Lower bound of the interval: what it means and how to read it

In the report: Lower — The lower bound of the confidence interval, at the level in the label.

How to read it

Together with the upper bound: a range of plausible values for the true value. The narrower the range, the more precise the estimate.

In plain words

A shop owner found that customers spend 4.72 dollars on average, but another week could give another average. She wanted to know how low the true average could reasonably be. She looked at the lower bound and it came out 4.03. Now she can say the true average is probably not below 4.03. Together with the upper bound, 5.41, she writes the average with the range 4.03 to 5.41. A narrow range means her average is precise. If the range had been 1 to 9 dollars, she would say she knows very little about the true average.

Example

The cell with Lower 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.

Upper bound of the interval — The upper bound of the confidence interval, at the level in the label.
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.

Get it in your sheet

One formula in a cell gives the whole report, Lower 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)