Problem Set for Research Methods - Master's Research and Thesis | FOR 500, Assignments of Forestry

Download Problem Set for Research Methods - Master's Research and Thesis | FOR 500 and more Assignments Forestry in PDF only on Docsity! Problem set for PSYC585, Research Methods This set of problems was designed to get you back into thinking about research issues, basic statistical issues, and general mathematical procedures. Please take a few hours (no less than 4 unless you can answer it faster, no more than 8) during the first week of the semester to work on it. Some of the problems might be very easy, whereas some others might be very hard at the moment (sometimes you might not even understand the question). Please test yourself and see whether you (a) think you can answer these problems, and then (b) actually try to answer them in as much detail as you want to. This is your first assignment and a means for you to assess whether you still know / remember quite a bit from you previous research methods / math / stats background or whether there are particular areas that you should work on right now. Please indicate on your answer how much time you have spent on each question. You will only be graded on your effort, not on your success in answering the questions. You may use any books / other sources to try to solve these problems. If you have any problems, you can come by and discuss some of the problems with me or talk to other students about them (of course it defeats the purpose if you have someone else do the problems for you!) Probabilities 1. Look at problems 1 and 2 on page 159 in K&L. Please try to solve the problems without looking at the answers first. 2. What is the number of different sequences of heads and tails when tossing a coin 16 times? Each time there are two possible outcomes – so the number of sequences is 2^16 (2 to the power of 16) 3. What is the probability of getting tails 16 times out of 16 for a balanced coin? There are two ways of looking at this problem. First, every time a coin is tossed the probability of getting a tail is .5. This has to occur 16 consecutive times, so the probability is .5^16. Another way to look at it is that this sequence is exactly one possibility of all sequences. In the previous example we computed that there are 2^16 possibilities. 1/2^16 is the resulting probability. 4. What is the probability of getting exactly 500 tails when tossing a coin 1000 times? (Can be an approximate answer) This is tricky. The probability is NOT .5 but instead very small. The reason for this is that we are looking for exactly 500 tails. The probability is around 3% and is the highest probability, but the probability of getting 499 or 501 tails is about the same. If the probability were .5 for 500, then adding the probabilities for 499 and 501 would result in a probability larger than 1 (which isn’t possible!) 5. What is the probability of getting a total sum of at least 10 from 2 dice if the first die shows a 5? For this you need to count the number of scenarios that are possible and then divide by 1 the total number of scenarios / outcomes / events. If the first dice shows a 5, you need at least a 5 or a 6 to get at least 10 points total. These are two events. There are 6 possible outcomes for the second dice. Therefore the probability is 1/3. Descriptive statistics 1. Try to define the three measures of central tendency (mean, mode, and median). Compare the three measures – what are the advantages, what are the disadvantages of each? Try to come up with a situation for each measure in which it would be the “best” measure to use. We will talk about this at length in class. 2. What is the advantage of using the standard deviation over the variance in reporting data? The basic advantage is that the standard deviation is expressed in the same unit as the data that you collected (for example, height in inches). The standard deviation can thus be easily related to the data. The variance is expressed in the square of the base unit – so for example if you measured the height of people in feet, then the variance would represent an area in square feet – and it is hard to see how that relates to your data of interest. 3. Correlations Can you sketch a scatterplot for each of the following situations: A: A high positive correlation The regression line has a positive slope (if the axes of the scatterplot conform to the usual conventions) AND MOST IMPORTANTLY the data points are close to the line! The slope itself tells you something about the sign of the correlation, but NEVER tells you how high the correlation is!!! B: A low negative correlation Negative slope, but the points are scattered widely around the regression line! Again, the slope doesn’t tell you anything about the strength of the correlation. C: A zero-correlation In this case you have a flat slope (the regression axes is parallel to the x-axis [and happens to go directly through the mean of the data set].) The points can be far away or they can all lie on the line. 2