Quant: Variances

When looking at the performance of two groups on a given task, one speaks of two kinds of variance (between-groups and within-groups). What does each represent?

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Variance is considered as measures of average dispersion (Field, 2013; Schumacker, 2014).  Variance is a numerical value that describes how the observed data values are spread across the data distribution and how they differ from the mean on average (Huck, 2011; Field, 2013; Schumacker, 2014).  The smaller the variance indicates that the observed data values are close to the mean and vice versa (Field, 2013). What happens when researchers want to study if the difference between two means from two groups of data is statistically significant from each other? Researchers could use ANOVA, which is an analysis of variances that test whether or not to reject the null hypothesis of the mean of one group is equal to the mean of another group (Huck, 2011; Schumacker, 2014).  ANOVAs usually test categorical independent variables (groups) and continuous dependent variables (Creswell, 2014).  One of the results of a one-way analysis of variance presents in a table the variance between groups and within groups (Huck, 2011).  Schumacker (2014), explained that the variance between groups indicates the variation between the overall grand mean of the groups, while variance within the groups indicates the variance within the means of the groups.  The variances between groups have a degree of freedom equal to the number of groups analyzed – 1, whereas the variance within the groups has a degree of freedom equal to the number of data points within each group – 1 – the number of groups (Huck, 2011).  Information from within and between the groups are used to calculate the F-statistic to establish statistical significance which can allow the researcher to reject or fail to reject their null hypothesis (Field, 2013; Huck, 2011; Schumacker, 2014).

References

  • Creswell, J. W. (2014) Research design: Qualitative, quantitative and mixed method approaches (4th ed.). California, SAGE Publications, Inc. VitalBook file.
  • Field, A. (2013) Discovering Statistics Using IBM SPSS Statistics (4th ed.). UK: Sage Publications Ltd. VitalBook file.
  • Huck, S. W. (2011) Reading Statistics and Research (6th ed.). Pearson Learning Solutions. VitalBook file.
  • Schumacker, R. E. (2014) Learning statistics using R. California, SAGE Publications, Inc, VitalBook file.

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