Week 7 — Summaries, tables, and the midterm

PROC MEANS, FREQ, and UNIVARIATE — and the midterm practical (Fri Oct 9)

The week question

Last week you joined the two tables of the wellness-program study and learned to trust the row count — an inner join of participants × screenings gives 594 rows, a left join gives 596, and the difference is the two enrolled participants who were never screened. You now have a clean, joined, analysis-ready dataset. This week’s workflow question is the next move: once the data are clean, how do you describe them in tables you and a reader can trust? That means producing the right summary — a mean and spread for a continuous variable, a count and percent for a categorical one, a distributional check before you commit to a model — and reading each table critically: how many rows actually went into it, how many were missing, and whether the statistic SAS computed is the one you meant to read. Three procedures do almost all of this work: PROC MEANS for descriptive statistics, PROC FREQ for counts and percents, and PROC UNIVARIATE for a deeper look at a distribution. This week also marks the midterm practical, Friday October 9, in class, which covers the workflow from the SAS environment through summaries and reporting.

Why this matters

Summary tables are the first output anyone actually reads, and they are where a quiet data problem becomes visible — or stays hidden. Three reasons this week is load-bearing. First, a summary is only as honest as its N. PROC MEANS reports a mean over the non-missing rows; if you do not look at how many rows that was, you can report a “mean” computed on far fewer observations than you think. Knowing the difference between N (how many values were used) and NMISS (how many were missing) is the whole discipline. Second, the right statistic for the variable’s type. A continuous variable like systolic_bp wants a mean, a standard deviation, and quantiles; a categorical variable like sex or arm wants counts and percents from PROC FREQ — a mean of sex is meaningless, while a mean of a 0/1 variable like goal_met is a proportion, which is exactly what you want. Third, summaries are the bridge to the procedures ahead. Before the t-test in week 9 or the regression in week 10, you describe the data — check the spread, look for impossible values, confirm the groups are balanced. A surprising mean or a lopsided frequency table caught here saves a wrong model later. The recurring test holds: would someone else, reading your table and its N, be able to understand and trust it?

Learning goals

By the end of this week you should be able to:

  • Produce a descriptive-statistics table with PROC MEANS (or PROC SUMMARY), request the statistics you want by name, and read N versus NMISS so you know how many rows the mean was actually computed on.
  • Build a one-way frequency table with PROC FREQ for a categorical variable, and read counts, percents, and the missing row, confirming the totals add up to what you expect.
  • Run a PROC UNIVARIATE distributional check — quantiles, the five lowest and highest values, a normality read — and use the extreme observations to catch impossible or out-of-range data before modeling.
  • Explain why the mean of a 0/1 variable is a proportion (so mean(goal_met) = 0.41 means 41% met goal), and why a mean of a categorical variable is the wrong statistic.
  • Summarize by group correctly — sort first (PROC SORT) or use a CLASS statement — and check that the group counts match the clean frequencies (arm: coaching 100 / usual_care 100).
  • After every summary, state what the log should say (rows read, no unexpected WARNING/ERROR) and run a verification check (N, NMISS, a sanity range), and interpret the table for the analytic question without overclaiming — the study is synthetic and observational, not a real health finding.

Core vocabulary

The week’s SAS terms, defined plainly. These mirror the SAS workflow glossary and the PROC reference; keep the variable’s type and the statistic’s meaning aligned.

  • PROC MEANS — the descriptive-statistics procedure for numeric variables. By default it prints N, Mean, Std Dev, Minimum, and Maximum; you can request others (MEDIAN, NMISS, Q1, Q3, CLM) by listing them on the PROC MEANS line. PROC SUMMARY is the same engine with output going to a dataset instead of the listing.
  • PROC FREQ — the frequency procedure for categorical variables. A one-way TABLES sex; gives the count, percent, and cumulative percent per level; a two-way TABLES arm*goal_met; cross-tabulates. It is the right tool to confirm category counts and spot a stray or misspelled level.
  • PROC UNIVARIATE — the distributional-detail procedure for one numeric variable: moments, a full set of quantiles, tests of location, and the five lowest / five highest values (the extreme observations) — the fastest way to see an impossible value like a baseline_bmi of 0.
  • N versus NMISS — N is the count of non-missing values a statistic used; NMISS is the count of missing values that were dropped. A mean is computed over N, never over N + NMISS. Always read both.
  • The mean of a 0/1 variable — for a numeric indicator coded 1/0, the arithmetic mean is the proportion of 1s. So mean(goal_met) = 0.41 is read as “41% met goal,” not as an abstract average.
  • CLASS versus BY — both summarize by group. CLASS arm; groups within one pass and needs no prior sort; BY arm; produces a separate sub-table per group but requires the data sorted by arm first (PROC SORT), or you get ERROR: Data set is not sorted.
  • Quantile / percentile — a value below which a given percent of the data falls; the median is the 50th percentile, Q1/Q3 the 25th/75th. PROC UNIVARIATE prints the full ladder.

