Designing an Experiment That Yields a Number

Does more bromide clean up the fog? is a question a strip and an afternoon can answer. How much base-plus-fog does 2 g/L of potassium bromide remove, what does it cost in effective speed, and is either figure larger than my apparatus can manufacture on its own? cannot be answered by an afternoon at all. It has to be written down first: a prediction with a size in it, a control that is still a control by the time it is compared, one variable, a spending plan for a finite number of strips, and a sentence — fixed before the first strip is exposed — saying how large a difference has to be before you are entitled to call it a difference.

That sentence is the whole difference between the two parts of this course. Part IX’s experimental design lesson built the skeleton: hypothesis, prediction, control, procedure, observations, data, interpretation and conclusion, with one variable moving and eleven held still. Nothing in it is retracted here. What this page adds is the arithmetic that becomes possible once a densitometer exists — and the discipline that becomes necessary, because an instrument that reports three decimal places will happily report a difference that is entirely its own.

The hypothesis, with a direction and a size

A Part IX hypothesis had to forbid something. A Part XXVII hypothesis has to forbid something of a stated size, because a direction can no longer be the answer. Compare:

Adding 1 g/L of potassium bromide to D-76 moves the threshold step and lowers base plus fog.

Adding 2 g/L of potassium bromide to D-76 1+1, at 20 °C for 11 minutes with the standard agitation script, lowers base plus fog by at least 0.03 density and moves the speed point at least 0.10 in log exposure — a third of a stop — in the direction of less speed.

The second is harder to write and much easier to kill. It names the bath, the dilution, the time, the temperature and the agitation, so somebody else could run it; it names two quantities rather than one, because a restrainer that bought fog reduction at no cost would be a remarkable thing and the cost is half the claim; and it puts numbers where a strip can contradict them.

Neither number in it is a course finding. 0.03 and 0.10 are what the writer of that sentence predicted before the session, and the course has published no measurement of what 2 g/L of bromide does to any film. They are there to show the shape of a testable claim, and if your own strips contradict them, your strips are the evidence and the sentence was wrong — which is what it was written to be able to be.

Three things feed those numbers, and they are three different kinds of statement, which is exactly what Rule 7 asks you to keep apart.

The direction comes from mechanism. Part VIII derives what a restrainer does and why: bromide ion in solution opposes the release of bromide from the crystal, so the developing agent’s attack on an unexposed grain is slowed more than its attack on one carrying a latent-image speck. That is established chemistry and it tells you which way the arrow points. It does not tell you how far.

The order of magnitude comes from published figures where they exist, and is marked as somebody else’s. Kodak’s process-control publication sets a contrast-index aim of 0.58 for negatives printed with a diffusion enlarger and puts its action limits at +0.07 to +0.20 and −0.07 to −0.12 around it. Those are Kodak’s numbers for Kodak’s process, and they are not a resolution figure — an action limit says when a professional laboratory investigates a drift, not what an instrument can see. But they are a useful calibration of scale: an organisation that measures film for a living treats a contrast-index deviation smaller than about 0.07 as not yet worth acting on.

The floor comes from your own apparatus, and this is the part most people leave out. If your certificate says your densitometer is good to 0.05 in the band where base plus fog lives, a hypothesis predicting a 0.03 change is not a bold hypothesis, it is an unfalsifiable one: no result you can obtain will contradict it. The remedy is not a smaller prediction. It is to predict a larger effect, use a larger dose, improve the instrument, or write down that this apparatus cannot answer this question — and that last is a legitimate finding, as the closing section of this page argues.

🧮Why a third of a stop, and not any other number

One stop is a factor of two in exposure, which is 0.30 in log exposure. A third of a stop is therefore 0.10 log H, and a nominal step of a Stouffer T2115 is 0.15, so the prediction is that the speed point moves about two-thirds of a step.

Now compare that with the exposure axis of your own budget. Part XIV’s worked error budget adds a wedge term of 0.02, uniformity 0.015, drift 0.01 and timing 0.002 to a bound of 0.047 log H on an uncalibrated wedge, or 0.029 on a calibrated one. Those are that page’s illustrative figures rather than a specification anything has met, and your own come from your own arms — but on figures of that size, a predicted shift of 0.10 log H is two to three times the budget. It is a prediction the apparatus can adjudicate.

Run the same arithmetic on a predicted shift of a sixth of a stop, 0.05 log H, and it lands on top of the budget. The experiment would be built to produce a shrug.

The control, and the three ways it stops being one

A control is the unchanged comparison, and the definition is deceptively easy to satisfy on paper. In a darkroom it decays, quietly, in three ways.

