant in
today’s well-known p < .05 and p < .01.
23. Type I and Type II Errors
• The hypothesis testing procedure has four possible
outcomes since the null hypothesis (H0) may be true or
false, and the decision to reject or accept it is based only
on the statistics taken from samples. As a result, there are
two possibilities for a correct decision and two possibilities
for an incorrect decision, as illustrated below.
