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Hypothesis Testing for SPSS

Hypothesis Testing for SPSS

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    Hypothesis testng Hypothesis testng Presentation Transcript

      • 1. T-test : Difference in means
      • to test the statistical significance in the difference in means
      • ex . income by gender, the num. of years at work by gender
      • 2. T-test : Difference in proportions
      • to test the statistical significance in the difference in proportions
      • ex . the proportion employed in government jobs by gender
      • 3. Contingency Table/Chi-Square Analysis
      • to test whether all categories contain the same proportion of values or not by comparing expected and actual values.
      • ex . the proportion employed in government jobs by gender
      Hypothesis Testing
      • 1. A Research Question
      • 2 . The Null Hypothesis
      • usually assumes NO difference 2 tailed-test
      • 3 . Select Cases
      • 4 . T-test or Contingency/Chi-Square Analysis
      • 5 . Interpret Test Results
        • t-score, significance level, confidence interval,
      • likelihood ratio (for Chi-Square Analysis)
      • 6 . “ Reject ” or “ Not reject ” the null hypothesis
      Hypothesis Testing Procedure
      • Research Question : Are there differences in income between male and female graduates and if so, what factors might explain this difference?
      • 1 . Is there a difference in average income between male and female graduates?
      • 2 . Is there a significant difference in average length of time on the job, between male and female graduates?
      • 3 . Is there a difference in the proportion employed in government jobs between males and females?
      Hypothesis Testing
      • Research Question :
      • Is there a difference in average income between male and female graduates?
      • H 0 : There is NO difference in average income between male and female graduates
      • Note : Limit the data to full-time employees or self- employed with income more than $20,000 and less than $400,000.
      1 . T-test : Difference in Means
    • Step 1 : Data/Select Cases
      • Select Data/Select Cases
    • Data/Select Cases
      • In a Select Cases dialogue box, you specify logical expressions to select cases.
        • Select the “ If condition is satisfied ” option
        • Click on the If… button
    • Data/Select Cases Specifying fullself and income range Type logical expression: fullself = 1 & income > 20000 & income < 400000 to limit cases to alumni who work full-time or are self-employed and make more than $20,000 and less than $400,000.
    • Data/Select Cases
    • Data/Select Cases
    • Step 2 : Independent T-Test Analyze/Compare Means/Independent-Samples T-Test
    • Step 2 : Independent T-Test income gender(? ?)
    • Step 2 : Independent T-Test Group 1: 1 for Female Group 2: 2 for male Note : The grouping variable can only have two categories.
    • Step 2 : Independent T-Test gender(1 2)
    • T-test : Results
      • Using the Unequal Variance model , we REJECT H 0 and conclude that there is a significant difference in average income between male and female graduates.
      >-1.96 < 0.05 -18,738 Doesn’t include 0
      • Possible explanation for the difference in income :
      • Male income is higher because men have been on the job longer than women.
      • Research Question :
      • Is there a difference in average length of time on the job (YEARS) between male and female graduates?
      • H 0 : There is NO difference in length of time on the job between male and female graduates
      1-2 . T-test : Difference in Means
    • Step 2: Independent T-Test Analyze/Compare Means/Independent-Samples T-Test
    • Step 2: Independent T-Test Years at Current Position [years] gender(1 2)
    • T-test: Results
      • Using the Unequal Variance model, we REJECT H 0 and conclude that there is a significant difference in average length of time on the job between male and female graduates.
      Does not include 0 >-1.96 < 0.05 -1.752
      • Possible explanation for the difference in income : Male income is higher because more females work for government than males.
      • Research Question :
      • Is there a difference in the proportion employed in government jobs between male and female graduates?
      • H 0 : There is NO difference in the proportion employed in government jobs between male and female graduates
      2 . T-test: Difference in Proportions
      • Create a new variable GOV that
        • has the value 1 if the EMPLOYER (1-6) indicates the alumnus works for a government organization.
        • has the value 0 if the EMPLOYER is not 1-6.
      • 1. Use Transform/Compute to convert the EMPLOYER variable into a new categorical variable GOV.
