One-way ANOVA--music training and spatial temporal reasoning in preschool children

This activity provides independent practice in use of one-way ANOVA within the context of the 4 steps of hypothesis testing:
 * 1) State the appropriate null and alternative hypotheses, Ho and Ha.
 * 2) Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic.
 * 3) Find the p-value of the test.
 * 4) Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.

Research question
Using a neuro-biological model of cognitive functioning as a framework, researchers hypothesized that music training may enhance young children's spatial-temporal reasoning. Participating children, from three preschools, were assigned to one of the following four groups to receive the indicated extra lessons: Assignment of children to groups was not completely random due to various scheduling issues. None of the participating children had received prior music or computer lessons and parent involvement was minimal.
 * Piano: private piano keyboard lessons and group singing lessons (n=34)
 * Computer: private computer lessons, unrelated to music (n=20)
 * Singing: group singing lessons, without piano instruction (n=10)
 * None: no special lessons (n=14)

Children's spatial-temporal reasoning skills were assessed before and after treatment using a standard, age-calibrated test.

Dataset
Obtain the dataset from one of the following:
 * class website: piano.por (portable file format)
 * "ta12_004.xxx" via the |00510|00520|00530|00540|00550|00560|00570|00010|00020|00030|00040|00050|00070|00080|00090|00100|00110|00120|00130|00140|01000|02000|03000|04000|05000|06000|07000|08000|09000|10000|11000|12000|13000|14000|15000|16000|17000|99000| Introduction to the Practice of Statistics website, available for various statistical software packages

Analyses
The following instructions and guiding questions will step you through the analysis process. Copy and paste the following section into a word processor. Provide responses as indicated.

Comparing spatial-temporal reasoning ability for groups of young children receiving a variety of extra lessons

 * What is the explanatory variable?
 * What is the response variable?


 * 1) State the null and alternative hypotheses being tested in this study.
 * Ho:
 * Ha:
 * 1) Data collection and examination
 * 2) *Look at the data. Using SPSS, calculate descriptive statistics and create histograms for each group. Create a chart with side-by-side boxplots for the four groups. Describe the data and shape of the distributions. Describe the comparison of distributions as displayed in the boxplot.
 * 3) *Explain why the conditions which allow us to safely use the ANOVA test are met.
 * 4) *Would it be valid to use the ANOVA test if the data in one of the groups were somewhat skewed? Explain.
 * 5) *Using SPSS, run the ANOVA F test procedure (in SPSS under Analyze > Compare Means).
 * 6) *Report the value of the test statistic and its degrees of freedom.
 * 7) *How is the F statistic calculated (write the formula)?
 * 8) *Describe what this F statistic value means.
 * 9) Report the p-value for the statistical test.
 * 10) * p =
 * 11) Interpret the analysis results in the context of the research question. Be sure to include important statistics from your analysis results to support your conclusion and to generalize your results to the relevant population(s).

Specific comparison of means
The researchers based the study design on a biological understanding of music capability and spatial reasoning. So, their primary focus was on the effect of music training, specifically piano lessons, on children's spatial-temporal reasoning. Although not specifically planned by the researchers, a contrast of the mean of the piano group with the average of the three other groups would have been relevant.
 * 1) Design the comparison to be tested.
 * Ho:
 * Ha:
 * 1) *Significance level:
 * 2) *Contrast:
 * 3) *Coefficient values:
 * 4) *State what test statistic will be used to summarize the data. Indicate whether a one-tailed or two-tailed test will be used.
 * 5) *Indicate what distribution will be used for the hypothesis test, including degrees of freedom.
 * 6) Open the dataset piano.sav in SPSS.
 * 7) *Calculate and report the test statistic.
 * 8) Find the p-value of the test
 * p=
 * 1) Interpret the analysis results in the context of the research question.

All pairwise comparisons
In fact, the researchers performed a post-hoc analysis of all pairwise comparisons between treatment groups using the Bonferroni method to assess the differences in the improvement score means
 * 1) Design the comparison to be tested.
 * 2) *Number of comparisons to be created:
 * 3) *For first comparison
 * Ho:
 * Ha:


 * 1) *Experimentwise significance level:
 * 2) *State what test statistic will be used to summarize the data. Indicate whether a one-tailed or two-tailed test will be used.
 * 3) *Indicate what distribution will be used for the hypothesis test, including degrees of freedom.
 * 4) Open the dataset piano.sav in SPSS. Run the Bonferroni post hoc analysis
 * 5) Review the results to determine which comparisons are significant.
 * 6) Interpret the analysis results in the context of the research question.