Testing Your Hypothesis

1
Testing Your Hypothesis

• In your previous assignments you were supposed to
  develop two hypotheses that examine a
  relationship between two variables.
• For example
• The researcher wishes to determine if there is a
  significant relationship between the age of the
  worker and the number of repetitive strain
  injuries they have had over the past year.
• In your final portion of the project, you will be
  testing your hypotheses to see if there are
  significant relationships between variables in
  your study.

2
Null and Alternative Hypotheses

• The Null Hypothesis states There is no
  significant relationship between ..
• Represented by H0
• The Alternative Hypothesis states the opposite or
  There is significant relationship between.
• Represented by H1

3
Testing Research Hypotheses

• When testing a research hypothesis statistically,
  we go at it somewhat backwards.
• Using the blue block hypotheses
• Null Hypothesis There is no significant
  relationship between .
• Alternative Hypothesis There is a significant
  relationship between .
• The statistical procedure really tests if the
  null hypothesis is true or not.

4
Testing the Hypothesis

• Null Hypothesis There is no significant
  relationship between .
• Alternative Hypothesis There is a significant
  relationship between .
• If our statistical is significant, we reject the
  null hypothesis and accept the alternative.
• If our statistical is not significant, we accept
  the null hypothesis.

5
Hypothesis Testing Process

• In order to statistically prove the relationship
  exists, we are really proving because the
  statement There is no significant relationship
  between . is false, the alternative statement
  There is a significant relationship between .
  must be true.

6
Hypothesis Testing for a Correlation

• Using a problem statement where you are testing
  for a relationship between two variables, the
  following process is followed
• The researcher wishes to determine if there is a
  significant relationship between the age of the
  worker and the number of repetitive strain
  injuries they have had over the past year.
• Null Hypothesis There is no significant
  relationship between the age of the worker and
  the number of repetitive strain injuries they
  have had over the past year.
• Alternative Hypothesis There is a significant
  relationship between the age of the worker and
  the number of repetitive strain injuries they
  have had over the past year.

7
Correlation Coefficients

• For Pearson, Point Biserial, and Spearman
  Correlations
• First calculate what your correlation coefficient
  (r) is
• Next, use a t-test to determine if the
  correlation coefficient is equal to zero or not.
• Remember correlation coefficients (r) can range
  from -1.00 to 1.00 with 0 representing no
  correlation present
• If we prove our r is not equal to 0 (no
  correlation exists), then a significant
  correlation must exist
• For Phi and Chi Squared procedures
• Use a Chi-square distribution and you will
  compare your obtained Phi or Chi Squared result
  to a cutoff score on the Chi Squared Table

8
Hypothesis Testing for a Correlation

• H0 There is no significant relationship between
  the age of the worker and the number of
  repetitive strain injuries they have had over the
  past year.
• When it is time to run the correlation procedure
  (i.e. Pearson Correlation, we are testing r0)
• H1 There is a significant relationship between
  the age of the worker and the number of
  repetitive strain injuries they have had over the
  past year.
• When it is time to run the correlation procedure
  (i.e. Pearson Correlation, we are testing r ? 0)

9
Testing the Correlation Procedure

• For Pearson, Point Biserial, Spearman Rank
• To determine if your correlation coefficient is
  significant, you will be using a t-test to do so
• Review Module 6 on how to run this test and
  determine significance
• Null Hypothesis r 0
• Alternative Hypothesis r ? 0

10
Alpha Level

• You will be using an Alpha level .05 in your
  significance tests
• You will be taking a 5 chance of committing a
  Type I error
• You will be taking a 5 chance of saying a
  significant correlation exists when it really
  doesnt

11
Dependent Variable Independent Variable Test
Interval or ratio Interval or ratio Pearson's
Ordinal Ordinal Spearman Rank Order
Dichotomous Dichotomous Phi Coefficient
Interval Categorical Eta Coefficient
Interval Dichotomous Point Biserial
Categorical Categorical Chi Squared
Ordinal or ratio Categorical Mann-Whitney
Ordinal Categorical Gamma
12
Examples

• In Module 6, you will find examples of the
  various correlation procedures
• You should know by now which correlation
  procedure you should be using for your project.
• If you determined you need to run either Eta,
  Gamma, or Mann-Whitney
• Due to the complexity of the math required to run
  these procedures by hand, you will need to recode
  your continuous variable into a categorical
  variable and use Chi-Squared

13
Recoding a Variable

• Lets say you collected your dependent variable
  as a ratio format variable and you need to recode
  it into a categorical variable
• You asked the subjects How many days have you
  missed from work over the past year? and they
  wrote in the number of days.
• Set up categories such as
• 0-2 days
• 3-5 days
• 6-8 days
• 9 or more days
• For those that wrote in 0, 1, or 2 days, they
  will be assigned to the first category
• For those that wrote in 3, 4, or 5 days, they
  will be assigned to the second category
• And so on