Statistical Significance

1
Statistical Significance

• Mathematical differences
• The numbers themselves are not exactly the same
• Statistical significance
• A particular difference is large enough to be
  unlikely to have occurred due to chance or
  sampling error
• Managerially important differences
• The difference is large enough to matter from a
  managerial perspective

2
Stating the Hypothesis

• The null hypothesis (HO) is the hypothesis that
  is tested against its complement, the alternative
  hypothesis (HA).
• HO can also be called the hypothesis of the
  status quo
• The hypotheses must be stated so that both cannot
  be true
• Often, we are interested in the alternative
  hypothesis (the research hypothesis of interest)

3
Structure of Hypotheses with an IV and DV
Ho Independent Variable (IV) Dependent Variable
(DV) ? Independent Variable (IV)
Dependent Variable (DV) Ha Independent
Variable (IV) Dependent Variable (DV) ?
Independent Variable (IV) Dependent Variable (DV)
Ho Mac users attitude toward personal computer
security ? Window users attitude toward
personal computer security Ha Mac users
attitude toward personal computer security ?
Window users attitude toward personal computer
security
Possible Independent Variables (IV) Gender Age In
come Usage rate
Possible Dependent Variables (DV) Attitudes
towards constructs of interest Proportion who
buy Proportion who visit Proportion who are heavy
users
4
Example Hypothesis
Ho Womens attitude toward the ease of use of
DVRs ? Mens attitude toward the ease of use of
DVRs Ha Womens attitude toward the ease of
use of DVRs ? Mens attitude toward the ease of
use of DVRs
Construct (DV) attitude toward the ease of use
of DVRs
Strongly Strongly
Disagree
Agree Recording shows on a DVR will be much
easier 1 2 3 4 5
6 7 than recording shows on a
VCR. Installing a DVR in my home will make using
1 2 3 4 5
6 7 my other TV related electronics more
difficult. Learning how to use the features of a
DVR 1 2 3 4
5 6 7 would be time consuming.
IV Gender
5
Turbo Example
Ho Turbo Users attitude toward the speed of the
swimwear ? Turbo Non-Users attitude
toward the speed of the swimwear Ha Turbo
Users attitude toward the speed of the swimwear
? Turbo Non-Users attitude toward the
speed of the swimwear
Ho Womens attitude toward swimwear
affordability ? Mens attitude toward swimwear
affordability Ha Womens attitude toward
swimwear affordability ? Mens attitude toward
swimwear affordability
Ho Turbo Users under 25 years old attitude
toward speed of the swimwear ?Turbo Users 25 and
over attitude toward speed of the swimwear Ha
Turbo Users under 25 years old attitude toward
speed of the swimwear lt Turbo Users 25 and over
attitude toward speed of the swimwear
6
Hypothesis Tests

• One-tailed tests are used when you believe that
  the alternative hypothesis can only go in one
  direction from the null hypothesis
• HA is stated as less than or greater than
• Ho Turbo Users attitude toward the speed of the
  swimwear ? Turbo Non-Users attitude toward the
  speed of the swimwear
• Ha Turbo Users attitude toward the speed of the
  swimwear ? Turbo Non-Users attitude toward the
  speed of the swimwear

7
Hypothesis Tests

• Two-tailed tests are used when the alternative
  hypothesis could go either way
• HA is stated as not equal
• Ho Turbo Users attitude toward the speed of the
  swimwear Turbo Non-Users attitude toward the
  speed of the swimwear
• Ha Turbo Users attitude toward the speed of the
  swimwear ? Turbo Non-Users attitude toward the
  speed of the swimwear

8

• An industrial marketing firm is considering the
  introduction of a new servicing plan for
  hydraulic parts. The plan will be introduced if
  it is preferred by more than 40 of the customers

9

• A firm was considering introducing a new
  product, if it could be expected to secure more
  than 10 of the market.

10

• A researcher wants to determine whether the new
  service plan is different (superior or inferior)
  from the current plan, which is preferred by 40
  of the customers.

11
Type I Error

• Suppose Ho is true but the researcher concludes
  it is false and rejects the Ho. She has made a
  type I error.
• The significance level (a) associated with a
  statistical test indicates the probability with
  which a type I error may be made.
• Note the true situation regarding the Ho is
  always unknown to the researcher.
• Note because sample information will always be
  incomplete there will always be some a error.

12
Hypothesis Tests

• If we reject HO then we are accepting HA.
• When we fail to reject HO it means we do not
  have enough evidence to accept HA. However, we
  phrase our findings as failing to reject HO not
  as accepting HO.
• Two possible outcomes
• Reject the Ho
• Fail to reject the Ho

13
Hypothesis Tests

• Test Statistic Procedure
• Specify HO and HA
• Specify the level of a (probability of Type I
  error)
• Use the appropriate formula to calculate the
  value of the test statistic
• Compare the calculated value to the critical
  value in the appropriate table
• State the result in terms of either rejecting or
  failing to reject the null hypothesis

14
Hypothesis Tests

• Degrees of freedom (df) are the number of
  observations in a statistical problem that are
  not restricted or are free to vary.
• The number of degrees of freedom is equal to the
  number of observations minus the number of
  assumptions or constraints necessary to calculate
  a statistic.