Concept development

PROC MEANS — descriptive statistics, and reading N vs NMISS

PROC MEANS is the workhorse for describing a numeric variable. The minimal call names the dataset, the variables, and (optionally) the statistics you want. List statistics on the PROC MEANS line itself; if you list none, you get the five defaults (N, Mean, Std Dev, Min, Max).

libname well "/home/u_wellness/data";   /* permanent library from week 2 */

proc means data=well.screenings n nmiss mean std min median max maxdec=2;
    var systolic_bp steps_k;
run;

The synthetic log confirms the rows read and the procedure completing without complaint:

SAS log (synthetic)
NOTE: There were 594 observations read from the data set WELL.SCREENINGS.
NOTE: PROCEDURE MEANS used (Total process time):
      real time           0.04 seconds
      cpu time            0.03 seconds

The synthetic output:

Output (synthetic, not executed)
                          The MEANS Procedure

 Variable        N    NMiss        Mean     Std Dev     Minimum      Median     Maximum
 ------------------------------------------------------------------------------------------
 systolic_bp   594        0      128.40       14.20       96.00      127.00      178.00
 steps_k       594        0        7.45        2.60        1.20        7.30       16.80
 ------------------------------------------------------------------------------------------

What the log should say. There were 594 observations read — exactly the joined screening grain from week 6 — and a clean PROCEDURE MEANS used line with no WARNING and no ERROR. Verification check. Read N = 594 and NMiss = 0 together: every screening row carried a systolic_bp, so the mean of 128.4 was computed on all 594, not a silent subset. Sanity-range the extremes — Minimum 96, Maximum 178 — against what a systolic blood-pressure reading can plausibly be; both are in range, so no impossible value slipped through. Interpretation. Across the 594 synthetic screenings, mean systolic pressure is 128.4 with a standard deviation of 14.2 — moderate spread, roughly symmetric since the median (127) sits close to the mean. The workflow move: you read the joined screenings table, created a descriptive table, the log confirmed the 594-row count, and you validated that nothing was missing and the range is sensible. This is a summary you could hand to a reader and defend.

PROC FREQ — counts, percents, and confirming the category levels

A mean is the wrong statistic for a categorical variable. For sex, arm, and site you want counts and percents, and PROC FREQ delivers them — one TABLES statement, one variable per request (or a * for a cross-tab).

proc freq data=well.participants;
    tables sex arm site;
run;
Output (synthetic, not executed)
                          The FREQ Procedure

 sex     Frequency     Percent    Cumulative Frequency    Cumulative Percent
 ---------------------------------------------------------------------------
 F             104       52.00                    104                 52.00
 M              96       48.00                    200                100.00

 arm           Frequency     Percent
 ----------------------------------------
 coaching          100       50.00
 usual_care        100       50.00

 site          Frequency     Percent
 ----------------------------------------
 North              70       35.00
 Central            66       33.00
 South              64       32.00

What the log should say. There were 200 observations read from the data set WELL.PARTICIPANTS — the cleaned participant count, not the 210 raw rows — and no WARNING/ERROR. Verification check. Add the frequencies down each table: sex 104 + 96 = 200; arm 100 + 100 = 200; site 70 + 66 + 64 = 200. All three totals equal the cleaned participant count, so no row was dropped or double-counted, and no stray level (a third sex value, a misspelled "Cental") appears. If PROC FREQ had silently omitted missing values, a footnote Frequency Missing = n would warn you — here there is none on these cleaned variables. Interpretation. The study is balanced by design: an even 100/100 split between the coaching and usual_care arms, a near-even sex split (104 F / 96 M), and three sites of similar size. That balance matters for the comparisons ahead — a lopsided arm split would complicate the week-9 t-test. The workflow move: you confirmed the category structure of the cleaned table before trusting any group comparison built on it.

