Picking Appropriate Statistical Tests II

• Correlation/ Regression: Utilized to understand the relationship between two quantitative continuous variables.
• Correlation/regression investigates whether changes in one variable predict changes in the other
• The test statistic used is the correlation coefficient (r), which indicates the strength and direction of the relationship.
• One sample t-test: This test compares the mean of a single quantitative continuous variable (sample) to a known or expected value (population).
• Chi-Square test of independence: Determines if there's a significant association between two categorical variables.
• What data is used within correlation tests?

  Two continuous quantitative variables
• What type of test statistic is used within a correlational text?

  A converted correlation coefficient r into a t value.
• How is the test statistic within a correlation test distributed under the null hypothesis?

  A t distribution within N-2 degrees of freedom
• What sort of test does this reflect, and what is the direction of the hypothesis

  • Null hypothesis there is no relationship or association between variable X variable
  • Alternative hypothesis there is a relationship or association between variable X variable ?

  Correlational test
• A coefficient r close to -1 indicates a strong negative relationship. As one variable increases, the other decreases.
• A coefficient r close to 1 indicates a strong positive relationship. As one variable increases, the other also increases.
• What test aligns with these hypothesises one way ANOVA

  • Null: There are no differences in the population between the means of the individual groups
  • Alternative: There is At least two group means different from each other in the population
• This is a One Way ANOVA

  
• Describe the variance of this ANOVA data:

  • There is large variance within-groups
  • There is a small variance between-groups

  
• Describe the variance of this ANOVA data:

  • There is small variance within-groups
  • There is a large variance between-groups

  
• The F value used within a One-Way ANOVA summarises what?

  How significant the between-group mean differences are, compared to the within-group mean differences
• A Two-way Factorial analysis of variance examines the influence of two independent variables with three factors (+3) on a dependent variable. 
• A One Way analysis of variance examines the influence of one independent variable with three factors (+3) on one dependent variable.
• There are three sets of null hypotheses in a Two-Way ANOVA:

  • The means of the dependent variable are the same across levels of the first factor.
  • The means of the dependent variable are the same across levels of the second factor.
  • There is no interaction between the two factors.
• What are the two independent variables called within a two way ANOVA?


  Factors 1 and Factors 2
• Example Question two way factorial ANOVA: Does blood type and gender have an influential effect on blood pressure
• If the variance by the Levenes test has a p-value greater 0.05, what can we conclude?

  That there is equal variance within-groups of a two way factorial ANOVA
• A 5 x 2 factorial ANOVA was performed; what do numbers "5" and "2" represent?

  The number of levels in each of the two predictor variables.

  • The first predictor factor variable has five levels,
  • Second predictor factor variable has two levels.
• What does a two-way factorial ANOVA layout look like?

  • Is there a main effect of factor 1 difference between mean x and mean x
  • Is there a main effect of factor 2 difference between mean x and mean x
  • Is there an interaction between the factors?
• ANOVA assumptions include?


  • Observations are independent (random sampling in experimental design)
  • Residuals are normally distributed - histograms and shapiro wilk
  • Equal Variance- Levenes test
• How is a repeated measure ANOVA different to one-way or factorial ANOVA?

  The measures made about participants are repeated there is no independence of measures
• When do we use repeated measures ANOVA?


  When observations of participants are at different time points but use the same participants twice
• Example: studying the effect of different diets (vegetarian, pescatarian, omnivore) on cholesterol levels and BMI requires what kind of test?

  MANOVA
• Example: studying the effect of different study techniques (flashcards, self-quizzing, rereading) on students' test scores, controlling for pre-test score, requires what kind of test?

  ANCOVA due to the nuisance variable
• MANOVA's Purpose: determines if the means of multiple outcomes differ across the levels of the predictor.
• ANCOVA's Purpose: determines if the means differ between levels of the predictor, after controlling for the nuisance variable.
• ANCOVA you have

  • one categorical independent variable with three or more levels,
  • one continuous dependent variable,
  • and one continuous nuisance variable.
• MANOVA you have

  • one categorical independent variable with three or more levels
  • and multiple continuous dependent variables.
• In a one-tailed test, we are only looking for a difference in one specific direction. Therefore, we consider the entire alpha level in that one tail of the distribution
• Power of the test ( 1-B ) a true positive

  
• Is this statement true of false: "The significance level (α) is the probability of incorrectly concluding that there is a difference between means, when testing samples that are in fact drawn from populations with the same mean" is True. This is a description of a Type I error?

  True because significance level (α) is about type one errors and rejecting the null
• Power (1-β) is the probability of correctly detecting a difference between means, when testing samples that are in fact drawn from populations with different means.
• The beta value (β) is the probability of incorrectly concluding that there is no difference between means, when testing samples that are in fact drawn from populations with different means.
• Ordinal scale consists of?

  • Pain score 1-5
  • Disease state mild, moderate, severe
  • Grade A-F
• What scale are men and women in?

  Nominal scale