Download Testing Hypotheses

Basic Research Designs
• Descriptive Designs:
– Descriptive Studies: thoroughly describe a single
variable in order to better understand it
– Correlational Studies: examine the relationships
between two or more quantitative variables as they exist
with no effort to manipulate them
• Inferential Designs:
– Quasi-Experimental Studies: make comparisons
between naturally-occurring groups of individuals
– Experimental Studies: make comparisons between
actively manipulated groups
Chain of Reasoning in Inferential Statistics
Random Selection
Population
With
Parameters
Sample
With
Statistics
Inference
Probability
Sampling
Distributions
Of the Statistics
Inferential Reasoning
• Population: group under
investigation
Random
Selection
Inference
• Sample: a smaller group
representing the population
– A sample that has been randomly
selected should be representative
of the population
Hypothesis Testing
• Hypothesis Testing: the process of using inferential
procedures to determine whether a hypothesis is supported
by the results of a research study
Hypothesis Testing
• Conceptual Hypothesis: a general statement
about the relationship between the independent and
dependent variables
• Statistical Hypothesis: a mathematical statement
that can be shown to be supported or not
supported. It is designed to make inferences about
a population or populations.
Hypothesis Testing
• In psychological research, no hypotheses can be proven to
be true.
• Modus Tollens: a procedure of falsification that relies on
the fact that a single observation can lead to the conclusion
that the premise or prior statement is incorrect
– Null Hypothesis (H0): statements of equality (no relationship; no
difference); statements of opposing difference
– Alternative (Research) Hypothesis (H1 or HA): a statement that
there is a relationship or difference between levels of a variable;
statements of inequality
Types of Research Hypotheses
• Nondirectional Research
Hypothesis: reflects a difference
between groups, but the direction of
the difference is not specified (twotailed test)
– H1: X ≠ Y
• Directional Research Hypothesis:
reflects a difference between groups,
and the direction of the difference is
specified (one-tailed test)
– H1: X > Y
– H1: X < Y
z = -1.96
p = .025
µ
µ
z = 1.96
p = .025
z = 1.645
p = .05
Rejecting the Null Hypothesis
• Alpha Level (α): the level of significance set by the
researcher. It is the confidence with which the
researcher can decide to reject the null hypothesis.
• Significance Level (p): the probability value used
to conclude that the null hypothesis is an incorrect
statement
– If p > α  cannot reject the null hypothesis
– If p ≤ α  reject the null hypothesis
Determining the Alpha Level
• Type I Error (α): the researcher
rejects the null hypothesis when in
fact it is true; stating that an effect
exists when it really does not
• Type II Error (β): the researcher
fails to reject a null hypothesis that
should be rejected; failing to detect
a treatment effect
Determining the Significance Level
(Probability)
• The distribution used to determine the probability of
a specific score (or difference between scores) is
determined by multiple factors.
• Regardless of the distribution used, the logic and
process used to determine probability is essentially
the same.
• All statistical distributions mimic the function of the
standard normal distribution.
The Normal Curve
•
Three Main Characteristics:
1. Symmetrical: perfectly
symmetrical about the mean;
the two halves are identical
2. Mean = Median = Mode
3. Asymptotic Tail: the tails
come closer and closer to
the horizontal axis, but they
never touch
The Normal Distribution and the Standard
Deviation
• In the normal distribution…
– 68% of scores fall between +/1 standard deviations
– 95% of scores fall between +/2 standard deviations
– 99.7% of scores fall between
+/- 3 standard deviations
• It is possible to determine the
probability of obtaining any
given score (or any
differences between scores).
The Normal Curve and Probability
•
•
•
The normal distribution is the
most commonly used
distribution in behavioral
science research.
The scores of variables can be
converted to standard z-scores,
which can be used to determine
the probability of a specific
score.
All probabilities are a number
between 0.0 and 1.0, and given
all possible outcomes of an
event, the probabilities must
equal 1.0.
µ
µ
z = 1.645
z = 1.645
z-scores
• z-score: represents the distance between an
observed score and the mean relative to the
standard deviation; a score on an assessment
expressed in standard deviation units
• Formula:
– z=X–M
s
– z=X–µ
σ
More Curves and Probability
µ
z = -1.645
p = .05
µ
z = 2.326
p = .01
µ
µ
z = 1.282
p = .10
z = 1.645
p = .05