The film batch changes. Two cassettes with different emulsion batch numbers are two materials, and a difference between them will sit inside your curve family looking exactly like chemistry. The professional answer is not to assume the batches match but to measure the mismatch: Kodak’s procedure for changing to a new batch of control strips is a crossover — one strip from each batch processed together in three separate runs, the three contrast indices, speeds and minimum densities averaged for each batch, the difference between the two averages computed, and that difference then applied to the aim values. Kodak publishes no figure for how large the difference usually is, which is itself the point: it is not a constant, so it is measured rather than looked up. Copy the shape of that procedure if you are forced to change stock mid-series, and if you can, buy one batch for the whole part.

The water changes. One supply is not one water: hardness, chlorination and temperature all move through a year, and a bath made up on a February evening from a cold tap is not the bath you made in August. You cannot hold this still, so you record it — source, whether it stood, its temperature — which converts an unknown into a term you can later point at when two sessions disagree.

The latent image ages between the control and the test. This is the one that catches careful people, because it looks like patience. A strip exposed in March and developed in June has spent three months in latent image keeping, and it is not the same strip as one developed the same evening.

!What the course can and cannot tell you about the interval

What is sourced. ILFORD states that no significant change in picture quality will be seen when MULTIGRADE RC papers are left for 24 hours between exposure and processing. HARMAN’s direct positive paper sheet instructs that paper be processed as soon as possible after exposure to minimise any risk of latent image regression. ILFORD’s FP4 Plus sheet instructs that exposed film be processed as soon as practical. Part IV covers the mechanism — a latent-image speck below the stable size can decay — and the glossary entry collects what the historical literature says about which materials suffer most.

What is not sourced. The course has not obtained a quantified latent-image-keeping figure for film from a manufacturer: no sheet in its corpus says “expect x per cent of speed lost per month at 20 °C”. Two of the three manufacturer statements above are about paper, and the third is an instruction rather than a measurement. Anyone quoting you a number for film should be asked where it came from.

What follows for your design. Treat the interval as an unquantified systematic term that grows with time, and defeat it structurally rather than numerically. Part IX’s mitigation is the one this part uses: every session develops a shared reference strip from the same exposure batch under the same standard condition, so drift between sessions is measured instead of assumed away. Keep the tin cool and dry, run the sessions close together, and never compare a strip developed today with a control developed last spring when a fresh control costs one strip.

One variable, and the compound change that pretends to be one

“Change one thing” is easy to say and often impossible to do, because the darkroom’s variables are not independent of one another. The classic trap in this part is pH.

Suppose you want to know what pH does, and you move it by replacing the borax in D-76 with sodium carbonate, or with a little sodium hydroxide. You have moved the pH. You have also moved at least three other things in the same gesture:

• The buffer capacity. Carbonate brings a conjugate pair with it and holds its pH as development produces acid; hydroxide brings no pair at all, so the bath’s pH falls while it works. Part VIII’s alkalis page works this out with the numbers. Two baths that start at the same pH can finish eleven minutes later at different ones.
• The ionic strength. Different alkalis at the same pH mean different total salt concentrations, and ion activities — including the bromide ion doing the restraining — are not the same in the two baths.
• The sulfite speciation. Sulfite and bisulfite are a conjugate pair, so the proportion present as the sulfite ion is set by the pH as well as by what you weighed.

Naming the riders is not the end of the work. Sizing them is, because a rider that turns out to be negligible can be dismissed with an argument instead of an experiment, and that is the cheapest strip you will ever save.

🧮Sizing the three riders before spending film on them

Sulfite speciation. OpenStax gives sulfurous acid K_a2 as 6.4 × 10⁻⁸, so pK_a2 is 7.19. The ratio of sulfite to bisulfite is 10 raised to (pH − 7.19). At the pH ILFORD publishes for fresh ID-11 stock, 8.60 to 8.70, that ratio is about 29, so roughly 96.6 per cent of the sulfur is already present as the sulfite ion. Take the same bath to pH 10.5 and the ratio is about 2000, or 99.95 per cent. The free sulfite rises by about three per cent of what you weighed. That is the course’s arithmetic on a published constant and a published pH, and its conclusion is that in the range a film developer actually occupies, this rider is small. Dismiss it in a sentence and move on.

Buffer capacity. Part VIII works an acid load of 0.005 mol/L into D-76 and gets a pH fall of about half a unit; a carbonate bath at the same load would barely notice it, and a hydroxide bath has no pair to resist with at all. Half a unit of pH during the run is not a small rider, and it is not the same rider in the two baths. This one you cannot argue away.

Ionic strength. The course can say the direction — activity coefficients depart further from unity as the salt load rises — and cannot give you a correction, because that arithmetic belongs to a physical-chemistry treatment this course has not read. Record it as an unquantified term.

So the honest statement of what a carbonate-against-borax experiment tested is: the difference between two named baths, of which pH is the largest but not the only difference. Written that way it is still a good experiment. Written as “the effect of pH” it is a claim the design cannot support.

The alternative design, where the material allows it, is to move the variable within one system: more or less of the same alkali, so the pair is the same pair and only its position moves. That is a cleaner experiment and a narrower one, and choosing between the two is a real decision rather than an oversight — provided you write down which you chose and why.

