数据统计 - One Way ANOVA

ANOVA: one-way analysis of variance

• used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups，两组情况下应该是用independent-samples t-test ).
• one-way ANOVA 只会告诉你有或者没有显著差异，并不会告诉你是哪两组或者哪几组有显著差异，it only tells you that at least two groups were different.
• 要解决以上的问题，需要用到 post hoc test

在做 One way ANOVA 之前，有以下6个假设：

• dependent variable should be measured at the interval or ratio level (i.e.，他们都是连续的，IQ值，时间，体重这些).
• independent variable should consist of two or more categorical, independent groups.
• should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.
• There should be no significant outliers. SPSS can help detect outliers
• dependent variable should be approximately normally distributed for each category of the independent variable. Shapiro-Wilk test can test normality
• Homogeneity of variances. You can test this assumption in SPSS Statistics using Levene’s test for homogeneity of variances.

Test Procedure in SPSS Statistics

1. Click Analyze > Compare Means > One-Way ANOVA… on the top menu
2. Click the SPSS Post Hoc Button button. Tick the Tukey checkbox
3. Click the Option button. Tick the Descriptive checkbox in the –Statistics– area

SPSS Statistics Output of the one-way ANOVA

• Descriptives Table: provides some very useful descriptive statistics, including the mean, standard deviation and 95% confidence intervals for the dependent variable for each separate group, as well as when all groups are combined (Total). These figures are useful when you need to describe your data.
• ANOVA Table: shows the output of the ANOVA analysis and whether there is a statistically significant difference between our group means. But we do not know which of the specific groups differed. Luckily, we can find this out in the Multiple Comparisons table which contains the results of the Tukey post hoc test.
• Multiple Comparisons Table: shows which groups differed from each other. The Tukey post hoc test is generally the preferred test for conducting post hoc tests on a one-way ANOVA, but there are many others.

Reference：
https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php