PROC UNIVARIATE — a distributional check, and the extreme observations

PROC MEANS gives you the headline numbers; PROC UNIVARIATE gives you the shape — a full quantile ladder, moments, location tests, and, most usefully for validation, the five lowest and five highest values. That extremes panel is the fastest catch for an impossible or out-of-range value before it poisons a model.

proc univariate data=well.screenings;
    var systolic_bp;
run;
Output (synthetic, not executed)
                          The UNIVARIATE Procedure
                          Variable:  systolic_bp

         Moments
 N                  594        Mean           128.40
 Std Deviation     14.20       Variance       201.64

         Quantiles (Definition 5)
 100% Max     178      75% Q3      138
  99%         164      50% Median  127
  95%         153      25% Q1      119
  90%         147      10%         110
                        0% Min      96

         Extreme Observations
   ----Lowest----        ----Highest----
   Value      Obs        Value      Obs
     96       311          168       402
     98        57          171       129
     99       220          174        88
    101       146          176        15
    102        490         178        47

What the log should say. Again There were 594 observations read, and PROCEDURE UNIVARIATE used with no WARNING/ERROR. Verification check. Scan the Extreme Observations: the five lowest run 96–102 and the five highest 168–178 — clinically high at the top, but all possible systolic readings, with no 0, no negative, no 999 placeholder. Compare the quantiles against the PROC MEANS summary: Median 127 and Max 178 match exactly, an internal-consistency check that the two procedures read the same column. The interquartile range (Q3 − Q1 = 138 − 119 = 19) confirms the moderate spread the standard deviation implied. Interpretation. The distribution is roughly symmetric and unimodal, slightly right-tailed at the top end, with no data-quality red flags in the extremes — so systolic_bp is in good shape to feed the group comparisons later. The workflow move: UNIVARIATE is a validation step, not just a description — you look at the tails specifically to catch the kind of impossible value (the baseline_bmi = 0 from week 5) that a mean would quietly absorb.

Summarizing by group — and the mean of a 0/1 variable

Two more moves complete the week. First, summarize by group. The simplest path in PROC MEANS is a CLASS statement, which groups within a single pass and needs no prior sort:

proc means data=well.screenings n mean std maxdec=2;
    class completed;
    var systolic_bp;
run;

Using BY completed; instead would do the same job but requires proc sort data=well.screenings; by completed; run; first — otherwise the log throws ERROR: Data set WELL.SCREENINGS is not sorted in ascending sequence. CLASS avoids that trap; reach for BY only when you genuinely want separate sub-tables.

Second, the mean of a 0/1 variable is a proportion. goal_met is numeric, coded 1 (met goal) / 0 (did not), so PROC MEANS will happily average it — and that average is the proportion meeting goal:

proc means data=well.screenings n sum mean maxdec=4;
    var goal_met;
run;
Output (synthetic, not executed)
 Variable      N        Sum         Mean
 -----------------------------------------
 goal_met    594     246.0000      0.4141
 -----------------------------------------

Verification check. Sum = 246 is the count of 1s; N − Sum = 594 − 246 = 348 is the count of 0s; and Mean = 246/594 = 0.4141. Cross-check against PROC FREQ of the same variable, which would show 1 = 246 (41.4%) / 0 = 348 (58.6%) — the proportion read two ways agrees. Interpretation. About 41% of screenings met the activity goal. The lesson is conceptual: for a 0/1 indicator the mean is the proportion, so the same number answers “what’s the average?” and “what fraction met goal?”. Read it as a percent — never as a blood-pressure-style “average of 0.41.”

Worked examples

Worked example — the wellness-program study summary table (the recurring slice)

The task. Produce the headline descriptive table for the wellness-program study: the spread of systolic_bp and steps_k across all screenings, the goal-met proportion, and the categorical balance of the participant table — the exact summary you would put at the top of the analysis report. The data are synthetic; seed set, call streaminit(20260824), and the study is observational — never a real health finding.

The code. One MEANS call for the continuous outcomes and the 0/1 outcome, one FREQ call for the categorical attributes:

libname well "/home/u_wellness/data";

proc means data=well.screenings n nmiss mean std min median max maxdec=2;
    var systolic_bp steps_k;
run;

proc means data=well.screenings n sum mean maxdec=4;
    var goal_met;
run;

proc freq data=well.participants;
    tables sex arm site;
run;

The synthetic log:

SAS log (synthetic)
NOTE: There were 594 observations read from the data set WELL.SCREENINGS.
NOTE: There were 594 observations read from the data set WELL.SCREENINGS.
NOTE: There were 200 observations read from the data set WELL.PARTICIPANTS.
NOTE: PROCEDURE FREQ used (Total process time):
      real time           0.05 seconds

