Basic Statistical Analysis in Excel NICAR 15 / Norm Lewis, University of Florida

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1 Basic Statistical Analysis in Excel NICAR 15 / Norm Lewis, University of Florida Installing Analysis ToolPak, Windows 2013 Click on the Data tab. The Analysis section on the far right should look like the box to the left. If it does not, install the ToolPak: 1) Click on the File tab. 2) Click on Options at the bottom of the list on the left-hand side. 3) Click on Add-Ins, which will trigger the dialog box seen at the lower left. 4) At the bottom of the box, if Manage: Excel Add-ins is showing, click on the Go button. Click on the Analysis Tool Pak box (seen below), then click OK. Installing Analysis ToolPak, Macintosh 2011 Microsoft no longer includes the Analysis ToolPak for Macintosh users. (Insert snarky commentary about Microsoft leaving Mac users at the curb.) Microsoft support refers us to StatPlus:mac LE from AnalystSoft for free, though with encouragement to upgrade to the paid Pro version. Average The most common statistic journalists use is average. Average comes in three flavors: Mean Sum divided by number of items. Excel function: AVERAGE() Median Midpoint of a sorted list. Excel function: MEDIAN() Mode Most frequent occurrence. Excel function: MODE() Mean is used so often it s the default. But it overstates what s typical for data that have outliers such as income, wealth and housing prices. In those cases, the median is better. (Mode is rarely used in journalism.)

2 Calculate Mean and Median Open the Faculty sheet. Go to the bottom. Leave a blank row. Write the word Mean. In the next cell, insert this formula: =AVERAGE(e2:e1054) Write the word Median. In the next cell, insert this formula: =MEDIAN(e2:e1054) You should get the data below. Which of these two figures should you use? The mean is higher because it is skewed by some big salaries. Thus, median is a better representation of a typical professor on a nine-month contract. When Average Isn t Enough: Standard Deviation Now let s put the Analysis ToolPak to use. 1. Click on a cell with a salary any single one will do. 2. Click on the Data tab. On the right, click on Data Analysis. 3. Choose Descriptive Statistics (below) and then OK. 4. In the ensuing dialog box (right), click on the box besides Summary statistics 5. In the Output Range box, insert G3 or click on the cell this tells Excel where to place the descriptive statistics The ensuing data look like this: The mean and median are just as we calculated them before, with the addition of the mode This tells us the smallest and largest salary in this data set Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 2

3 The standard deviation tells us how much this data set varies from the mean. That can be useful in evaluating a data set like this, which varies considerably. Standard deviation is a measure, plus or minus, from the mean. One standard deviation includes two-thirds (66.7%) of all of the data points in this case, salaries. The larger the standard deviation relative to the mean, the more variance in the data. The standard deviation here is 43, Thus, two-thirds of the 1,053 salaries in this list are between: 101, , = 58, and 101, , = 144, That s a fairly large range, which tells us that university salaries vary considerably from the mean. Thus, defining typical pay is difficult if we use just the mean or even the more representative median. Consider another example to see why standard deviation matters. To the left is a graphical representation of Amazon customer ratings of a book by Ann Coulter. The mean would be about 3 stars. But neither the median nor the mean would be representative of what customers think about the book. Raters tend to either love or despise the book. Thus, the standard deviation would give us an important statistic beyond the average. Correlation Correlation measures whether two things are related. Does one go up when the other does? Does one go down when the other goes up? Consider height and weight, as in the chart to the right. As people grow taller, they tend to weigh more. Shorter people tend to weigh less. Thus, height and weight are correlated. Further, they are positively correlated as one goes up, the other goes down. Consider drinking alcohol and dexterity, as shown in the chart to the left. The more drinks one has, the less dexterity the person has. As one goes up, the other goes down. This is an example of a negative correlation. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 3