✕A pH number is a measurement too, and it has its own error

Experiments in this part rest on pH readings — some taken at the bench, some copied off a Part IX sleeve months old — so a pH needs the same scepticism as a density. Harvey’s analytical chemistry text gives the glass electrode’s response as valid over roughly pH 0.5 to 9; above that the membrane responds to sodium and potassium ions as well as to hydrogen, and reads low. The text works a case at a true pH of 12.7 in 0.05 molal sodium where the error reaches −0.5 of a unit. A carbonate developer sits well above the stated range but well below that worked case, and sodium is exactly the interfering ion, so treat the worked figure as a bound on the size of the problem rather than as the size of your own error.

Two consequences. Calibrate at 7 and 10 so the sample is bracketed rather than extrapolated to, as the meter SOP sets out, and record the temperature of the measurement. And treat a high-pH reading as a repeatable fingerprint of your own bath rather than as a verdict on its true pH — which is enough for an experiment comparing your baths with one another, and not enough to argue with a manufacturer’s published figure.

One honesty about the source: this figure comes from an analytical chemistry text, not from an electrode manufacturer’s own documentation, which the course has not obtained. Part III teaches the bounding procedure that lets you report your own alkaline error as a bound rather than a value.

Replication: what the second strip buys, and what the tenth reading buys

A single strip is an anecdote, and not because one measurement is worthless. It is because one measurement carries no information whatever about how far it would have moved had you made it twice: the number and its scatter arrive as the same object and cannot be separated. Everything you can say about a lone strip you brought with you.

The second strip is the first that tells you something new. It does not give you a trustworthy spread — two numbers estimate a spread badly, which is one of the reasons this part stops short of a formal significance test — but it gives you the thing one strip cannot: a range. A pair agreeing to 0.005 in contrast index and a pair disagreeing by 0.08 licence entirely different sentences about the same cell, and the second pair is telling you to stop the experiment and repair the bench before any more film is cut. That is worth a strip on its own.

Beyond two, there are two kinds of repeat in this part and they measure different things. Confusing them is how a budget ends up describing the wrong apparatus.

Repeat the reading — the same step of the same strip, read ten times, lifting and replacing the film between readings — and you have measured your densitometer and your hands. This is the Type A term of the density axis. It costs no film, no chemistry and about ten minutes, which makes it the cheapest number in the whole part.

Repeat the strip — several strips, identically exposed and identically developed, side by side — and you have measured everything: the exposure, the bath, the temperature, the agitation, the wash, the drying and the reading, all at once. This is the number that decides what counts as a difference, and it is the expensive one.

The relationship between them is the useful part. If the strip-to-strip spread is barely larger than the reading-to-reading spread, your processing is already better than your instrument and the way to a sharper answer is a better densitometer. If the strip spread is several times the reading spread, no improvement to the instrument will help, and the work belongs in the water bath and the agitation. Which of the two you have is not something this course can tell you in advance — it is a fact about your bench, and the two ten-minute measurements below settle it.

🧪An evening that costs no film

You can measure the reading term tonight, from strips you already have.

Take one archived strip. Choose a step near the middle of the straight line and read it ten times, lifting the strip out of the carrier and replacing it between each reading, with the instrument warmed up and zeroed by its own rule. Write down all ten. The spread is your Type A density term at that density.

Then do the same at a step near base plus fog and at a step near maximum density. Three numbers, not one, because an instrument’s repeatability changes across its range — which is why Part XV writes its statement per density band rather than as a single figure.

If the ten readings at the dense step scatter far more widely than the ten at the middle, you have found your instrument’s working ceiling by the cheapest route available, and every plot you make from now on knows where to stop.

Then the spending decision. Averaging n identical strips narrows the uncertainty of their mean roughly as 1 ÷ √n, so three strips buy a factor of about 1.7 and nine buy a factor of three: replication gets expensive fast, in film and in evenings. Against that, every strip spent on a repeat is a strip not spent on another level of the variable, and an experiment with two levels and three repeats each tells you less about a curve’s shape than one with six levels and no repeats.

Part IX resolved this by replicating the control and running the cells singly, and accepting the consequence in writing: a difference smaller than the control set’s spread is not reported. That decision carries forward here, with the addition that the reading term is now measured separately and cheaply, so the control set no longer has to carry the instrument’s share of the blame.

The uncertainty budget, written before the first strip

The budget is the deliverable of this page. It is a list of every term that can move a number, each one sized, each one labelled as a property of your instrument or of your process, kept on the correct axis, and combined by a stated rule.