The synthetic output (the load-bearing numbers, all locked):

Output (synthetic, not executed)
 systolic_bp:  N=594  NMiss=0  Mean=128.40  Std=14.20  Min=96  Median=127  Max=178
 steps_k:      N=594  NMiss=0  Mean=7.45    Std=2.60
 goal_met:     N=594  Sum=246  Mean=0.4141        (246 met goal / 348 not)
 sex:   F 104 (52%) / M 96 (48%)        arm:  coaching 100 / usual_care 100
 site:  North 70 / Central 66 / South 64

The verification check. Three counts must line up. The two MEANS calls read 594 screening rows (the week-6 inner-join grain), NMiss = 0 so the means used every row; the FREQ call read 200 cleaned participants, and each one-way table sums to 200 (104+96, 100+100, 70+66+64). The goal-met arithmetic checks: Sum 246 / N 594 = 0.4141, and 594 − 246 = 348 not met. The systolic_bp range (96–178) is plausible. With all three reconciled, the table is trustworthy.

The interpretation. Across 594 synthetic screenings, mean systolic pressure is 128.4 (SD 14.2) and mean daily steps 7.45 thousand; 41% of screenings met the activity goal. The participant pool is balanced — an even 100/100 arm split, 104 F / 96 M, three comparably sized sites. This is a clean, honest descriptive picture and the launch pad for the procedures ahead. State the limits plainly: these are synthetic values, and the study is observational — any later arm difference will be associational, not causal, because the synthetic arms are not described as randomized. The summary describes the sample; it does not, by itself, support a health claim.

Worked example — transfer: a UNIVARIATE distributional check on enrollment age

The task. Switch context to a new variable and procedure pairing: before anyone models age, run a PROC UNIVARIATE distributional check on age in the cleaned participants table to confirm the week-5 cleaning actually worked — specifically that the impossible age typo of 199 was coerced to missing and no longer sits in the data. Same synthetic study, different variable, different validation question.

The code.

proc means data=well.participants n nmiss min max maxdec=1;
    var age;
run;

proc univariate data=well.participants;
    var age;
run;

The synthetic output:

Output (synthetic, not executed)
 The MEANS Procedure
   age:  N=199  NMiss=1  Min=22.0  Max=64.0

 The UNIVARIATE Procedure   Variable: age
   Quantiles:  100% Max 64   75% Q3 51   50% Median 44   25% Q1 36   0% Min 22

   Extreme Observations
     ----Lowest----        ----Highest----
     Value   Obs           Value   Obs
       22    188             61      19
       23     74             62     143
       24    101             63      57
       25     12             64      90
       26    160             64     167

The verification check. Read NMiss = 1 against N = 199: of the 200 cleaned participants, one age is missing — that is the former 199 typo, now correctly coerced to a SAS missing . during week-5 cleaning, so it was excluded from the statistics rather than averaged in. Confirm it in the extremes: the highest value is 64, not 199 — the impossible value is gone from the tail. The range (22–64) is plausible for an adult wellness program. The interpretation. The cleaning held: the age typo is missing, not lurking as a 199-year-old participant that would have dragged the mean upward and corrupted any age-based model. The workflow move is the same one as the recurring example — read N against NMISS, then look at the extremes — but the purpose here is to verify a prior cleaning step downstream. A summary table is not just a description; it is where you confirm the data are what you think they are before you trust a procedure built on them.

A common mistake

The week’s trap has three faces, all the same root error — reading a statistic without reading the N behind it, or reading the wrong statistic for the variable’s type.

  • Trusting a mean without its NMISS. PROC MEANS computes the mean over non-missing rows. If NMISS is large and you do not look, you report a “mean over 594 screenings” that was really computed on far fewer. Always print N and NMISS together and read them as a pair. A mean is only as honest as the count it was built on.
  • Forgetting that missing-value handling differs by procedure. PROC MEANS silently drops missing values from the statistic; PROC FREQ by default excludes missing from percents but prints a Frequency Missing footnote — and a filter like if age > 30 would exclude missings while if age < 30 would include them (missing sorts below any value). The fix is the same: check NMISS, read the missing footnote, and never assume a procedure handled missing the way you expected.
  • Averaging a categorical variable, or mis-reading a 0/1 mean. A “mean of sex” is meaningless — that is a PROC FREQ job. Conversely, the mean of the 0/1 goal_met is a proportion (0.41 = 41% met goal), not an abstract average; read it as a percent. Match the statistic to the type: counts/percents for categorical, mean/SD/quantiles for continuous, and a proportion for a 0/1 indicator.

