Mean by group as a chart (2 to 12 groups, also without a test)
In brief
For the building block "Explore by groups" and for the group comparison with more than two groups, Statable shows the mean of each group as a chart, also without a test. The default is dots (every person) with the mean and the 95% confidence interval; bars are a choice and always start at 0. Under the axis is "n = …" for each group. The groups are in the order of the column (value labels), never by size. Statable does not show more than 12 groups as a chart.
What the whiskers are
The 95% confidence interval is calculated for each group with its own spread and the t distribution (m ± t·s/√n, df = n − 1), not with a common spread. Alternatively ± 1 standard deviation or no whiskers. Statable does not offer the standard error alone, because it is read as an interval although it is only about a 68% interval.
Trap: overlapping intervals
Overlapping intervals do not rule out a difference, and the chart does not replace a test. Two equally wide 95% intervals touch only at a distance of 3.92 standard errors; the difference is significant from 2.77. Example chickwts: horsebean (160.2 g) against linseed (218.8 g) overlap by 2.3 g, and the Welch test gives p = .0069. Overlap alone therefore says little: in ToothGrowth (OJ against VC) the intervals overlap, and here the difference is not significant either (p = .06). Only a test decides. The sentence on this is always under the chart.
More traps
- Bars hide how the values are spread; dots show them (up to a limit of dots; the means always use all values).
- Without a random sample the intervals only describe the data.
- With a survey weight and "drawn individually: yes" the degrees of freedom of the sampling design apply per group (number of cases in the group minus 1), as for the group means in the group comparison. If R is used with the degrees of freedom of the whole design (degf), the intervals become somewhat narrower (example with 30 cases in 3 groups: 9 against 29 degrees of freedom).
- A group with one person has no interval (only the mean); under 5 people the interval is wide and uncertain.
- Case weight: a frequency weight calculates (n = sum of weights, like repeated rows). A survey weight without the answer "people drawn individually: yes" shows only means, without whiskers; with "yes" the whiskers come from the survey design.