General Questions

• Why are statistics important? Who uses this anyway? 

  • Statistics are useful in helping people understand the world around them and what makes people tick. Statistics can be used for public relations, medicine, psychology, sociology, mathematics, teaching, and many other fields of study. Even if your field does not use statistics, studying this topic can help you know how different topics relate to one another and why people do the things they do.  

• What classes should I take before research and statistics?

  • Taking the Intro to Statistics class is helpful and needed before taking Research and Statistics 

• What is the difference between a dependent and independent variable? 

  • Independent variables (also known as “IVs”) are the things that are measured or changed to see how they influence something else. The word “influence” is important! An example of an independent variable would be something like this: Let’s say that a researcher wants to see if giving candy to students before a test will help them do better. The giving (or not giving) candy is the IV because it is what is influencing something else, in this case, test performance. 

  • Dependent variables (or “DVs”) are the things being impacted by the IVs, and are usually changeable. Back to the earlier example with candy and test performance, the DV would be the test scores because they are being impacted by the candy (or lack thereof).

• When should I use n-1 instead of just n?

  • When you are working with a sample size, you’re going to use n-1, and when you are working with the population size, you’re going to use n to find the standard deviation. 

• What is the difference between an experiment and observation? 

  • An experiment requires manipulations or involvement with a participant somehow. There are two main types of experiments: True experiments and quasi-experiments. True experiments involve a manipulation of some kind, such as giving two types of therapy to two groups of people and seeing which one works better. Quasi-experiments, on the other hand, usually happen when something cannot be ethically manipulated or changed, but the researcher wants to know how that thing impacts something else. For example, a researcher might want to know if people who own dogs are happier than people who own cats. Since he or she can’t force someone to own a cat or dog, the researcher will simply interview people who already own cats or dogs. Nothing was manipulated or changed in that scenario. 

  • Observations occur when researchers do not interfere or interact with the observed objects/animals/persons. The researcher will simply watch from a distance and record what happens. 

• What is the difference between dependent and independent t-tests?

  • With dependent t-tests, there are two groups being compared to each other, but they overlap in some way. For example, if a group of students take a pre-test at the beginning of a class and a post-test at the end of the class, the teacher might compare the scores from the beginning and end of the semester. Because the students completed both tests, the groups are not separate from each other (this is also known as a within-subjects design)

  • With independent t-tests, there are two groups being compared that do not overlap at all. For example, a researcher might want to know if different political party members prefer different types of fast food. He or she would compare Democrats and Republicans, which are two separate, distinct groups. 

• What is the difference between nominal, ordinal, interval, and ratio data? 

  • Nominal data refer to categories of information that have no numerical value and are simply groups or categories (i.e. – male or female; Republican, Democrat, or Independent, yes or no; etc.)

  • Ordinal data refer to numbers that are perhaps not evenly spaced out, such as getting 1st, 2nd, or 3rd in a race (since the space of time might be 1 minute, and the space between 2nd and 3rd might be 5 minutes, the three numbers aren’t equal in spacing)

  • Interval data refer to numbers that are equally spaced out and do not have a true zero (for example, degrees in Fahrenheit do not actually have a real zero – that would mean there is actually a point where there is no temperature) 

  • Ratio data refer to numbers that are equally spaced out and have a true zero (like age, weight, and height)

• What is the difference between quantitative data and qualitative data? 

  • Quantitative data is any data that uses numbers, scales, or categorical questions. These are easy to compute, and are typically easy to measure

  • Qualitative data is usually gathered through essays, interviews, or open-ended questions. These types of data are usually analyzed and coded by a group of readers or listeners who take all of the data and try to quantify it or categorize it in some way 

• What is the difference between a percentile and a percentage? 

  • Percentile: Shows how well someone did in comparison to everyone else. For example, if you scored in the 80th percentile on the ACT, this means that you scored better than 80 percent of the other test-takers

  • Percent: This shows any kind of proportion out of 100 (for example, if you get 4 out of 5 questions right on a quiz, you scored an 80% because you understood 80% of the information)

• What does it mean to be at a certain percentile?

  • It means that you have scored higher than that many other people who completed the test/task/assignment. For example, if you scored in the 90th percentile on a standardized test, then you scored higher than 90% of other exam takers. This does not mean that you got 90% of the information correct; it just means you did better than 90% of the other participants

• What is the difference between a permutation and a combination? 

  • With a combination, the order does not matter. For example, when choosing a lottery ticket, if your card matches all of the numbers selected, then you win (regardless of if the numbers are in the same order or not). 

  • For permutations, order does matter. For example, if I want to know the probability of placing three different paintings in a certain order, then I would be working with a permutation  

     Descriptive Statistics

• What does variance mean? 

  • Variance refers to the spread of the data (basically, how close together or far apart are the numbers in the data set?). An example of small variance would be if the scores on a test ranged from 90 to 100, while a larger variance might have a range from 30 to 100 on that specific exam. 

• What is the difference between variance and standard deviation? 

  • The standard deviation is the square root of the variance, and because of this, the standard deviation is the same unit/measurement as the mean, while the variance is the square of that unit/measurement

• How do you find mean, median, and mode? 

  • The mean is the most well known form of “average” in mathematics. To find it, you simply add all of the numbers up and divide by how many numbers you have (i.e. – if you have five students and want to find the mean test score, add all of the test scores together and divide by five). 

