statistical analysis

statistical analysis

1. descriptive analysis

   • central tendency
     • mode
       • nominal
     • median
       • ordinal
     • mean
       • interval/ ratio
   • variability
     • frequency, range, SD

2. test for differences

   • one sample t test
     • compare the mean of the question answered by ONE group of subjects against a constant
       • M= , t df = , p value
       • H0: mean (male) = 3, H1: mean (male) > 3
   • independent samples t test
     • compared the mean of a question answered by TWO different groups of subjects on metric data
       • if p> 0.05, levene's test - equal variances assumed
         • (M female = , M male = , t df = p value)
         • H0: mean (male) = mean (female)
   • paired samples t test
     • compare TWO means of TWO different questions answered by the SAME group of subjects on metric data
       • H0: mean (1st time) = mean (2nd time), H1: mean (1st time) < mean (2nd time)
       • M july = , M feb =, tdf = , p value
   • ANOVA
     • compare the means of question answered by MORE THAN TWO different groups on metric data
       • H0: mean (G1) = mean (G2) = mean (G3), H1: at least one group's mean is different
         • if p> 0.05 - equal variances assumed, H1 is accepted, continue with post-hoc analysis, check p value in the "test for homogeneity of variance" table,
           • p> 0,05 - equal variance assumed
             • tukey or bonferroni
           • p< 0.05, equal variance not assumed
             • games-howell
           • check p value in "multiple comparisons" table
             • p< 0.05
               • significant difference between compared paired of means
         • F(df between groups, df within groups) = , p value, further, tukey/games-howel post-hoc analysis shows that... (compare means of different groups)

3. test for associations

   • 3. presence of association
   • 2. direction of association
   • 1. strength of association
   • chi-square analysis
     • DOES NOT measure strength and direction
     • 2 nominal variables
     • H0: there is no association between the 2 variables
     • results are invalid when >20% of the cells have an expected count of <5
       • if > - regroup/ merge categories
     • chi square symbol(df, sample size)= , p value, report % of each category/variable
   • spearman rank ORDER correlation
     • measure strength and direction
     • at least 1 is ORDINAL
     • H0: there is no correlation between the 2 variables
     • correlation coefficients
       • weak (0.21-0.40), moderate (0.41-0.60), strong (0.61-0.80), very strong (0.81-1)
   • pearson product moment correlation coefficient
     • strength and direction
     • 2 INTERVAL/ RATIO
     • H1: there is a positive correlation between the 2 variables

4. regression analysis

   • bivariate regression
     • linear relationship between an interval/ ratio scaled IV and an interval/ ratio scaled DV
     • unstandardised coefficient - strength of r/s between x and y
     • R^2
       • how well the regression line matches the real data points, shows the % of variance in the DV explained by the IV
     • B= , p value
     • H0: b1=0, b1~= 0
   • multiple regression
     • linear relationship
       • multicollinearity
         • when IVs are moderately or highly correlated
         • consequences
           • hard to detect the effect of individual IVs, unstable prediction eqn
         • detection
           • tolerance stat <= 0.10 - smaller values indicate multicollinearity
           • VIF >= 5 - larger values indicate multicollinearity
       • check collinearity stats in coefficients table, check p value in ANOVA table, if p<0.05, check STANDARDISED coefficient for dir and strength of r/s, R^2 ADJUSTED
         • beta= , p value
       • dummy variables
         • include nominal/ ordinal, choose base category, dummy var coded 1 / 0
     • overall mode testing - H0: b1=b2=b3... bi = 0, H1: at least one b ~= 0
       • if p < 0.05, statistically sig - at least 1 IV explains DV
   • assumptions
     • DV are measured with interval/ ratio scales
     • variables are normally distributed
     • assume linear relationship between IV and DV
     • error terms are normally distributed and independently distributed