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Tutorial 6:
ANOVA 1&2

Last updated:
02 May 2005

Assumed knowledge

  • t-tests

  • one-way ANOVA

Francis

  • Do / Review Francis 3.3 (Analysing Differences)
  • Do / Review Francis 5.2 (ANCOVA)
  • Do / Review Francis 5.3 (MANOVA)
    (note indepth knowledge of MANOVA is not examinable, but understanding when you would use MANOVA is important)

Data files

Review of t-tests & one-way ANOVAs

  • Conduct and interpret your own _________________ (include an appropriate graph)
    • independent samples t-test
    • paired samples t-test
    • one-way ANOVA
    • repeated measures ANOVA
    • factorial ANOVA
    • split-plot ANOVA (SPANOVA or mixed ANOVA)
    • ANCOVA
    • MANOVA
      (note indepth knowledge of MANOVA is not examinable, but understanding when you would use MANOVA is important)

Understanding Interactions

  • Create your own data set for conducting some mock 2-way ANOVA analyses
  • Adjust the data and / or ANOVA analyses in order to create the following (include ANOVA results and appropriate graphs):
    1. No effects
    2. Main effect A, no main effect B, no interaction
    3. Main effect A, no main effect B, interaction
    4. No main effect A, main effect B, no interaction
    5. No main effect A, main effect B, interaction
    6. Main effect A, main effect B, no interaction
    7. Main effect A, main effect B, interaction
    8. Interaction, no main effects
  • If unsure, you can download and try out interactions.sav (dataset), interactions.sps (syntax file), and interactions.spo (output file).

ANOVA Writeup

  1. This is a chance to demonstrate your understanding of ANOVA.  Pre-prepare your answer electronically for submission for the ANOVA quiz.  This question has a 250 word maximum limit and is worth 2 out of 10 marks for the ANOVA quiz.
  2. Using the QFS data, design and conduct any type of ANOVA
  3. Write up a summary of your analysis (max. 250 words), including:
    1. Brief background rationale for the analysis and brief explanation of the relevant variables and data
    2. Brief comment on relevant descriptive statistics
    3. Brief summary of assumption-testing
    4. Summary of ANOVA results, including significance, effect sizes and direction of any effects
    5. Brief comment on the implications of the results
    6. Do not include graphs or tables (because it needs to be text which can be pasted into a WebCT quiz).
  4. Marking for this question will be based on a combination of the quality of the answer and the level of difficulty (e.g., a well performed ANCOVA or 2-way ANOVA will score better than a well-performed 1-way ANOVA -- much like the way scoring works for diving at the olympics -- if in doubt, you are better off doing a simpler analysis well than a complex one poorly)

Detailed Tips for Writing Up An ANOVA Analysis

Note these notes on writing up an ANOVA are an overkill for the 250 word summary exercise.  They are pitched at students writing up full lab reports.  Nevertheless, they offer a guideline as to the kinds of topics to think through and choose from when presenting your ANOVA summary.

  • Test the assumptions, esp. check levels of measurement, normality, univariate and multivariate outliers, homogeneity of variance, min. n in each cell
  • Present the descriptive statistics in table or text
  • Consider presenting a figure to illustrate the data
  • Report in table or text the ANOVA results of interpret
  • Consider power, effect sizes and confidence intervals
  • Conduct planned or post-hoc testing as appropriate
  • State whether or not results support hypothesis (hypotheses)

Introduction

- Ask an interesting, logically derived “are groups different” type of question (with an overview of relevant theory / research)
e.g., Does students’ academic performance in English and Mathematics differ according to gender and socio-economic status?
 

- Present a logical argument and hypotheses. Supportive references are helpful, but more important is having a solid question and clear grounds for the question and hypotheses.

Method

- Explain how the critical alpha level is calculated especially if there are multiple post-hoc tests (e.g., Bonferroni’s)

Results

- Summarise recoding (if any)
 

- Descriptive statistics
 

- Briefly summarise univariate descriptive statistics and any notable features. Present the means and SD for each cell in sentences or in a table. Also include the marginal means and their SDs (i.e., sub-totals).
 

- Important for ANOVA reporting because the means and standard deviations are the basis of the ANOVA analysis, just as correlations are building blocks for regression analysis
 

- Where there are too many statistics to describe, use a table instead (see Table 1). How many is too many? Rule of thumb: More than about 5 statistics.

- Present a graph to illustrate the ANOVA analysis is recommended if it helps the reader to understand the results.
 

- Note, however, that graphs shouldn’t be bulky and distract from the flow onto the main analysis. Extra descriptive statistics graphs can be included in an appendix. (e.g., see Appendix A)
 

- Present ANOVA results
 

- State what type of ANOVA is used and clearly indicate the DV and the IVs. Were assumptions met? The F, df, eta-squared and possibly power for each result should be presented, with comment on the size of the effect. For any effects, the direction of the effect needs to be pointed out. This may require post-hoc testing or planned comparisons.
- e.g., A 2 x 2 mixed design ANOVA was conducted. SES is the between subjects variable with two levels (low and high); Type of academic achievement is the within subjects variable with two levels (maths and english)
 

- Succinctly present and explains the ANOVA results, including the F, df, p, and strength of effect
 

- Main effects?
- e.g., The main effect of socioeconomic status (SES), a between-subjects variable, was significant using a critical alpha of .05 (F (1, 156) = 5.20, p = .02). The direction of the effect shows that high SES students had higher academic grades (M = 69.4, SD = 9.2) than students with low SES (M = 66.1, SD = 9.0), a medium sized effect (eta-squared = .03).
- The main effect of academic achievement (AA), a with-in subjects variable, was not significant using a critical alpha of .05 (F (1, 156) = .001, p = .98, eta-squared = .00).
 

- Interaction effects
- The interaction between SES and type of AA is significant using a critical alpha of .05 (F(1, 156) = 14.79, p = .00). This is a strong effect (eta-squared = .09). Table 1 and Figure 1 show that high SES children do particularly well in Maths compared to low SES children, whereas both high and low SES children do about the same for English.
 

- Post-hoc tests (if needed / used)

Discussion
 

- Revisit the purpose of the ANOVA and relevant hypotheses. Consider this theory in light of the data from the current study.
 

- Explain the limitations and generalizability of the current study.
 

- Offer insight and explanation into the current study’s ANOVA results and discuss how/whether these ideas might contribute to theory and applications.