Ertugliflozin and Sitagliptin Co-administration Factorial Study (VERTIS FACTORAL, MK-8835-005)

Inclusion Criteria: * Type 2 diabetes mellitus as per American Diabetes Association guidelines * On metformin monotherapy (\>=1500 mg/day) for \>=8 weeks with a Visit 1/Screening A1C \>=7.5% and \<=11.0% (\>=58 mmol/mol and \<=97 mmol/mol) OR On metformin monotherapy (\>=1500 mg/day) for \<8 weeks with a Visit 1/Screening A1C \>=7.5% and \<=11.0% (\>=58 mmol/mol and \<=97 mmol/mol) OR On metformin monotherapy \<1500 mg/day with a Visit 1/Screening A1C \>=8.0% and \<=11.5% (\>=64 mmol/mol and \<=102 mmol/mol) * Body mass index (BMI) \>=18.0 kg/m\^2 * Male or female not of reproductive potential * Female of reproductive potential who agrees to remain abstinent from heterosexual activity or to use 2 acceptable combinations of contraception Exclusion Criteria: * History of type 1 diabetes mellitus or ketoacidosis * History of other specific types of diabetes (e.g., genetic syndromes, secondary pancreatic diabetes, diabetes due to endocrinopathies, drug- or chemical-induced, and post-organ transplant * A known hypersensitivity or intolerance to any sodium glucose co-transporter 2 (SGLT2) inhibitor or sitagliptin * Has been treated with any of the following agents within 12 weeks of study start or during the pre-randomization period: Insulin of any type (except for short-term use \[i.e., \<=7 days\] during concomitant illness or other stress), other injectable anti-hyperglycemic agents (e.g., pramlintide, exenatide, liraglutide), pioglitazone or rosiglitazone, other SGLT2 inhibitors, alpha glucosidase inhibitors or meglitinides, dipeptidyl-peptidase 4 inhibitor (DPP-4 inhibitor), sulfonylureas (SUs), bromocriptine (Cycloset™), colesevelam (Welchol™), any other antihyperglycemic agents (AHA) with the exception of the protocol-approved agents * Is on a weight-loss program or weight-loss medication or other medication associated with weight changes and is not weight stable prior to study start * Has undergone bariatric surgery within the past 12 months or \>12 months and is not weight stable prior to study start * A history of myocardial infarction, unstable angina, arterial revascularization, stroke, transient ischemic attack, or New York Heart Association (NYHA) functional class III-IV heart failure within 3 months of study start * Active, obstructive uropathy or indwelling urinary catheter * History of malignancy \<=5 years prior to study start, except for adequately treated basal cell or squamous cell skin cancer or in situ cervical cancer * A known history of human immunodeficiency virus (HIV) * A blood dyscrasia or any disorder causing hemolysis or unstable red blood cells, or a clinically important hematological disorder (e.g. aplastic anemia, myeloproliferative or myelodysplastic syndromes, thrombocytopenia) * A medical history of active liver disease (other than non-alcoholic hepatic steatosis), including chronic active hepatitis B or C, primary biliary cirrhosis, or symptomatic gallbladder disease * Any clinically significant malabsorption condition * Current treatment for hyperthyroidism * On thyroid replacement therapy and not on a stable dose for at least 6 weeks prior study start * On a previous clinical study with ertugliflozin * Estimated glomerular filtration rate (eGFR) (using the 4-variable Modification of Diet in Renal Disease Study Equation (MDRD) equation) \<60 mL/min/1.73 m\^2 * Serum creatinine \>= 1.3 mg/dL (115 µmol/L) for males and \>= 1.2 mg/dL (106 µmol/L) for females * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \>2 times upper limit of normal * Hemoglobin \<12 g/dL (120 g/L) for males and \<11 g/dL (110 g/L) for females. * Participated in other studies involving investigational drug(s) 30 days prior to study start * Surgical procedure within 6 weeks prior to study start or major surgery planned during the trial * Positive urine pregnancy test * Pregnant or breast-feeding, or planning to conceive during the trial, including 14 days following the last dose of study medication * Planning to undergo hormonal therapy in preparation for egg donation during the trial, including 14 days following the last dose of study medication * Routinely consumes \>2 alcoholic drinks per day or \>14 alcoholic drinks per week or engages in binge drinking * Donated blood or blood products within 6 weeks of study start