Upper bound of the interval: what it means and how to read it
In the report: Upper — The upper bound of the confidence interval, at the level in the label.
How to read it
Together with the lower bound: a range of plausible values for the true value. The narrower the range, the more precise the estimate.
In plain words
A coach found that team A ran a long race faster than team B, and she wanted to know how big the gap could be at most. She looked at the upper bound of the gap and it came out 9.6 seconds, with the lower bound at about 1 second. Now she can say the true gap is probably somewhere between 1 and 10 seconds: team A is faster, but anywhere from just a little to quite a lot. Since the whole range lies above zero, the teams do look different. If the lower bound had been below zero, she would say the gap could be nothing at all.
Example
The cell with Upper is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two steps; pass is coded 0 and 1
=STATS_LOGISTIC(Data!A1:T51, "pass", "x1,x2|x", 0, 50, 1e-8) - —
=STATS_BOOTSTRAP(Data!A1:T51, "y", "x1,x2", 2000, "pairs", 0.95) - —
=STATS_PEARSON(Data!A1:T51, "x,y,x1",0.95,"two-sided")
Where you see it
STATS_LOGISTIC— Binary logistic regression with optional ridge regularization (lambda >= 0).STATS_BOOTSTRAP— Bootstrap confidence intervals for regression via resampling.STATS_PEARSON— Pearson correlation (r).STATS_SPEARMAN— Spearman rank correlation (rho): the correlation for rating scales, ranks and skewed data — does one go up as the other goes up?STATS_KENDALL— Kendall rank correlation (tau-b): the correlation of the order of two columns — for small samples and scales with many tied answers.STATS_PARTIAL— Partial correlation: the Pearson correlation of two variables with the controls held constant (SPSS PARTIAL CORR). Two variables give one correlation, three or more a matrix, as STATS_PEARSON.STATS_PAIRED— Paired-samples t-test for two related measurements (e.g., pre vs post).STATS_INDEPENDENT— Independent-samples t-test for two groups: the two selected columns are the groups.STATS_ANOVA— One-way ANOVA: each selected column is a group. Classic (Student) or Welch ANOVA, chosen by welch (auto by default), with homogeneity of variances and post-hoc comparisons.STATS_ONE_SAMPLE— One-sample t-test against mu0.STATS_CI— Calculates the confidence interval of the mean for filtered columns (Student's t).STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- p of the F change — The p of F Change: P(F(df1, df2) > F Change). Empty when F Change is.
- Confidence interval — The confidence interval of the estimate: its level and its two bounds.
- Confidence level — The confidence level of the interval: ciLevel, 0.95 by default.
- Significance of the partial correlation — The p of the partial correlation, as SPSS names it, for the chosen alternative. Empty in the same cases as Correlation.
- Alternative hypothesis — The hypothesis tested: two-sided — the means differ in either direction; greater — the first is larger; less — the first is smaller.
Get it in your sheet
One formula in a cell gives the whole report, Upper bound of the interval included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)