Sensitivity and specificity: two rates, two errors

Today you complete one Sensitivity and specificity data table with five parts. Part A defines the two rates and labels the layout. Part B sorts ten supplied practice rows and counts the cells. Part C computes the two rates from your counts. Part D computes them for Tuesday's 1,000-person practice table and reads its positive column. Part E states two limits. One table, submitted once.

Every row and count is practice for the made-up Infection Q from Tuesday. No real disease, real test or real person appears here. No classroom ELISA well, plate photo or lab result is used, and you will see in R6 why it could not be.

Tuesday you argued about a false alarm and a missed case. Today each error gets a rate.

Sensitivity is the proportion of people who have the condition whose test comes back positive. In the StatPearls chapter on diagnostic testing accuracy (NCBI Bookshelf, Issues of Concern), it is "the proportion of true positive tests out of all patients with a condition." Formula: sensitivity = true positives ÷ (true positives + false negatives), written a ÷ (a + c).

Specificity is the proportion of people who do not have the condition whose test comes back negative. The same chapter calls it "the percentage of true negatives out of all subjects who do not have a disease or condition." Formula: specificity = true negatives ÷ (true negatives + false positives), written d ÷ (b + d).

The letters come from the layout in F1: a is a true positive, b a false positive, c a false negative, d a true negative. Sensitivity uses only the row of people who have the condition (a and c). Specificity uses only the row of people who do not (b and d). A plain way to hold them: sensitivity counts the people with the condition who were caught; specificity counts the people without it who were cleared.

Write A1 in your own words and copy both formulas, naming the letters. Label A2.

A 2x2 table has rows for what is actually true and columns for what the screen said. To place anyone in a row, someone has to know whether that person really has the condition. That knowledge comes from a reference standard: a screening test is assessed by its agreement with a recognised gold standard method of establishing the diagnosis (NCBI Bookshelf, Methods of assessing diagnostic test accuracy). In Tuesday's scenario, the reference standard was the confirmatory laboratory test.

Your ten practice rows each carry a supplied status, decided by that scenario's reference standard, and a supplied screen result. You can sort them only because the status is given. Keep that fact for E2.

Read the supplied status first, then the supplied result.

• Has Infection Q and screen positive: true positive (TP, cell a).
• Has Infection Q and screen negative: false negative (FN, cell c).
• Does not have Infection Q and screen positive: false positive (FP, cell b).
• Does not have Infection Q and screen negative: true negative (TN, cell d).

The name of a cell is the result (positive or negative) plus whether the result was right (true or false). Sort all ten rows in B1, then count in B2. Your four counts must add to 10, and TP + FN must equal the number of rows that have Infection Q. If they do not, one row is missing or doubled; find it before computing anything.

For C1 and C2, use your own counts. Write each rate as a fraction, then a decimal, then a percent rounded to the nearest whole percent. If a decimal repeats, write about before the percent. Rounding is not a measurement claim; it is a way to report a fraction.

First, the thing that confuses people here. The ten rows you just sorted and this 1,000-person table are two different groups from the same scenario. The ten are not ten of the 1,000. That is why the rates you compute in C1 and C2 will not match the ones you compute in D1, and it is not a mistake in either. A small batch gives a rough estimate of the same two underlying rates; a bigger one gives a steadier estimate. Sensitivity is a property of the TEST, not of whichever pile of people you happen to be holding.

Tuesday's practice table is reprinted on your handout: 100 people with Infection Q, of whom 95 screened positive and 5 negative; 900 without it, of whom 90 screened positive and 810 negative; 185 positive screens and 815 negative screens in all. Compute both rates in D1 using the row totals 100 and 900 as denominators.

Then read only the positive column for D2. Count the positive screens and count how many of them are true positives. Write one sentence on why a positive screen result is not a confirmation, using those two numbers. A screening result is never a confirmation; in the scenario, only the confirmatory test settles the question. If you want a name for the share of positive screens that are true, the StatPearls chapter calls it the positive predictive value, a ÷ (a + b). It is optional vocabulary today, not a required calculation.