  • To find the median, place all of the data points in order from lowest to highest and count to the middle number (based on how many numbers you have). Back to the test score example, if the scores on the test were 45, 67, 72, 91, and 96, the median score would be 72, because it is the middle data point out of five. If the number of data points is even (meaning that there is no clear middle point), then add the two middle numbers together and divide by two 

  • With the mode, you simply find which number has been repeated the most in all of the data points

     Correlations and Regressions

• What is the difference between a positive and negative correlation? 

  • A positive correlation means that as one measure increases or decreases, so does the other. One example would be the correlation between amount of sleep and test scores (the more sleep you get, the higher your test score will be, and the less sleep you get, the lower your scores)

  • A negative correlation refers to when, as one measure increases, the other decreases (or vice versa). For instance, the more time you spend with friends, the less you will feel depressed (as your time with friends increases, your levels of depression decrease). 

• When do I run a regression instead of a correlation? 

  • For regression, the main question is “How much does X predict Y?” For example, if I wanted to see how promotion on social media impacts record sales of a new Coldplay album, then I would want to use a regression rather than just a correlation. Regression has the ability to predict data, which correlation cannot do. 

  • Correlation is used to simply see how closely related two variables are. For instance, if I wanted to know if there was any relationship between amount of sleep someone takes and test scores, then I would simply run a correlation. It is important to note that correlation does NOT equal causation. All this means is that just because there is a relationship between the two variables, this does not mean that one variable causes the other. It simply says there is some kind of relationship between the two. 

• What is the difference between r and r²? 

  • With correlations, “r” is used to show how closely related the variables are on a range of -1 to 1. The closer Pearson’s r is to 1 or -1, the stronger the relationship, and the closer to 0, the weaker the relationship. 

  • For r², it primarily looks at the line of best fit, and shows how well the line predicts or fits the data. Because it is squared, the range is from 0 to 1, since there cannot be a negative value when squared. The closer to 1, the better the line fits the data. 

• How do I know if a correlation is strong, moderate, or weak? 

  • A strong correlation will have an r of 0.6 to 1.0 (or -0.6 to -1.0)

  • A moderate correlation will have an r of 0.59 to 0.3 (as well as the negative forms of these)

  • A weak correlation will have an r of 0.29 to 0 (or the negatives)

  • It is important to note that some statisticians have this broken down even more into very weak, weak, moderate, strong, and very strong. The values given are rough estimates of the categories because people have different values for these categories 

• How do I describe the correlation of a scatter plot based on the graph or r-value?

  • The closer the plot points are to one another, the stronger the relationship. If the points are positive, then they will increase on the x-axis as they increase on the y-axis (for example, if the first plot point is (1,3), then the next would be something like (4,5)). 

  • The farther apart the points, the weaker the relationship. If the points are negative, then the values on the y-axis will decrease as the values on the x-axis increase (for example, the first point might be (1,10) and the next would be (4,6))

     Distribution 

• When is a bell curve skewed left or skewed right?

  • As they say, “The tail tells the tale.” When the tail of the curve is on the left side of graph, then it is skewed left. If the tail is on the right side, then it is skewed right. 

• What is a z-score used for? 

  • A z-score is used for standardizing data. It helps to show how the data fits in a normal distribution

     Analysis and Graphs

• What is an ANOVA? 

  • ANOVA is used to see if there are any differences between groups based on a certain factors (for example, if you want to know if there is a difference in levels of happiness between Republicans, Democrats, and Independent voters after election)

• What is a p-value? 

  • A p-value shows the likelihood that the data you found is based on chance or coincidence. The smaller the p-value, the less likely it is that the difference is just by chance. When a p-value is less than .05, then you can reject the null (the null means that there is no difference between the groups) and can say that there is in fact a difference 

• What is the alpha value? 

  • The alpha value is the number that determines if you can or cannot reject the null hypothesis. In statistics, this value is usually .05, but in some sciences such as medicine, the value is even smaller (.01). 

• How do you interpret the p-value? 

  • Depending on the alpha value, if the p-value is less than the alpha value, then you can reject the null. If it is greater than the alpha value, then you must accept the null and say there is no difference between the groups. 

• What is the difference between a histogram and a bar graph? 

  • A bar graph is used when one of the variables is nominal. For example, if I want to compare average hours of sleep per night between males and females, then the graph would show the two groups separated on the x-axis, with the hours of sleep being shown on the y-axis

  • A histogram shows the spread or distribution of the data, with both variables being interval or ratio. For example, if I wanted to see the polling rates over the last 20 years, I would show each year across the x-axis and the polling numbers on the y-axis. 

  • You can usually tell the difference between the charts by looking at the x-axis. If the bars are distinguished by things like “Males,” “Females,” “Republican,” or “Democrat,” which are nominal, then you are looking at a bar graph. If the x-axis is distinguished by interval or ratio data (like years or periods of time), then you are likely looking at a histogram. Histograms also do not have spaces between the bars. They basically look like the inside of a bell curve. 

     Tutoring

• When are the math tutoring lab hours? 

  • The hours are from 4 PM to 8 PM on Mondays through Thursdays

• Who are the tutors in the math lab? 

  • The tutors are most likely mathematics majors from Lee. Sometimes students with different majors are tutors, but they are all qualified to tutor.

• Where is the tutoring lab? 

  • The tutoring lab is located in the SMC on the third floor (room 357). This is room is on the hallway above Dunkin’ Donuts side of the SMC.