Two axes, and the single bridge between them

1. 1Log exposure terms — where a step sits sideways — wedge, uniformity, drift, timing. Properties of the sensitometer
2. 2Density terms — where a point sits vertically — repeatability, certificate, non-linearity, stray light. Properties of the densitometer, per band
3. 3The bridge — divide a density term by the local gradient G to move it onto the exposure axis, and write G down beside it
4. 4The resolution decision — three blanks, filled before the first strip is exposed, in the units the experiment will report

The figures shown are the worked illustrations from the two calibration pages, not specifications any instrument has met. What is real in the drawing is the shape: two axes that must not be added together, one legal bridge between them, and a decision at the bottom that has to be taken before the data exists.

The two axes, and the bridge

Part XIV’s budget owns the rule and this page does not re-derive it: log exposure terms and density terms are different quantities, and adding them because both are “about 0.02” is how a budget becomes fiction. The bridge between them is the local gradient of the characteristic curve:

Δ log H = Δ D ÷ G

Moving a density term onto the exposure axis

Δ D is a spread in density, G is the gradient of the curve at the density where you measured it, and Δ log H is what that spread is worth as an exposure error. The division is the whole content: the same 0.03 of density scatter is worth 0.05 log H on a straight line of gradient 0.6 and 0.20 log H out on the shoulder where the gradient has fallen to 0.15. Write G down beside every conversion, because a conversion without its gradient is a number with no units of meaning.

The combining rule is Part II’s and is not re-argued here: the terms are added, giving a bound, because that is arithmetic anybody can check. You may compute the root-sum-square as well — it will be roughly half — but you must say which rule produced which figure, and never print the smaller one bare.

!Why this part does not teach a significance test

The obvious next move is a formal comparison of two means — the test a science course would reach for when asked whether two sets of strips differ. This course does not teach one, and the decision is the course’s rather than a fact about statistics, so it is stated as a decision.

It has not read the right book. Part XV made the same admission about a plain-language uncertainty guide: the course could not obtain one meeting its own sourcing standard, and Rule 1 forbids paraphrasing a method from memory. A test misapplied is worse than no test, because it converts a judgement into a number that looks as though it came from somewhere.

The apparatus cannot feed it. A difference-of-means test needs an estimate of the spread within each group, and two or three strips estimate a spread badly — which is precisely the situation the earlier spending decision leaves you in. The machinery would be doing arithmetic on a number the experiment did not really measure.

The people who measure film for a living do not use one either. Kodak’s and ILFORD’s process control is a chart with an aim, an action limit and a control limit, and Part XIV sets those at two and three standard deviations taken from your own instrument certificate rather than from anybody’s published table. That is a decision rule fixed in advance, which is the thing that actually protects a result.

So what this part teaches is the bound, converted into a resolution decision, taken before the data exists. If you already know how to run a difference-of-means comparison and want to, run it as well, name the test, and report both answers — the resolution decision is what the later experiments assume, and it is the one that has to be in the plan.

The resolution decision

Now the sentence the whole page exists for. Convert the budget into the units the experiment will actually report, and write down, in advance, the smallest difference you will be entitled to call a difference.

Three anchors help you sanity-check the figure you get.

The construction’s own spread. The course’s contrast-index convention is stated arithmetically so that two people working from the same table of densities get the same answer, and Part XIII expects it to agree with the straightedge version to about 0.02. Within one series, worked the same way throughout, that term cancels. The moment a figure of yours is compared with one somebody drew with a straightedge — including a manufacturer’s — it does not, and 0.02 is the floor on that comparison before any instrument is involved.

A commercial instrument’s published figures. X-Rite’s brochure for a desktop transmission densitometer states a repeatability of ±0.01 D and a linearity of ±0.02 D from 0.0 to 5.0 D. That is what a metal-cased instrument claims about itself in a specification table, and it is the floor a home-built head is working towards rather than a figure it has met.

The industry’s own action threshold. Kodak’s tightest action limit on contrast index is 0.07 either side of aim. ILFORD’s process-control introduction makes the same point from the other end, stating plainly that a visual assessment of density cannot be used for accurate process control because it is not a measurement.

Put those together and the course’s expectation — which is an interpretation of three published figures and not a measurement of anything — is that a careful home bench lands somewhere between about 0.03 and 0.08 in contrast index. Treat that as a sanity check on your own arithmetic rather than as a value to adopt: a budget that comes out at 0.005 has a term missing, and one that comes out at 0.3 has an instrument fault to find before any film is spent. The number itself is not one this course can give you. It comes out of your own certificates, and the only thing this page insists on is that you write it down before you look at the data.

Confounds that belong to processing

Some of these are on Part IX’s list and are here again because instruments make them visible; the rest are new, and they are the ones a long series creates.

The bath drifts while the series runs. Kodak states that a developer temperature varying by more than 0.3 °C affects process control and image quality, and ILFORD’s compensation chart shows the leverage: on its 8-minute row, 20 °C becomes 9 minutes 45 seconds at 18 °C and 6 minutes 30 seconds at 22 °C, from which the course takes about 9 per cent of development time per degree near 20 °C. A six-cell series run over two hours in a room that warms up has a systematic trend built into its order.

