Chapter 9 Stats

• Three Research Question Type:

  • Relationship
  • Difference
  • Prediction
• Data Type of Relationship:

  • Continuous - Parametric Assumption
  • Categorical - Chi-Squared Association Test
• Parametric Assumption:

  • Yes - Pearson
  • No - Spearman's Rank
• Data Type of Difference:

  • Categorical - Chi-Squared Test for Difference
  • Continuous - No. of Groups/Samples
• No. of Groups/Samples:

  • ≥ 3 - No. of Independent Variable
  • Two - Individual Sample T-Test (Individual Measure) and Paired Sample T-Test (Repeated Measure)
• No. of Independent Variable:

  • One - One Way Anova
  • Two - Two Way Anova
• Data Type of Prediction:

  • Categorical - Logistic Regression
  • Continuous - No. of Ind. Var
• No. of Ind. Var

  • One - Simple Regression
  • ≥ Two - Multiple Regression
• ANOVA - stands for Analysis of Variance
• ANOVA is the statistical procedure for testing variation among the means of more than two groups
• In ANOVA, we focus on variances because when you want to know how several means differ, you are asking about the variation among those means.
• You could use the ANOVA for a study with only two groups, but the simple T-Test gives the same result
• Null Hypothesis in an analysis variance is that the several populations being compared all have the same mean
• Research Hypothesis would be that the mean differs among the different populations
• Two ways of estimating population variances:

  • Within-Groups estimate of the population variance
  • Between-Groups estimate of the population variance
• Within-Groups Estimate of the Population Variance are average of estimates figured entirely from the scores within each of the samples
• Within-Groups Estimate of the Population Variance is not affected by whether the null hypothesis is true
• Within-Groups Estimate of the Population Variance focuses only on the variation inside each population
• Within-Groups Estimate of the Population Variance is an estimate based on chance (or unknown) factors that cause different people in a study to have different scores
• Between-Groups Estimate of the Population is the estimate of the variance of the population of the individuals based on the variation among the means of the groups studied.
• When the null hypothesis is true, all populations are identical and thus they have the same mean, variance, and shape
• When the null hypothesis is true, the variability among the sample mean is influenced by the same chance factors that influence the variability among the scores within each sample.
• When the null hypothesis is true, the within-groups and between-groups estimates are based on the same thing (that is, the chance variation within populations)
• When the null hypothesis is true, the variation among the means sample taken from identical populations is related directly to the variation of the scores in each of those populations.
• Implication: it should be possible to estimate the variance in each population from the variation among the means of our samples.
• The larger the variation within the populations, the larger the variation will be among the means of samples taken from the populations.
• However, our goal is to reject the null hypothesis and for the research hypothesis to be true.
• Our RH indicates that the mean differs among the different populations. There is a significant difference among the population means.
• When the research hypothesis is true, variation among the means of the samples is not just caused by the variation within the scores of the population, but also with variation among the population means.
• When the research hypothesis is true, the means of the samples are spread out for two different reasons:

  • Because of variation in each of the populations (due to chance factors)
  • Because of variation among the population means
• The central principle of the analysis of variance is that when the null hypothesis is true, the ratio of the between-groups population variance estimate to the within-groups population variance estimate should be about 1. When the research hypothesis is true, this ratio should be greater than 1.
• F-Ratio is the ratio of the between-groups population variance estimate to the within-groups population variance estimate.
• F-ratio Formula:

  
• F-Distribution is a mathematically defined curve that is the comparison of distribution used in an analysis of variance
• F-Table is the table of cutoff scores on the F distribution.
• The graph of the F distribution is always positive and skewed right
• The reason for the positive skew is that an F distribution is a distribution of ratios of variances, variances are always positive numbers.
• A Post-Hoc test is done to identify exactly which groups differ from each other
• Assumptions:

  You need to check if your data met these assumptions because it is only appropriate to use a one-way ANOVA if your data "passes" these required assumptions to give you a valid result.
• Assumptions:

  When analyzing your own data using SPSS, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real world data. However, don’t worry. Even when your data fails certain assumptions, there is often a solution to overcome this.