Analysis

Historical Comparison

The Historical Trends section (year-over-year profile, weekday × month heatmap, lag-1 scatter plot) and the Comparisons section (two periods or two categories, mean difference, relative change, Cohen's d).

Historical Trends

The Historical Trends section shows recurring structure in the selected data: seasonal patterns across years, weekday effects within months, and day-to-day persistence. All three views use the current selection, including the category filter.

Year-over-year monthly profile

One line per calendar year, with the twelve months on the horizontal axis. Each point is the mean of all selected observations in that month of that year.

profile(y, m) = mean of xᵢ with year(dateᵢ) = y and month(dateᵢ) = m

Months without observations in a year have no point, so a date range that starts in March shows no January or February values for its first year. Lines that keep the same shape but move up or down from year to year indicate a stable seasonal pattern with a change in level. To see whole years, set the date range to All data or to custom dates that start on 1 January.

Weekday × month heatmap

A grid of 7 rows (Monday to Sunday, ISO weekdays) and 12 columns (January to December). Each cell shows the mean value of all selected observations that fall on that weekday in that month, pooled across all years in the selection.

cell(w, m) = mean of xᵢ with weekday(dateᵢ) = w and month(dateᵢ) = m

Weekdays are determined from the UTC calendar day.

Read rows to compare weekdays within the same month, and columns to compare months for the same weekday. In the Regional Electricity Demand dataset, for example, the Saturday and Sunday rows are lower in every month because the generator applies a weekend factor of 0.92. Cells that contain no observations are left empty. With short date ranges, some cells rest on very few observations; widen the range before drawing conclusions from single cells.

Lag-1 scatter plot

The lag-1 scatter plot shows how a day's value relates to the previous day's value. It uses the daily mean series: for each date, the mean of all selected observations on that date (across the selected categories). Each point is one pair (previous day, current day). Only pairs of consecutive calendar days are used; if a day is missing, the day after it is not paired.

r = Σ (uᵢ − ū)(vᵢ − v̄) / √( Σ (uᵢ − ū)² · Σ (vᵢ − v̄)² )

Pearson correlation of the pairs (uᵢ, vᵢ) = (daily mean on day t − 1, daily mean on day t). Requires at least 3 pairs and variation in both.

r close to +1 means that high days tend to follow high days (strong persistence, often caused by trend or seasonality). r close to 0 means little linear relationship between consecutive days. r is not available when there are fewer than three pairs or when either side has no variation.

Correlation is descriptive

Lag-1 correlation describes the selected history. It is not a forecast model and does not state that the relationship will hold for future values.

Comparisons

The Comparisons section places two groups of observations side by side. Choose one of two modes:

Two periods (A vs B): Group A and group B are observations from two date ranges, for example the same quarter in two consecutive years.
Two categories: Group A and group B are two categories of the dataset, for example North and South.

For each group the section shows the side-by-side statistics of the summary table (n, mean, median, SD and the other statistics described in Distributions), followed by the comparison measures below. B is compared with A, so A acts as the reference.

Mean difference

Δ = x̄_B − x̄_A

In the dataset's unit.

Relative change

relative change = (x̄_B − x̄_A) / |x̄_A|

Shown as a percentage. Not available when x̄_A = 0.

Cohen's d

d = (x̄_B − x̄_A) / s_p, s_p = √( ((n_A − 1)·s_A² + (n_B − 1)·s_B²) / (n_A + n_B − 2) )

Standardised mean difference with pooled sample standard deviation. Requires n ≥ 2 in each group and s_p > 0.

Cohen's d expresses the difference between the means in units of the pooled standard deviation. For example, with A = (1, 2, 3) and B = (3, 4, 5), the mean difference is 2, the relative change is +100% and d = 2. Conventional reference points are about 0.2 (small), 0.5 (medium) and 0.8 (large), but these are rough guides and depend on the subject matter.

Not a significance test

Cohen's d is a descriptive effect size. The workspace does not compute p-values or confidence intervals and does not test whether a difference is statistically significant. Time-series observations are usually not independent, which is one more reason not to read d as a test result.

Relative-frequency comparison

Below the statistics, the distributions of A and B are drawn as relative frequencies on identical bins, built from the values of both groups with the bin rules in Frequency Analysis. Because each group is normalised by its own n, periods of different length or categories with different numbers of observations are directly comparable.

Choosing comparable groups

Compare periods of the same length and season. A winter month against a summer month mostly measures seasonality.
Keep the category filter the same when comparing periods, otherwise the groups differ in composition as well as in time.
Check n for both groups. Very small groups make every statistic unstable.
Use the year-over-year profile first to see whether a difference is part of a recurring pattern.

To export the selection and its summary statistics, see Reports.