The first film of a session is not the fifth. Kodak’s publication describes seasoning trends in which a fresh solution’s speed reading declines as the bath settles into its working state, and every film through a reused bath adds bromide and removes agent. If the series is developed in order of the variable, the drift and the variable move together and are inseparable afterwards. Running one-shot removes most of this: Kodak’s own sheet dilutes D-76 1+1 — its own wording is 1:1 — immediately before use, uses it once and neither reuses nor replenishes it, and ILFORD’s sheet gives a diluted working solution no more than 24 hours.

The thermometer is precise and wrong. A systematic offset of half a degree shifts every point in the family the same way, which is exactly what a chemical effect looks like. ILFORD’s process-control sheet recommends checking a built-in sensor against a good-quality liquid-in-glass thermometer, on the grounds that very little can go wrong with one — and the bench check SOP makes it a habit rather than an intention. This is accuracy against precision: a repeatable instrument reading against a wrong reference is precisely wrong every time.

The water is a chemical. Hardness varies by supply and by season, and it is the one input on this list you can neither hold nor measure with what the course has built. Record it and treat it as an unquantified systematic term.

The order of development is itself a variable. Every confound above enters the session in a sequence, so if the sequence follows the variable, none of them can be told apart from it afterwards. That is a design fault with a free remedy, and it is the next section.

Run order, and blinding what is still a judgement

Two different disciplines, often confused.

Randomise the order so that anything drifting through the session cannot line up with the variable. Three orders matter and all three are cheap: the order in which the strips are developed, so that a warming room does not masquerade as a dose-response; the order in which they are read, so that instrument drift is scattered across the family rather than concentrated at one end; and, where several strips share a tank, the position each occupies. Draw the order from shuffled cards, write it in the notebook before the session, and follow it even when it is inconvenient — particularly then, because the temptation to run the interesting cell first is exactly the correlation you are trying to break.

Blind the judgements that are still judgements. The densitometer is indifferent to your hopes, and to that extent the number needs no protection. But this part still asks for judgements no instrument makes: grain, image colour, apparent sharpness, evenness along a strip, and — in the closing assignment — which of four prints is better. Those are made by the person who mixed the developer, who is not a neutral observer of it.

Part IX’s scheme is the one to use, and it is not improved by elaboration: an assistant, or a shuffled set of cards, assigns each dried strip a random two-digit number written on the sleeve; the key goes in a closed page; every reading and every judgement is recorded against the random number, in one sitting, with the strips compared against each other rather than against memory; the key is opened only when the table is full.

Two caveats, both honest. Blinding fails on a sample that announces itself — a strip fogged grey to its edges is recognisable whatever number is on the sleeve — and it repairs nothing about a confounded design. It protects the close calls, which is where the arguments live.

Planning the programme against the material you have

An experiment you cannot afford to run is a design fault, not bad luck, and the arithmetic that catches it takes ten minutes.

Film. At the exposure geometry Part IX specified, a 36-exposure cassette yields ten or eleven strips of about 135 mm. Count in cassettes, and buy the whole part’s worth from one emulsion batch at one time.

Developer. Part IX’s standard cell is one strip in its own 100 mL measuring cylinder with at least 80 mL of solution, standing in the water bath. One-shot at 80 mL a strip, a litre of stock diluted 1+1 makes two litres of working solution and therefore about twenty-five strips — before any is lost to rinsing the cylinder or to a spoiled run.

Sessions. One exposure batch can serve several experiments, and this is where a programme is won or lost. Expose every strip a run of experiments will need in one sitting from one lamp at one distance, and the exposure stops being a variable at all. Store them in one labelled tin, develop the sessions as close together as the calendar allows, and put a shared reference strip through every session.

Then make the spending decision explicitly, on paper, before anything is cut.

The choice	What it buys	What it costs
More levels of the variable	The shape of the response — whether it is a straight line, a plateau or a reversal	No estimate of scatter at any level, so only differences larger than the control set’s spread may be reported
More repeats at fewer levels	A narrower uncertainty on each mean, as 1 ÷ √n	Two or three points cannot show a shape, and a plateau read as a straight line is a wrong conclusion drawn confidently
Repeats of the control only	The resolution limit itself, which applies to every cell	Nothing about whether one particular cell was an unlucky strip
Repeats of the reading only	The instrument’s share of the blame, for no film	Nothing at all about the processing, which is the term the strips have to measure

Where a series stops being able to tell its own points apart

• Kodak H-740 answer key, six published values

Show the numbers behind this plot

Six published points of contrast index against development time rise from 0.51 at five minutes through 0.55 at six, 0.62 at eight, 0.67 at ten and 0.72 at twelve to 0.73 at thirteen minutes, steeply at the left and almost flat at the right. A horizontal shaded band 0.07 tall, drawn between contrast indices of 0.665 and 0.735 and labelled as an example resolution, covers the last three points: the ten, twelve and thirteen minute values all lie inside it. The drawing's point is that the three minutes from five to eight buy 0.11 of contrast index, which any reasonable apparatus can resolve, while the three minutes from ten to thirteen buy 0.06, which lands inside the band and cannot be reported as a difference at that resolution. A series planned to run to thirteen minutes therefore spends three of its six strips on differences its instrument cannot adjudicate, and the fix is to space the levels by the expected effect rather than by equal intervals of time.

