CREATE TABLE "Tests"
(
"TestGroup" VARCHAR(5) COLLATE "ANSI_CI" NOT NULL,
"Test" VARCHAR(5) COLLATE "ANSI_CI" NOT NULL,
CONSTRAINT "indPrimaryKey" PRIMARY KEY ("TestGroup", "Test")
)

INSERT INTO "Tests" VALUES ('FAT','CHOL')!
INSERT INTO "Tests" VALUES ('FAT','HDL')!
INSERT INTO "Tests" VALUES ('FAT','LDL')!
INSERT INTO "Tests" VALUES ('FAT','TRIG')!
INSERT INTO "Tests" VALUES ('FATS','CHOL')!
INSERT INTO "Tests" VALUES ('FATS','HDL')!
INSERT INTO "Tests" VALUES ('FATS','LDL')!
INSERT INTO "Tests" VALUES ('FATS','TRIG')!
INSERT INTO "Tests" VALUES ('LFT','ALB')!
INSERT INTO "Tests" VALUES ('LFT','ALP')!
INSERT INTO "Tests" VALUES ('LFT','ALT')!
INSERT INTO "Tests" VALUES ('LFT','AST')!
INSERT INTO "Tests" VALUES ('LFT','GGT')!
INSERT INTO "Tests" VALUES ('LFT','TBIL')!
INSERT INTO "Tests" VALUES ('LIPID','HDL')!
INSERT INTO "Tests" VALUES ('LIPID','LDL')!
INSERT INTO "Tests" VALUES ('TAM','ALT')!
INSERT INTO "Tests" VALUES ('TAM','GGT')!

First version:

SELECT T1.TestGroup, T2.TestGroup,
    Count(*) AS C1, Count(T2.Test) AS C2,
    (SELECT COUNT(*) FROM Tests AS T3 WHERE T3.TestGroup = T1.TestGroup) AS C3,
    (SELECT COUNT(*) FROM Tests AS T4 WHERE T4.TestGroup = T2.TestGroup) AS C4
 FROM Tests AS T1
    INNER JOIN
        Tests AS T2
            ON T1.Test = T2.Test AND T1.TestGroup < T2.TestGroup
GROUP BY T1.TestGroup, T2.TestGroup
HAVING
  C1 = C3 AND C2 = C4

Second version:

SELECT T1.TestGroup, T2.TestGroup,
    Count(*) AS C1, Count(T2.Test) AS C2,
    (SELECT COUNT(*) FROM Tests AS T3 WHERE T3.TestGroup = T1.TestGroup) AS C3,
    (SELECT COUNT(*) FROM Tests AS T4 WHERE T4.TestGroup = T2.TestGroup) AS C4
 FROM Tests AS T1
    INNER JOIN
        Tests AS T2
            ON T1.Test = T2.Test AND T1.TestGroup < T2.TestGroup
GROUP BY T1.TestGroup, T2.TestGroup
HAVING
   count(*) = (SELECT COUNT(*) FROM Tests AS T3
               WHERE T3.TestGroup = T1.TestGroup)  AND
   count(T2.Test) = (SELECT COUNT(*) FROM Tests AS T4
                     WHERE T4.TestGroup = T2.TestGroup)