Exams are usually 30-40% of the overall course grade. I give in-class exams, the questions are mostly open-ended/short-answer. I let students go about 10 minutes after the class ends but no longer. However, if there is a foreign student who has language problems, I may give them the test in my office and allow more time. I announce this option for all students. I use exams to motivate the students to study and keep up to date. I see them as a way to facilitate student learning. I do get some useful information from them about what difficulties students may be having. Cheating hasn't been a problem. I do walk around the room periodically and keep my eye on students (e.g., don't sit and read while they are being tested.
It depends on the class. I NEVER have students memorize formulas or definitions. Sometimes they are allowed to bring one page of notes, sometimes they can use study questions that are used to guide their reading of the textbook. Knowing they can use these study questions on tests motivates students to answer them, which helps draw their attention to the important ideas in the textbook. The only restrictions are either page length (one page both sides, standard paper size) or type (study question sheets I've passed out).
I try to have students complete some questions using computer software. They may use a calculator but usually don't need it.
I usually think of an idea or skill to assess, and then look for good items or data sets to use. I don't always use real data sets, but I try to provide contexts for any phony data sets. I try to have each piece of information worth a point. A question with many parts and answers is worth more points.
In creating a test, I think about the content that the exam is to cover, and decide what are some key concepts and competencies I want to assess. I think of things that students may misunderstand that I think are important, so that I may see if any one is misunderstanding the material. I try to have a balance of items that assess basic literacy as well as challenging items that require students to reason about data or concepts and explain their reasoning. I never try to include "everything" studied in a unit but try to sample from each general topic area covered on the exam. If there's time I ask my TA to review the exam and check it for clarity and any typos. I usually have a pretty good sense of time, and try to keep the exams brief, realizing for every minute it takes me to solve a problem it will take the students about 10! Therefore, I do "take" the exam myself, writing down the correct answers, before I give it. I have also discovered many errors this way! I know it's a good exam if the students do not misunderstand the questions (as evidenced by questions in class as well as responses on the questions) and if I get a negatively skewed distribution with most students doing well, and at least some students getting all answers correct. (My students are graduate students who study and try to succeed in this class.) My goal is for all students to master the material and I design the test to help me determine if this has happened.
I start at 0 and add points earned. I don't curve exams. Students accumulate points in the course for HW, projects, tests, etc., and then the course grade is based on percentage of total points earned in the course. It's a mastery system.
I like to have students tell me what they have learned in the unit, as a review. For example, I'll ask them: tell me everything you know about bivariate data. Then they tell me what they know and we talk about the different concepts and skills. If there's something missing, I try to give hints so they will think of it. I review during part of the class session before an exam. Sometimes I bring a sample exam to class and students work on that together and we discuss questions they have.
I write comments on the exams and take off points where things are wrong or missing. I sometimes go over the whole exam quickly, but if everyone did well I just talk about the main items people missed. I encourage students to come see me to discuss questions they have about answers and grading. Sometimes if students did very poorly I'll give the whole class a chance to correct errors they made, by writing up each missed problem that they did wrong, and how to do it right. This is before telling them the answers!