Series	Development time, minutes	Contrast index
Kodak H-740 answer key, six published values	5.00	0.51
Kodak H-740 answer key, six published values	6.00	0.55
Kodak H-740 answer key, six published values	8.00	0.62
Kodak H-740 answer key, six published values	10.00	0.67
Kodak H-740 answer key, six published values	12.00	0.72
Kodak H-740 answer key, six published values	13.00	0.73

The six points are Kodak's published values for the worked example in its sensitometry workbook, which names neither the film nor the developer and calls them XYZ and A; they describe no material you can buy. The band is an illustration of a resolution and not a measurement of anything - yours comes from your own budget, and where you draw it decides how many of your levels are worth exposing.

Read that plot as a design instruction rather than as a result. The lesson is not that thirteen minutes is a bad development time; it is that levels should be spaced by the expected size of the effect, not by equal intervals of the variable. Where a response flattens, equal steps buy less and less, and a series that keeps marching in equal steps eventually spends film on differences no instrument in the room can adjudicate.

The table before the data, and the analysis rule before the numbers

Draw the data table before the session, in full, with a row for every cell you intend to run and a column for every number you intend to write. A table drawn afterwards has a way of acquiring exactly the columns that turned out to be interesting.

Three of the course’s printable sheets already carry the fields, and using them saves you inventing a fourth format. The lab notebook sheets carry the session: what you set out to test, what you actually weighed, what you saw and the one change you will make next, split across four sheets by when each half is filled in, so the sheet says on its face which part is a prediction. The curve-plotting sheet carries one strip — the conditions that made it, the twenty-one step readings with the reading method’s own resolution beside them, and the four figures read off the plot with their constructions named. The formula version record carries the bottle.

Decide the plot in advance too: which quantity on which axis, and what shape would count as agreement with the mechanism.

And then the rule that does the most work of anything on this page.

!Fix the analysis before you see the numbers

Every construction this part uses contains choices. Contrast index depends on where you put base plus fog and which two points the chord cuts. The speed point depends on the criterion. An average gradient depends on which two densities you name. A “spoiled strip” depends on what counts as spoiled.

Made before the data exists, each of those is a definition. Made afterwards, with the numbers in front of you, each is a lever — and it is entirely possible to move a null result into a finding without ever writing down a figure you know to be false. Nobody has to be dishonest for this to happen; wanting the answer is enough.

So the plan names the construction, names the base-plus-fog source, names the exclusion rule for a bad strip, and names the resolution. Then it is signed and dated, and the strips are developed. If the analysis has to change afterwards — and sometimes it does, because you learn something — change it, record that you changed it, say why, and report both answers. A stated deviation is evidence. An unstated one is the reason somebody else cannot reproduce you.

The version number, and the three ways to stop

A curve tied to “D-76 with a bit more bromide” is a curve nobody can check, and a result nobody can check is not a result. The developer variants this part generates are versioned in the course’s own scheme rather than published as formulas — they are not formulary entries and are not offered as such — and the versioning SOP owns the procedure.

The code is STEM-INITIALS-SEQUENCE: a stem naming the published parent, a variant marker where any quantity departs from it, the initials of whoever mixed it because a systematic error travels with the hand, and a sequence number never reused. D76b-EB-004 is a claim about parentage, an identifiable pair of hands and one litre nobody else made. Issue it before anything is weighed, write it on the label before the bottle is filled, and cite it on every sleeve, strip, plot and print the batch produces.

Two sheets of that record are an experiment plan in disguise, and this page’s work lands directly on them. Sheet FV-3, the proposal, asks for five things and no more: the code and its parent, the single change as a quantity, the evidence from your own strips, the prediction stated so that it can fail, and the test that decides it. Sheet FV-4, completed after the run, asks what the control gave, what the variant gave, whether the prediction failed and where, your resolution limit, and the next version or none.

That last phrase — or none — is the stopping rule, and there are three legitimate ways to reach it.

The result is in. The measured difference exceeds your resolution, in the direction predicted or against it, and the number goes into the notebook with its uncertainty and its conditions beside it. A prediction failing is one of the ways this ending arrives, and it is the more interesting one: the hypothesis said “at least 0.06” and you measured 0.03 against a resolution of 0.02, so the effect is real, the direction was right and the size was wrong — which is a finding about that dose in that bath, and a correction to whatever gave you 0.06.

The result is null, and the null is informative. The difference is smaller than your resolution, and your resolution is small enough for that to mean something. “At this dose, in this bath, the effect is smaller than 0.03 in contrast index” is a genuine upper bound and a genuine contribution — provided the budget is stated, because a null from a blunt apparatus says nothing at all.

