A salary model's experience slope is 2,400 dollars/year with a 95% interval of [900, 3,900] — do you act on it?
answer
- decide from the range, not the midpoint
- back out the implied standard error first
- ask what changes at each endpoint
- halving the width costs four times the data
- narrowness never repairs confounding
basics
~20 sDecide from the interval, not the point estimate. The data put the slope anywhere from 900 to 3,900 dollars per year, so act only if the same decision holds at both ends; otherwise the effect is not yet sized.
solid answer
~50 sFirst read what the numbers say. The half-width is 1,500 and the critical value is near 2, so the implied standard error is about 750 and the t-statistic about 3.2 — the positive direction is solidly established. But the top of the interval is more than four times the bottom, so *how much* is barely pinned down. The decision test is whether anything changes across that range: if the compensation policy you would set at 900 dollars per year of experience is the same one you would set at 3,900, ship it and stop measuring. If the break-even sits inside the band, the answer is that you cannot size this yet, and the money goes to more data or a better-controlled design rather than to the decision. Also flag that this is an observational fit: the interval prices sampling noise only, so a narrow interval on a confounded slope is confidently wrong.
go deeper
Be ready to state the slope in its units — dollars of salary per additional year of experience — and to quote the interval alongside it rather than the bare number.
Expect to reconstruct the implied standard error of about 750 from the half-width, and the t-statistic near 3.2 that follows from it.
Show that you check whether the decision flips anywhere inside the interval, and that you can price what narrowing it would actually cost in data.
Own the call: decide whether the residual uncertainty is worth buying down, and separate that from the design question of whether the slope answers the causal question at all.
## Read the numbers first The reported slope is 2,400 dollars of salary per additional year of experience, with a 95% interval of `[900, 3,900]`. Two facts fall out immediately. **The interval is symmetric around the estimate**, with a half-width of 1,500. Since the interval is `estimate +/- (critical value) * SE` and the critical value is close to 2 for any reasonable sample size, the implied standard error is roughly `1500 / 2 = 750`. That in turn gives `t = 2400 / 750 = 3.2`, comfortably past the usual bar. So there is nothing marginal about the *sign* of this relationship. **The interval is wide relative to the estimate.** The upper end is more than four times the lower end. In outcome units, the data are compatible with an extra year of experience being worth anything from a modest 900 dollars to a substantial 3,900. Anyone quoting "experience is worth 2,400 a year" without the band is over-claiming. ## The decision test The useful question is not *is it significant* but *does any decision change across the interval*. Run the two endpoints through whatever the number feeds: - **Same call at both ends.** If the compensation band, the hiring policy or the budget line you would set at 900 is the same one you would set at 3,900, then the imprecision is irrelevant to this decision. Act, note the uncertainty, and do not spend anything narrowing it. - **The break-even sits inside the band.** If a policy is worth doing at 3,000 and not worth doing at 1,200, the interval straddles the decision boundary. The honest report is *we cannot size this yet* — not a recommendation dressed in a point estimate. This is where more measurement is genuinely worth buying. - **Even the low end is decisive.** If 900 already justifies the action, the wide interval is a nice problem to have; the downside case still clears the bar. This framing is what separates a lead from an analyst. The analyst reports the estimate and its interval; the lead maps the interval onto the decision and says whether the residual uncertainty is expensive. ## What narrowing it costs If the band does straddle the break-even, know the price before promising a tighter number. Standard errors fall as roughly one over the square root of the sample size, so halving the width takes about four times the data. Frequently the cheaper routes are elsewhere: reducing residual noise by specifying the model better or measuring the outcome more cleanly, or getting more variation in the experience variable itself by widening who is in the sample. Quadrupling headcount data is rarely on the table; a better-specified model often is. ## The limit of what the interval covers The most important caveat is one that no amount of extra data will fix. This interval quantifies **sampling variability only** — how much the estimate would move across samples drawn from the same process. It says nothing about whether the slope answers the causal question anyone actually cares about. In an observational salary fit, experience is entangled with role, seniority, tenure at the firm and cohort effects, so the 2,400 mixes the return to experience with whatever else moves alongside it. Collect ten times the data and you get a beautifully narrow interval around a number that still is not the causal effect. Precision and correctness are independent, and confidence in a biased estimate is the more dangerous failure. So the complete answer has two branches: given the model, the effect is positive but loosely sized; and separately, whether the model licenses the interpretation the decision needs is a design question the interval cannot speak to. ## How to report it Never ship 2,400 alone. Report it as *about 2,400 dollars per year, with the data consistent with roughly 900 to 3,900*, state which decision the range does and does not settle, and name the assumptions the causal reading rests on. If a stakeholder asks for one number, give the number that is conservative for their decision rather than the midpoint, and say why. ## What an interviewer is listening for That you back out the standard error and t-statistic from the printed interval without being asked; that you convert statistical uncertainty into a decision question rather than a threshold check; that you know the cost of narrowing; and that you do not mistake a tight interval for a trustworthy estimate.
- What standard error and t-statistic does that reported interval imply?The half-width is 1,500 dollars and the 95% critical value is close to 2, so the standard error is around 750 dollars per year. That puts the t-statistic near 3.2, well past the usual bar. So the direction is solidly established even though the magnitude spans a factor of more than four — a useful reconstruction when a report gives you an interval but no standard error column.
- The team wants a narrower interval before the next planning cycle. What do you buy?Understand the price first: standard errors fall as one over the square root of n, so halving the width needs roughly four times the observations, which is usually not available on a headcount timescale. The cheaper levers are reducing residual noise through better specification or cleaner outcome measurement, and widening the range of experience represented in the sample. Sometimes the right answer is to accept the width.
- Would a much narrower interval make you comfortable treating 2,400 as the causal return to experience?No. The interval prices sampling variability under the fitted model and says nothing about whether experience is entangled with role, seniority or cohort. More data shrinks the band around whatever the model is actually estimating, bias included, so a narrow interval on a confounded slope is confidently wrong. Trust in the causal reading comes from the design, not from the width.
saying these in an interview costs you the question
- Quotes the point estimate without the interval
- Treats significance as a green light to act
- Assumes a narrow interval means the estimate is unbiased
- Promises a tighter interval without pricing the extra data
- Reads the interval width as a statement about individual salaries