INTRODUCTION TO INFERENTIAL
STATISTICS
INFERENTIAL STATISTICS

Statistical techniques used to make generalizations
from samples to populations through drawing
inferences from the existing data


to reach conclusions that extend beyond the immediate
data alone
2 types


Estimation
Hypothesis Testing (Hyp Test)
HYPOTHESIS TESTING – STATING THE
HYPOTHESIS

Null Hypothesis (Ho)




States that there is NO relationship and/or NO difference
between the variables
Statement of equality
States that the findings are due to error; purely chance
Examples (also see Table B4 Handout from Class)
Ho :Sleep deprivation has no effect on performance.
 Ho : There is no relationship between reaction time and
problem-solving ability
 Ho : There is no difference in the average score of 9th graders
and the average score of 12th graders on a depression scale.

STATING THE HYPOTHESIS

Research (Alternative) Hypothesis (Ha) or (H1)

States that there IS a relationship and/or there IS a difference
between the variables

Due to a real effect plus chance variation
Can be one or more than one (Ha)
 Statements of inequality
 Can be directional (one-tailed) or non-directional (two-tailed)


Examples
Ha :Sleep deprivation has an effect on performance.
 Ha : There is a direct relationship between reaction time and
problem-solving ability
 Ha : The average score of 9th graders is higher than the
average score of 12th graders on a depression scale.

TYPE I AND II ERRORS

Type I


Reject the Null when the Null is true
Type II

Accept the Null when the Alternative is true
True States
Ho
Accept
Ho
No Error
Reject Ho Type I
Ha
Type II
No Error
True States
No Fire
Fire
No Alarm No Error
Type II
Alarm
No Error
Type I
TYPES OF ERRORS IN HYP. TESTING
HOW INFERENCE WORKS

The researcher selects representative samples of
2 groups of subjects/objects

samples are representative of the population from
which they are chosen
Each subject/object is subjected to some type of
treatment/test and data is collected to be
compared
 A conclusion is made as to whether or not the
difference/lack there of, is due to error
 Generalizations are made back to the population

HYPOTHESIS TESTING

Steps in Hypothesis Testing

State the Hypotheses
State the Null Hypothesis
 State the Research (Alternative) Hypothesis

Choose and compute (from raw data) the appropriate Test
Statistic
 Determine the value needed to reject the Null (from a critical
value chart)
 Compare the obtained value and the critical value
 Make a decision and state the conclusion

HYPOTHESIS TESTING - REGRESSION
Looking at the relationship between the quality
of marriage and the quality of the parent/child
relationship
 State the Hypotheses


State the null hypothesis


State the research hypothesis


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Ho: Pxy = 0 There is no relationship between quality of
marriage and quality of the parent/child relationship.
H1: Pxy ≠ 0 There is a relationship between quality of
marriage and quality of the parent/child relationship.
Two tailed test
Compute the appropriate test statistic

Can use sample r value as test statistic by comparing
it to critical values chart (Table B4)

Or can follow Flow Chart – t Test
CHOOSING THE APPROPRIATE TEST STATISTIC
Each Ho has an associated test statistic
F-test
F-test
CHOOSING/COMPUTING
TEST STATISTIC
THE
APPROPRIATE
SET THE APPROPRIATE THRESHOLD

Once the appropriate test statistic type is chosen,
the value is computed based on the data collected

rxy = .393

Computed from the data in Table B4 Handout
Referred to as the Obtained Value
 Set the appropriate threshold (α)
 The value that the p-value must be below in
order for the findings to be statistically
significant
 Based on industry standards/previous research
 Typically never above .05


For this course, our threshold value will be α = .05
HYPOTHESIS TESTING - REGRESSION

Determine the critical value
Value needed to reject the Null Hypothesis
 Located from Critical Value charts or software packages
 Must know the threshold and df, and tailed-ness (one/two)


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threshold value α = .05
Determine the degrees of freedom (df)
Approximates the sample size
 Different for each test statistic
 For our test statistic, df = n-2 (n = 29)
 df = 29-2
df = 27


Using the α and df and two-tailed, to find the critical r
value in the chart
Two tailed , α =.05, df = 30 as it is the closest next highest value to
our df
 Critical r value = .349