The apparatus cannot answer the question, and saying so is the finding. The predicted effect is smaller than your budget and you cannot shrink the budget without buying something. Write that down, name the term that dominates, and stop. Kodak’s own advice on reading a control chart is not to react to random variation, because over-controlling a process that is only making noise makes it worse; the experimental form of the same discipline is not to publish a difference your instrument invented. A page of your notebook that reads “this bench cannot resolve this question; the wedge term at 0.02 log H is the largest single term in the budget, it is the one term no amount of building can improve, and a calibrated wedge is the fix” is worth more than a plot with a conclusion under it that the plot does not support.

Alternative route

This page needs no facility: it is worked at a table with a pencil, the two calibration certificates and the manifest of what you have. But the plan it produces has to fit the facility you actually have, and two adjustments belong in the plan rather than in an apology afterwards.

With no darkroom, the whole measured programme still runs — a changing bag, a daylight tank, a tap and the two instruments are enough, and the archived strips are read in room light. What you cannot design in is any cell whose outcome is a print, so the closing assignment’s print comparison is out and the matrix rows that depend on it stay empty. Say that in the plan and in the report, and leave the cells blank with the reason written in; a comparison that names what it could not test is still evidence.

Working alone, the blinding scheme loses its assistant. Use the shuffled-card method, seal the key before the strips are dry, and accept the honest limit that self-blinding is weaker than the real thing — then write that limit into the plan as a stated weakness rather than discovering it in the discussion.

The plan, on one page

The order the plan is written in, which is not the order the session happens in

1. 1The question, in one sentenceWhat you want to know, before it is dressed as an experiment.
2. 2The hypothesis, with a sizeDirection from mechanism, magnitude from published figures or your own earlier strips, floor from your budget. It must be capable of being wrong.
3. 3The controlSame film batch, same exposure batch, same session, differing in exactly one thing — plus the shared reference strip that measures drift between sessions.
4. 4The one variable, and its ridersName what travels with it, size each rider, dismiss the small ones with an argument and carry the rest into the conclusion.
5. 5The levels, and where they sitSpaced by the expected effect rather than by equal intervals, and stopped where the response flattens below your resolution.
6. 6The uncertainty budgetEvery term sized, on the correct axis, combined by Part II’s bound, with the root-sum-square figure labelled if you want it.
7. 7The resolution decisionThe smallest difference that counts, in the units the experiment reports, written down and dated before any strip is exposed.
8. 8The replication and spending planHow many strips, at how many levels, with how many repeats, and how many the film in the tin actually allows.
9. 9The run order and the blinding schemeDevelopment order, reading order, tank position, and the sealed key for every judgement made by eye.
10. 10The data table and the analysis ruleEvery column drawn, the constructions named, the exclusion rule for a spoiled strip stated, the plot chosen.
11. 11The stopping ruleResult, informative null, or a statement that this apparatus cannot answer this question — and which term would have to shrink for it to.

Steps two, seven and eleven are the ones that make the difference between this part and Part IX. They are also the three that are impossible to add honestly once the data exists.

Recap

An experiment yields a number when the plan says in advance what would count as one. The hypothesis carries a direction taken from mechanism and a size taken from published figures and from your own budget, and it names the bath, the dilution, the time, the temperature and the agitation so that somebody else could run it. The control shares everything but the variable, and stops being a control when the film batch, the water or the interval since exposure changes underneath it. One variable moves, its riders are named and sized rather than assumed away, and what the experiment actually tested is written as what it tested.

The budget is built before the film is cut, on two axes that are never added together, with one legal bridge between them; from it comes the resolution decision, which is the sentence that separates a finding from an impression. Strips are spent deliberately between more levels and more repeats, the reading term is measured separately because it is nearly free, the run order is randomised and every judgement made by eye is blinded. The table is drawn and the analysis fixed before the numbers exist. Every bottle carries its version code, and the plan says in advance which of three endings it will accept — including the one where the honest answer is that this bench cannot see this effect.

Check your understanding

Question 1. Your certificate gives your densitometer a combined uncertainty of 0.05 D in the band where base plus fog sits. You write the hypothesis "adding 2 g/L of potassium bromide lowers base plus fog by at least 0.02 density". What is wrong with it as an experimental design?

• Nothing: a small predicted effect is a cautious prediction, which is good practice
• The predicted effect is smaller than the apparatus can resolve, so no obtainable result can contradict it and the experiment cannot fail
• The dose is too large, and 2 g/L will fog the film rather than restrain it
• Base plus fog is not a quantity a densitometer can measure

Show the answer and why

Answer: The predicted effect is smaller than the apparatus can resolve, so no obtainable result can contradict it and the experiment cannot fail

A hypothesis earns its keep by forbidding an outcome. If the whole predicted effect is inside the uncertainty, every possible measurement is consistent with the claim, so the film is spent producing a shrug. The remedy is a design change made before the session, not a caveat added after it: predict a larger effect, use a larger dose, attack the dominant term in the budget, or record that this apparatus cannot answer this question. That last option is a legitimate outcome and is worth more than a plot whose conclusion the plot cannot support.

