One-way ANOVA
        Introduction
        •   We will introduce the one-way ANOVA (ANalysis Of VAriance) 
            method, in particular we will:
             •  Learn when we can use ANOVA
             •  Learn the assumptions under which we can use ANOVA
             •  Learn how to use ANOVA in real applications
        •   This presentation is intended for students in initial stages of 
            Statistics. No previous knowledge is required.
                                                                                        2
                One-way ANOVA
       • The t-test is used to compare the means of two-
        groups.
       • One-way ANOVA is used to compare the means of 
        two or more groups.
       • We can use one-way ANOVA whenever the 
        dependent variable (DV) is numerical and the 
        independent variable (IV) is categorical.
       •The independent variable in ANOVA is also called 
        factor. 
                                                                          3
                         Examples
    The following are situations where we can use 
    ANOVA:
    • Testing the differences in blood pressure among 
      different groups of people (DV is blood pressure and 
      the group is the IV).
    • Testing which social media affects hours of sleep 
      (type of social media used is the IV and hours of 
      sleep is the DV).
    • Testing differences in SAT score among male and 
      female children (male/female is the DV and score is 
      the DV).
                                                                          4
     Assumptions of ANOVA 
     • The observations in each group are normally 
        distributed. 
          This can be tested by plotting the numerical variable      
     separately for each group and checking that they all have a 
     bell shape.
     Alternatively, you could use the Shapiro-Wilk test for 
     normality.
                                                                            5
     Assumptions of ANOVA 
     • The groups have equal variances.
     Similar to before, you can plot each of group separately and 
     check that they exhibit similar variability. 
     Alternatively, you can use Levene’s test for homogeneity.
     • The observations in each group are independent.
     This could be assessed by common sense looking at the study 
     design. 
     For example, if there is a participant in more than one group, 
     your observations are not independent.
                                                                           6