      • 2. Use Transform/Recode/Into Different Variables to create a new categorical variable GOV.
      Step 1: Create a new variable (GOV)
    • OUTPUT: Analyze/Descriptive Statistics/Frequencies 7-11 Private Missing Values 1-6 Government
    • Transform/Recode/ Into Different Variables
    • Transform/Recode/ Into Different Variables Select the income variable, type “GOV”, click the “Change” button, click the “Old and New Values” button…
    • Transform/Recode/ Into Different Variables
    • Transform/Recode/ Into Different Variables
    • Transform/Recode/ Into Different Variables
    • Transform/Recode/ Into Different Variables
    • Transform/Recode/ Into Different Variables Save the data file!!
      • Analyze/Descriptive Statistics/Frequencies
      Step 2: Create a frequency table for GOV Thirty five percent of the graduates employed full time or self-employed and making more than $20,000 and less than $400,000 work in government jobs.
    • Step 2: Independent T-Test Analyze/Compare Means/Independent-Samples T-Test
    • Step 2: Independent T-Test gov gender(1 2)
    • T-test: Results
      • Using the Unequal Variance model, we CANNOT REJECT H 0 and cannot conclude that there is a significant difference between male and female graduates with respect to the proportion working in the government sector.
      <-1.96 > 0.05 Includes 0
    • 3. Contingency Table/ Chi-Square Analysis
      • The same question can be analyzed by a contingency table with GOV and GENDER and testing using the Chi-Square statistic.
      • H 0 : There is NO relationship between employment sector and gender.
    • Analyze/Descriptive statistics/Crosstabs
    • Analyze/Descriptive statistics/Crosstabs Counts : Observed Percentages : Row Column Select “ gov ” for “ Row ” & “ Gender ” for “ column .”
    • Contingency table Analyze/Descriptive statistics/Crosstabs
    • Contingency table Analyze/Descriptive statistics/Crosstabs Chi-Square value = 0.032 < 3.84 (1.96 2 = Cutoff value at 95% confidence level at 1 df). We CANNOT REJECT the null hypothesis and cannot conclude there is a statistically significant relationship between gender and whether or not a person works for the government. > 0.05 < 3.84 > 0.05
    • OUTPUT: Analyze/Descriptive Statistics/Frequencies Missing Values 7-11. Private
    • 3-2. Contingency Table/ Chi-Square Analysis
      • How about analyzing the difference in the proportion of males and females in the private sector by a contingency table with PRIVATE and GENDER.
      • H 0 : There is NO relationship between employment sector and gender.
      • Create a new variable PRIVATE that
        • has the value 1 if the EMPLOYER ( 7-11 ) indicates the alumnus works for a government organization.
        • has the value 0 if the EMPLOYER is not 7-11 (else) .
      • Method 2 .
      • Use Transform/Recode/Into Different Variables to create a new categorical variable PRIVATE.
      Step1: Create a new variable (PRIVATE)
    • Analyze/Descriptive statistics/Crosstabs Counts: Observed Percentages: Row Column Select “ private ” for “ Row ” & “ Gender ” for “ column .”
    • Contingency table Analyze/Descriptive statistics/Crosstabs
    • Contingency table Analyze/Descriptive statistics/Crosstabs Chi-Square value = 2.411 < 3.84 (1.96 2 ). We CANNOT REJECT the null hypothesis and cannot conclude that the difference in the proportion of males and females in the private sector is statistically significant . < 3.84 > 0.05
      • The degrees of freedom in the chi-square test of a contingency table:
      • d.o.f = (r-1)*(c-1)
      • where
      • r & c are the number of rows and columns (or the number of categories of two variables) in a table.
      • The number of d.o.f is the number of comparisons between actual and expected frequencies minus the number of restrictions imposed on these frequencies.
      • Since the number of cells in a contingency tables is r*c, there are r*c actual frequencies to be compared with the corresponding expected frequencies. Because the sum (total) of the frequencies in each row and each column are given, there are r+c-1 restrictions.
      • Therefore, the number of d.o.f is: r*c - (r+c-1) = (r-1)*(c-1).
      The degrees of freedom in the chi-square test
      • What other factors may influence income?
      • Control for job sector (government, private, non-profit), and examine a difference in average income between males and females within each sector.
        • Select cases: Data/Select Cases
        • if STATUS =1 & INCOME >20000 & INCOME > 400000 & GOV = 1
        • if STATUS =1 & INCOME >20000 & INCOME > 400000 & PRIVATE = 1
        • Compare means/Independent Sample T-test
      • If we see differences within each sector, other factors besides job sector are influencing income.
      Extensions to the Analysis