Question 2. You move a developer from borax to sodium carbonate to test the effect of pH, and the contrast index rises. Which statement is the honest report of what you measured?

• Raising the pH raises the contrast index by the measured amount
• The carbonate bath gave a higher contrast index than the borax bath; pH is the largest difference between them, but the buffer capacity and the ionic strength changed with it, so the comparison is between two named baths rather than between two pH values
• The result is void because more than one thing changed
• The result is about the carbonate ion, since that is the ingredient that was added

Show the answer and why

Answer: The carbonate bath gave a higher contrast index than the borax bath; pH is the largest difference between them, but the buffer capacity and the ionic strength changed with it, so the comparison is between two named baths rather than between two pH values

Naming a compound change does not spoil the experiment; pretending it was a single change does. Both alkalis were sized before the session: the sulfite speciation rider turned out to be worth about three per cent of the weighed sulfite across the range a film developer occupies, small enough to dismiss with arithmetic, while the buffer capacity rider is worth roughly half a pH unit during a run and cannot be dismissed. The narrower experiment — more or less of the same alkali, so the conjugate pair stays the same pair — is available and is a real design choice, not a correction.

Question 3. You read one archived strip’s middle step ten times, replacing the film between readings, and get a spread of 0.008 D. You then read three identically exposed and identically developed strips once each, and their densities at that step spread by 0.045 D. What does the comparison tell you to do next?

• Improve the densitometer, since it is clearly the limiting instrument
• Nothing: the two numbers measure the same thing and the larger one is simply a better estimate
• Work on the processing — the water bath, the agitation script, the timing — because the strip-to-strip term is about six times the reading term and no improvement to the instrument can move the total
• Discard the three-strip result as an outlier and repeat it

Show the answer and why

Answer: Work on the processing — the water bath, the agitation script, the timing — because the strip-to-strip term is about six times the reading term and no improvement to the instrument can move the total

The two repeats measure different things. Re-reading one strip isolates the instrument and your hands; re-developing identical strips carries the exposure, the bath, the temperature, the agitation, the wash, the drying and the reading all at once. When the second is several times the first, the instrument is already better than the process, and the whole value of writing a budget is that it ranks the work: it tells you which habit is worth changing and which is not. Kodak’s figure that 0.3 °C of developer drift affects process control, and ILFORD’s 9 per cent of development time per degree near 20 °C, both point at the same bench.

Question 4. Which of these belongs in the plan before the strips are exposed, rather than in the analysis afterwards?

• The exclusion rule that says what counts as a spoiled strip
• The observation that the fourth cylinder was knocked during agitation
• The interpretation of why the toe moved less than the shoulder
• The comparison of your figures with a manufacturer’s published curve

Show the answer and why

Answer: The exclusion rule that says what counts as a spoiled strip

An exclusion rule written afterwards is a lever: with the numbers visible it is possible to remove the strip that spoils the trend without ever writing down a figure known to be false, and nobody has to intend it for it to happen. The same applies to the contrast-index construction, the base-plus-fog source and the resolution figure. The other three items are genuinely retrospective and belong where they are — an observation is recorded when it happens, and an interpretation and a comparison with somebody else’s published curve can only be made once your own numbers exist. If a fixed rule does have to change afterwards, change it, record the change, say why, and report both answers.

Question 5. A time series measures contrast indices of 0.67 at ten minutes, 0.72 at twelve and 0.73 at thirteen, against a stated resolution of 0.07. What is the correct report?

• Contrast index rises steadily with development time throughout the series
• The three points are not distinguishable from one another at this resolution, so the series has spent three strips where it cannot adjudicate; the response has flattened and the levels should have been spaced by the expected effect rather than by equal intervals of time
• The thirteen-minute point is an outlier and should be dropped
• The resolution of 0.07 is too conservative and should be reduced so that the differences become significant

Show the answer and why

Answer: The three points are not distinguishable from one another at this resolution, so the series has spent three strips where it cannot adjudicate; the response has flattened and the levels should have been spaced by the expected effect rather than by equal intervals of time

The widest gap among the three is 0.06, inside the stated 0.07, so no pairwise difference among them survives the budget. Reducing the resolution because the answer would be nicer is the failure mode the advance decision exists to prevent. The useful conclusion is about design: where a response flattens, equal steps in the variable buy less and less, and strips should be moved to the steep region or the series stopped. Kodak’s published values for its own unnamed example show the same shape - three minutes from five to eight buy 0.11, while the last minute buys 0.01 - which is why the workbook uses the curve to read a time off a chosen contrast index rather than the other way round.

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