A quieter version: running BY arm; without sorting first, which stops the step with ERROR: Data set is not sorted. Either PROC SORT ... BY arm; first, or use CLASS arm;, which needs no sort. And remember the build-wide caveat — every number here is synthetic and unverified; a clean-looking table is not a verified one.

Low-stakes self-checks (ungraded)

These are for self-study only — ungraded, no submission.

  1. Write a PROC MEANS call that reports N, NMISS, MEAN, STD, and MEDIAN for systolic_bp on the 594-row screenings table. What value should NMISS be, and what does that tell you about the mean of 128.4?
  2. Run PROC FREQ on arm and site in your head. What three numbers should the arm table show, and what three should site show? Confirm each table sums to the cleaned participant count of 200.
  3. Explain in one sentence why mean(goal_met) = 0.4141 is a proportion. From it, recover the count of screenings that met goal and the count that did not (you should get 246 and 348).
  4. You want a separate systolic_bp summary for each completed level. Write it two ways — once with CLASS, once with BY — and say which one requires a PROC SORT first and why.
  5. PROC UNIVARIATE on a numeric variable prints an Extreme Observations panel. In one sentence, why is that panel the fastest way to catch a data-quality problem like the week-5 baseline_bmi = 0?
  6. A classmate reports “the average sex is 0.52.” Name the mistake using this week’s vocabulary, and say which procedure they should have used instead.

Reading and source pointer

This week’s procedures are documented in the official SAS documentation (documentation.sas.com): the PROC MEANS / PROC SUMMARY page for descriptive statistics and the statistic keywords you request (N, NMISS, MEAN, STD, MEDIAN, and the CLASS versus BY distinction); the PROC FREQ page for one-way and cross-tabulated frequency tables and how missing values are handled in the counts and percents; and the PROC UNIVARIATE page for the quantile ladder, the moments, and the extreme-observations panel used as a validation check. Read those pages as a pointer to the authoritative syntax and option list — learning to check the documentation is itself a course skill — but note they are proprietary, so consult them at the source rather than expecting them reproduced here. These notes are the course’s own synthesis: grounded in the SAS documentation and open statistics references, but not copied from them. SAS® and all SAS Institute product names are the property of SAS Institute Inc.

Verification & reproducibility status

verified: false. The SAS programs, log excerpts, and every numeric value on this page are hand-authored, synthetic, and were NOT run — SAS is proprietary and is not executed in this build. The course SAS execution/output gate is BLOCKED; a rendered, syntax-highlighted code block or a typed listing is not evidence that the code runs or that the numbers are right. The load-bearing values here — systolic_bp mean 128.4, SD 14.2, min 96, median 127, max 178 over N = 594; steps_k mean 7.45; goal_met sum 246 / N 594 / mean 0.4141 (246 met, 348 not); the FREQ counts sex 104 F / 96 M, arm 100 / 100, site 70 / 66 / 64 summing to the cleaned 200; and the transfer-example age summary (N = 199, NMiss = 1, range 22–64, the 199 typo now missing) — are the locked values of the synthetic wellness-program study (call streaminit(20260824)), drafted “as if run” and cross-checked only for internal and narrative consistency. The data are synthetic and the analysis observational; nothing here is a real health finding. Do not treat any value as a confirmed reference until the human/SAS-run sign-off in the course’s private notation and verification ledger §5 is complete.

Public vs. graded

These notes, the SAS examples, and the practice here are public and ungraded — study material only. No graded prompts, answer keys, rubrics, point values, or due dates appear on this site. Graded SAS workflow checkpoints, skill checks, homework, analytics labs, the midterm practical, the final analytics project, and the final practical live in Blackboard (the LMS), which is authoritative for due dates, submissions, and grades. If this page and Blackboard ever disagree, follow Blackboard.

Looking ahead

Next week we take these same summaries from tables to pictures: PROC SGPLOT for a histogram of systolic_bp, and ODS for sending report-ready output to HTML and PDF. The descriptive numbers you locked this week — mean 128.4, the moderate spread, the goal-met proportion — become the figure captions and the report tables you can hand to a reader. The midterm practical (Friday, October 9, in class) sits at the end of this week and covers the workflow so far: the SAS environment and project setup, libraries and datasets, variable attributes, DATA step logic, importing, cleaning, validation, PROC SQL joins, and the summaries and reporting from this week. The authoritative date, format, and logistics for the midterm live in Blackboard.

See also