Why does a clinic have to choose? The StatPearls chapter states the general pattern: "Sensitivity and specificity are inversely related: as sensitivity increases, specificity tends to decrease, and vice versa." The word *tends* matters; it is a common pattern, not a law for every test. For E1, take a position: which error should the scenario's clinic most avoid, a false negative or a false positive, and why? Use Tuesday's stipulations, reprinted here: after a positive screen, a confirmatory test and about three days at home; after a negative screen, nothing further unless symptoms appear; Infection Q can be passed to others while a person has it and is treatable once confirmed. Name the error, name what happens next to that person, and connect it to the rate that error lowers. This is your position about a practice scenario, not a rule and not medical advice.

You may run an ELISA in this course. A run like that has positive and negative controls: references with an expected result, used to check that the test worked (September 18 reading). A control tells you about the run. It does not tell you the true status of any other sample on the plate. A sample's positive or negative interpretation also needs the test's decision rule and the known control results. None of that supplies a reference standard for unknown samples, so a classroom run, by itself, cannot place its wells in the rows of this table or produce a sensitivity or specificity. Your practice rows could be sorted only because each row's status was supplied. Write E2 from this paragraph, in one sentence.

Hand the paper table to Mr. Mendoza before leaving, or submit one PDF to Wk5 Data table: Specificity vs sensitivity by the due time shown in Schoology. Use your period and code. Do not submit twice. Keep the table with Tuesday's CER record.

This is local John Hay practice connected by title to PLTW Medical Interventions Activity 1.1.6, Final Diagnosis. It does not complete that official activity, it plots no standard curve and it estimates no unknown; those need measured data this lesson does not supply.

If you were absent, or lose your place: the ten rows and the 1,000-person table are on the handout and the portal page. Complete A1 and A2, sort and count, compute, read the column, write the two limits, and submit once. No lab, photo or separate absence response.

References opened for this lesson: StatPearls, Diagnostic Testing Accuracy: Sensitivity, Specificity, Predictive Values and Likelihood Ratios, section Issues of Concern; Methods of assessing diagnostic test accuracy, NCBI Bookshelf. Background, not extra assignments.

R1. Your one data table

Today you complete one Sensitivity and specificity data table with five parts. Part A defines the two rates and labels the layout. Part B sorts ten supplied practice rows and counts the cells. Part C computes the two rates from your counts. Part D computes them for Tuesday's 1,000-person practice table and reads its positive column. Part E states two limits. One table, submitted once.

Every row and count is practice for the made-up Infection Q from Tuesday. No real disease, real test or real person appears here. No classroom ELISA well, plate photo or lab result is used, and you will see in R6 why it could not be.

R2. Two rates, two names

Tuesday you argued about a false alarm and a missed case. Today each error gets a rate.

Sensitivity is the proportion of people who have the condition whose test comes back positive. In the StatPearls chapter on diagnostic testing accuracy (NCBI Bookshelf, Issues of Concern), it is "the proportion of true positive tests out of all patients with a condition." Formula: sensitivity = true positives ÷ (true positives + false negatives), written a ÷ (a + c).

Specificity is the proportion of people who do not have the condition whose test comes back negative. The same chapter calls it "the percentage of true negatives out of all subjects who do not have a disease or condition." Formula: specificity = true negatives ÷ (true negatives + false positives), written d ÷ (b + d).

The letters come from the layout in F1: a is a true positive, b a false positive, c a false negative, d a true negative. Sensitivity uses only the row of people who have the condition (a and c). Specificity uses only the row of people who do not (b and d). A plain way to hold them: sensitivity counts the people with the condition who were caught; specificity counts the people without it who were cleared.

Write A1 in your own words and copy both formulas, naming the letters. Label A2.

R3. The table needs a reference standard

A 2x2 table has rows for what is actually true and columns for what the screen said. To place anyone in a row, someone has to know whether that person really has the condition. That knowledge comes from a reference standard: a screening test is assessed by its agreement with a recognised gold standard method of establishing the diagnosis (NCBI Bookshelf, Methods of assessing diagnostic test accuracy). In Tuesday's scenario, the reference standard was the confirmatory laboratory test.

Your ten practice rows each carry a supplied status, decided by that scenario's reference standard, and a supplied screen result. You can sort them only because the status is given. Keep that fact for E2.

