Basic guidelines regarding statistical tests ChiSquare

1
Basic guidelines regarding statistical tests
(Chi-Square)

• If you want to know if theres a relationship
  between two categorical variables (with two of
  more levels each) the appropriate test is a
  chi-square.
• Examples
• Is there a relationship between gender and hair
  color?
• Is there a relationship between state of
  residence and whether or not one is married or
  unmarried?
• Is there a relationship between make of car one
  drives and ethnicity?
• Ho is that there is no relationship between the
  two variables while Ha is that there is a
  relationship.
• Interpretation
• If the calculated chi-square exceeds the critical
  value of the chi-square or if the associated p
  value is less than alpha (in our class were
  using .05 for alpha), you would conclude that Ha
  is supported and that there is a significant
  relationship.

2
Basic guidelines regarding statistical tests
(Ttest)

• If you want to know if theres a difference
  between two groups (a categorical variable with
  exactly two levels) on a continuous variable the
  appropriate test is a ttest.
• Examples
• Is there a difference between men and women in
  terms of how many hours per week they devote to
  housework?
• Is there a difference between whether one is in
  management or not and how satisfied one is with
  the job (measured continuously)?
• Do individuals who have at least one month of
  vacation per year have lower blood pressure than
  those who have less than one month of vacation
  per year?
• Ho is that there is no difference on the
  continuous variable between the two groups while
  Ha is that there is a difference (two-tailed
  test) or that one group is greater than the other
  (one-tailed test).
• Interpretation
• Initially test for whether the variances are
  equal. If the p lt .1 use the ttest for unequal
  variances else use the ttest for equal variances.
• If the absolute value of the calculated t
  statistic exceeds the critical value of the t
  statistic or if the associated p value is less
  than alpha (in our class were using .05 for
  alpha), you would conclude that Ha is supported
  and that there is a significant difference.

3
Basic guidelines regarding statistical tests
(one-way or single-factor ANOVA)

• If you want to know if theres a difference
  between groups (a categorical variable with more
  than two levels) on a continuous variable the
  appropriate test is a one-way ANOVA.
• Examples
• Is there a difference between people in
  managerial, professional, and blue collar
  occupations in terms of how many hours per week
  they devote to housework?
• Is there a difference between individuals less
  than 30 years old, individuals between 30 and 50,
  and individuals over 50 in job satisfaction
  (measured continuously)?
• Do average household income levels vary depending
  on state of residency?
• Ho is that there is no difference on the
  continuous variable between the groups while Ha
  is that there is a difference.
• Interpretation
• If the p value value associated with the one-way
  ANOVA is less than alpha (in our class were
  using .05 for alpha), you would conclude that Ha
  is supported and that there is a significant
  difference.

4
Basic guidelines regarding statistical tests
(correlation)

• If you want to know if theres a relationship
  between two continuous variables the appropriate
  test is a correlation.
• Examples
• Is there a relationship between age and income?
• Is there a relationship between number of years
  of education and cholesterol level?
• Is there a relationship between number of close
  friends an individual reports having and number
  of days work is missed per year?
• Ho is that there is no relationship between the
  two continuous variables while Ha is that there
  is a relationship (either positive or negative).
• Interpretation
• If the p value value associated with the
  correlation coefficient is less than alpha (in
  our class were using .05 for alpha), you would
  conclude that Ha is supported and that there is a
  significant relationship. NOTE To get the p
  value in Excel, you must use the regression test
  the correlation test does not return the
  associated p value.

5
Basic guidelines regarding statistical tests
(simple linear regression)

• If you have two continuous variables and 1) one
  of the variables can be considered the dependent
  variable and the other can be considered the
  independent variable, and 2) you are interested
  in prediction, the appropriate analysis is simple
  linear regression.
• Examples
• Is income predicted by the number of years of
  education one has?
• Is the demand for new dishwashers in a year
  predicted by the average age of installed
  dishwashers?
• Is the price of a stock predicted by the general
  move of the stock market as measure by the
  Russell 5000?
• Ho is that the model (the independent variable is
  predictive of the dependent variable) is not
  significant while Ha is that the model is
  significant.
• Interpretation
• If the p value value associated with the model is
  less than alpha (in our class were using .05 for
  alpha), you would conclude that Ha is supported
  and that the model is significant.
• You would also want to look at the values for r
  square that expresses the percentage of variation
  in the dependent variable that is accounted for
  by the independent variable. And if the model is
  statistically significant, youd normally be
  interested in developing the prediction equation
  in the form Y a bX.

6
Basic guidelines regarding statistical tests
(multiple regression)

• If you have more than two continuous variables
  and 1) one of the variables can be considered
  the dependent variable and the others can be
  considered as independent variables, and 2) you
  are interested in prediction, the appropriate
  analysis is multiple regression.
• Examples
• Is income predicted by the number of years of
  education one has and age?
• Is the demand for new dishwashers in a year
  predicted by the average age of installed
  dishwashers, the number of new housing starts,
  and the unemployment rate?
• Is the price of a stock predicted by the general
  move of the stock market as measure by the
  Russell 5000, the stocks price/earnings ratio,
  and earnings per share?
• Ho is that the model (the independent variables
  are predictive of the dependent variable) is not
  significant while Ha is that the model is
  significant.
• Interpretation
• If the p value value associated with the model is
  less than alpha (in our class were using .05 for
  alpha), you would conclude that Ha is supported
  and that the model is significant.
• You would also want to look at the value for r
  square that expresses the percentage of variation
  in the dependent variable that is accounted for
  by the independent variables. And if the model
  is statistically significant, youd normally be
  interested in developing the prediction equation
  in the form (for two independent variables) Y a
  bX1 bX2. Finally, and only if the model is
  significant, youd interpret the significance
  level of each of the independent variables.

7
Basic guidelines regarding statistical tests
(other tests)

• If you have a categorical dependent variable with
  two levels and one or more continuous independent
  variables youd use logistic regression or probit
  or some similar technique.
• If you have a continuous dependent variable and a
  combination of continuous and categorical
  independent variables one technique that would be
  appropriate would be dummy variable regression.
• If you have a continuous dependent variable and
  more than one categorical independent variable
  youd use analysis of variance (ANOVA) or dummy
  variable regression.