- 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)
Review of t-tests & one-way ANOVAs
- Conduct and interpret your own _________________ (include an
- independent samples t-test
- paired samples t-test
- one-way ANOVA
- repeated measures ANOVA
- factorial ANOVA
- split-plot ANOVA (SPANOVA or mixed ANOVA)
(note indepth knowledge of MANOVA is not examinable, but
understanding when you would use MANOVA is important)
- Create your own data set for conducting some mock 2-way ANOVA
- Adjust the data and / or ANOVA analyses in order to create the
following (include ANOVA results and appropriate graphs):
- No effects
- Main effect A, no main effect B, no interaction
- Main effect A, no main effect B, interaction
- No main effect A, main effect B, no interaction
- No main effect A, main effect B, interaction
- Main effect A, main effect B, no interaction
- Main effect A, main effect B, interaction
- Interaction, no main effects
- If unsure, you can download and try out
file), and interactions.spo
- 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.
- Using the QFS data, design and conduct any type of ANOVA
- Write up a summary of your analysis (max. 250 words), including:
- Brief background rationale for the analysis and brief explanation of the
relevant variables and data
- Brief comment on relevant descriptive statistics
- Brief summary of assumption-testing
- Summary of ANOVA results, including significance, effect sizes and direction
of any effects
- Brief comment on the implications of the results
- Do not include graphs or tables (because it needs to be text
which can be pasted into a WebCT quiz).
- 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
- Test the assumptions, esp. check levels of measurement, normality,
univariate and multivariate outliers, homogeneity of variance, min. n in
- 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)
- 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.
- Explain how the critical alpha level is calculated especially if there
are multiple post-hoc tests (e.g., Bonferroni’s)
- 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
- 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
- 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 =
- 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)
- 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