R4. How to sort a row

Read the supplied status first, then the supplied result.

• Has Infection Q and screen positive: true positive (TP, cell a).
• Has Infection Q and screen negative: false negative (FN, cell c).
• Does not have Infection Q and screen positive: false positive (FP, cell b).
• Does not have Infection Q and screen negative: true negative (TN, cell d).

The name of a cell is the result (positive or negative) plus whether the result was right (true or false). Sort all ten rows in B1, then count in B2. Your four counts must add to 10, and TP + FN must equal the number of rows that have Infection Q. If they do not, one row is missing or doubled; find it before computing anything.

For C1 and C2, use your own counts. Write each rate as a fraction, then a decimal, then a percent rounded to the nearest whole percent. If a decimal repeats, write about before the percent. Rounding is not a measurement claim; it is a way to report a fraction.

R5. Read the 1,000-person table, then read one column

First, the thing that confuses people here. The ten rows you just sorted and this 1,000-person table are two different groups from the same scenario. The ten are not ten of the 1,000. That is why the rates you compute in C1 and C2 will not match the ones you compute in D1, and it is not a mistake in either. A small batch gives a rough estimate of the same two underlying rates; a bigger one gives a steadier estimate. Sensitivity is a property of the TEST, not of whichever pile of people you happen to be holding.

Tuesday's practice table is reprinted on your handout: 100 people with Infection Q, of whom 95 screened positive and 5 negative; 900 without it, of whom 90 screened positive and 810 negative; 185 positive screens and 815 negative screens in all. Compute both rates in D1 using the row totals 100 and 900 as denominators.

Then read only the positive column for D2. Count the positive screens and count how many of them are true positives. Write one sentence on why a positive screen result is not a confirmation, using those two numbers. A screening result is never a confirmation; in the scenario, only the confirmatory test settles the question. If you want a name for the share of positive screens that are true, the StatPearls chapter calls it the positive predictive value, a ÷ (a + b). It is optional vocabulary today, not a required calculation.

Why does a clinic have to choose? The StatPearls chapter states the general pattern: "Sensitivity and specificity are inversely related: as sensitivity increases, specificity tends to decrease, and vice versa." The word *tends* matters; it is a common pattern, not a law for every test. For E1, take a position: which error should the scenario's clinic most avoid, a false negative or a false positive, and why? Use Tuesday's stipulations, reprinted here: after a positive screen, a confirmatory test and about three days at home; after a negative screen, nothing further unless symptoms appear; Infection Q can be passed to others while a person has it and is treatable once confirmed. Name the error, name what happens next to that person, and connect it to the rate that error lowers. This is your position about a practice scenario, not a rule and not medical advice.

R6. What a classroom run cannot tell you, and how to submit

You may run an ELISA in this course. A run like that has positive and negative controls: references with an expected result, used to check that the test worked (September 18 reading). A control tells you about the run. It does not tell you the true status of any other sample on the plate. A sample's positive or negative interpretation also needs the test's decision rule and the known control results. None of that supplies a reference standard for unknown samples, so a classroom run, by itself, cannot place its wells in the rows of this table or produce a sensitivity or specificity. Your practice rows could be sorted only because each row's status was supplied. Write E2 from this paragraph, in one sentence.

Hand the paper table to Mr. Mendoza before leaving, or submit one PDF to Wk5 Data table: Specificity vs sensitivity by the due time shown in Schoology. Use your period and code. Do not submit twice. Keep the table with Tuesday's CER record.

This is local John Hay practice connected by title to PLTW Medical Interventions Activity 1.1.6, Final Diagnosis. It does not complete that official activity, it plots no standard curve and it estimates no unknown; those need measured data this lesson does not supply.

If you were absent, or lose your place: the ten rows and the 1,000-person table are on the handout and the portal page. Complete A1 and A2, sort and count, compute, read the column, write the two limits, and submit once. No lab, photo or separate absence response.

References opened for this lesson: StatPearls, Diagnostic Testing Accuracy: Sensitivity, Specificity, Predictive Values and Likelihood Ratios, section Issues of Concern; Methods of assessing diagnostic test accuracy, NCBI Bookshelf. Background, not extra assignments.