Chapter 7 & 9 (4.1):
Descriptive Statistics
❖Describes a sample’s characteristics
❖Descriptive statistics describe the data, but can not make
any conclusions
Inferential Statistics
❖Used to infer something about the population based on the
sample’s characteristics.
❖Inferential statistics draw conclusions about the data. Can
determine whether or not one variable causes an effect in
another.
How Inferences Work
1. A claim is made (hypothesis)
2. A sample representative of the population is chosen
3. A test is given, and results are computed and compared
4. A conclusion is reached as to whether the scores are
statistically significant
5. Based on the results of the sample, an inference is made
about the population
Hypothesis
❖A hypothesis is a statement about the value of a
populationparameter or a population model
❖We want to decide whether the hypothesis is true or false
❖It's an educated guess
❖Translates the problem or research statement into a form
that can be tested
❖There are two different types of hypothesis
➢Null Hypothesis
➢Research (Alternative) Hypothesis
❖Cations:
➢Before you make a hypothesis, you have to clearly
identify the question that you are interested in
studying
➢A hypothesis is not the scientific question
➢It is an educated testable prediction about what will
happen
➢It predicts cause and effect
➢Answering some research questions may require multiple
hypothesis and/or multiple experiments
❖Creating a hypothesis:
1. Brief and to the point
2. Stated in declarative form rather than a question
3. Defines expected relationship between variables
4. Reflects theory or literature on which it is based
(consistent with data)
5. Testable includes variables that can be measured
Null Hypothesis
❖Two or more variables are equal to one
another
➢No effect on the experiment
❖Written as H 0
❖Starting point for research
❖Status quo
❖Assume it to be true
❖Benchmark to compare the actual outcomes
Research Hypothesis
❖Known as alternative or alternate hypothesis
❖A relationship between two variables
➢There will be an effect on
the experiment
❖Can be written as H or Hₐ ₁
❖Can be …
Directional
■ Direction of
difference is
specific
■ One-tailed test
■ Includes a < or > in the numeric statement
➢Non-Directional
■ Reflects differences, not direction
specific
■ Two-tailed test
■ includes a ≠ in the numeric
statement
❖3 types of equations
➢(not equal) = H 1: μ 1/ μ 2
➢(greater than) H 1: μ 1> μ 2
➢(less than) H 1: μ 1< μ 2
Rejection Regions
Region of rejection
➢Represents the values of a
statistic whose combined
probability is low enough that
we could reject H 0
Region of non-rejection
➢Represents the values whose
probability is not low enough
to allow us to reject H 0
Notes
❖Significance level is represented by
➢Alpha = α
❖Entire Curve - represents all possible outcomes from a null
hypothesis
❖Low probability
➢Critical Value(cv) - The point beyond which the
obtained outcomes are judged to be so rare that we
conclude the outcome is not due to chance
■ If the obtained value is more extreme than
critical value, we reject the null hypothesis
■ If the obtained value is less extreme than the
critical value, we fail to reject the null
hypothesis
➢P-Value - Probability of obtaining an effect as
extreme as your test statistic, if the null hypothesis
is true (p < 0.05 (%5))
■ If the p-value is less than the level of
significance, we reject the null hypothesis
■ If the p-value is greater than the level of
significance, we fail to reject the null
hypothesis
■ If p is low, the null most go!
➢When making conclusions we’ll only or reject fail to
reject the null hypothesis, we’ll never accept the
null
➢If the p-value is greater than the level of
significance, we will the null fail to reject
hypothesis
➢If the p-value is less than or equal to the level of
significance, then we the null hypothesis and reject
conclude that the test is statistically significant at
that level of significance
➢
Significance Test
❖Comparing p-value to significance level
❖Comparing test statistic to significance level
Statistical Significance
❖Comparing significance level (alpha) to p-value
❖Comparing test statistic to critical level
❖Gives you evidence to reject the null hypothesis
❖Probability that our findings would occur if the null
hypothesis is true
Clinical Significance
❖Known also as clinical importance, practical significance,
or meaningful
❖Is concerned with whether or not the effect seen is enough
to alter practice
❖This is a matter of judgment
❖Large effect sizes may indicate clinical significance
Statistical Vs. Clinical Significance
❖A study can be statistically significant but not very
meaningful
❖Statistical significance can be interpreted only in terms
of the context in which it occurred
❖Statistical significance should not be the only goal of
scientific research
❖Statistical significance is influenced by sample size
➢The larger the sample, the more likely you will find a
significant result of some kind
Factors:
❖Sample size
➢Larger samples make it
more likely that we can
reject H 0
❖Alpha
➢The smaller the value
of,the more difficult it
is to reject H 0
❖Nondirectional hypotheses
have regions of rejection
inboth extremes of the
distribution, and are called
two-tailed
❖Directional hypotheses
have a region of rejection
only one extreme of the
distribution, and are
called one-tailed
