CDAA No 4 - ANOVA (25)

EPS 525 – I NTRODUCTION TO S TATISTICS CDAA N O . 4 – O NE - WAY A NALYSIS OF V ARIANCE A researcher conducted a study to examine the effects of secure, anxious, and avoidant attachment styles on the physiology of sleep. Participants were selected using a stratified random sampling approach to ensure representation of each of the three styles. The sleep patterns of 30 secure, 30 anxious, and 30 avoidant children were monitored. Of primary importance to the researcher was the overall percentage of time each child spent in deep (delta) sleep. Following is the average amount of time that each child spent in delta sleep, expressed as a percentage of total sleep time (ranging from 0.0 to 100.0). For the attachment styles, 1 = secure, 2 = anxious, and 3 = avoidant. 1. (2 points) What would the null hypothesis be for this study? Show/write the appropriate symbols and expression in words. 2. (2 points) What would the alternative hypothesis be for this study? Show/write the appropriate symbols and expression in words. 3. Prior to examining whether the group means differ; you need to test the underlying assumptions of the one-way analysis of variance. 3.a. (2 points) Has the assumption of independence been met for this data? Indicate how you made your determination. 3.b. (2 points) Has the assumption of normality been met for this data, using an alpha level of .001? Indicate how you made your determination. Be sure to include all applicable values and symbols. 3.c. (2 points) Has the assumption of homogeneity of variance been met for this data, using an alpha level of .05? That is, is this assumption met or not met? Indicate how you came to your conclusion. Be sure to include all applicable values and symbols. 4. (3 points) The next question that needs to be answered is whether all of the groups are the same in their percentage of time in deep (delta) sleep using an alpha level of .05. If applicable (or indicate why not), use the Welch statistic. What is your conclusion ( at this point ) from this analysis? Indicate how you came to your conclusion. Be sure to include all applicable values and symbols.