4 Correlations vary between -1 and +1, like this: -1 Perfect negative correlation As one thing goes up the other goes down at the same rate (or vice versa) 0 No correlation The two things have nothing in common +1 Perfect positive correlation As one thing goes up the other goes up at the same rate (or both go down) In the physical world, perfect correlations are not uncommon. But in our everyday world of people in the social sciences, few things are correlated beyond -0.7 or That s because rarely is any one thing solely correlated with something else usually more than one factor is involved. Consider heredity and height. Heredity and Height Click now on the Height sheet in the Excel data set. You ll see two columns of data from 100 pairs of fathers and sons, measuring their height in inches. The scatter chart of blue dots illustrates that there s a messy relationship between the two. As dads get taller, sons do, too sort of. The chart shows the correlation coefficient is , or There s no negative mark, so the number is positive by default. This 0.53 means that for each inch of height a father gains, the son gains about half an inch. As you might guess, other factors are at play specifically, the mother s height and nutrition during childhood. NFL 2014 Correlations (For this data, a hat tip goes to Steve Doig of Arizona State University, who used a similar data set in a handout a few years ago.) Open the NFL sheet for the 2014 regular season, according to ESPN statistics. Click on the Data tab, and then on Data Analysis on the right-hand side. You ll see a dialog box. Choose the Correlation option and click OK. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 4

5 With the cursor in the Input Range box, use your mouse/cursor to select the columns with numbers in them (in this data set, all but team names). Include the column headers (row 1), as below. Then click on the Labels in First Row box. Click here Place the cursor in the Output Range box and click on a blank cell, such as J4. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 5

6 The result looks like this: Let s interpret the correlation table. These 1 s are perfect correlations because they are identical: yards gained = yards gained This area is blank because it would just repeat what is below the string of 1 s This is the strongest correlation. Points scored has the highest correlation with wins. This also is a strong correlation, in the negative: The more points given up, the less likely the team is to win. Not surprisingly, points scored or points allowed have the strongest correlation with wins. A statistician would say the two are associated. One cannot say that one causes the other points do not cause a win. But the two are related. More points scored = more wins. More points allowed = fewer wins. Thus, points are associated with wins. What else does this table tell us? It tell us that other factors, such as takeaways and giveaways (fumbles and interceptions), have a weaker correlation with wins. They matter, but not as much as, say, yards gained. Correlations give us useful data about associations. We can learn even more through a linear regression. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 6

7 Linear Regression While social scientists use linear regression to predict, journalists usually use linear regression to determine the amount of change that can be attributed to one factor over another. Danger, Will Robinson! Danger! Regression is a much more complicated statistic than we can address here. It is very powerful when used correctly. It is misleading when used incorrectly. So a little knowledge can be dangerous. If you really want to do linear regression, use something more powerful than Excel, such as SAS, SPSS or R. And consult a local stats nerd. Our purpose here is to use regression to introduce us to a more valuable concept: statistical significance. Statistical Significance Most everything in life is a combination of performance and chance. Statistics help to differentiate performance from chance to tell us when something probably wasn t just the luck of the draw. Note the weasel word probably. Certainty is illusive in everyday life. For example, let s say you ve created a new medicine to cure the common cold. In order to justify putting the new medicine on the market, you need to show that its effects weren t just by chance. Generally in medicine, the standard is less than 1 in 100 (0.01) or 1 in 1,000 (0.001) that the cure was just dumb luck. You can never prove beyond the shadow of a doubt that it works. And like all approved medicines, it will work for many but not for all. In situations involving people, the standard is usually 5 in 100, or 0.05 (written as p <.05). Why a lower standard? Because our social lives involve so many interwoven factors that it s difficult to isolate variables. Consider the NFL data. Whether a team wins or loses involves much more than yards gained or points allowed. It involves preparation, skill, injuries, motivation, coaching, home-field advantage, late-night carousing, etc. In that milieu, getting to a less than 5 percent probability that something occurred by luck is, well, pretty good. At the same time, the 0.05 standard is a bit of luck itself created by pioneering British statistician R.A. Fisher without any theoretical basis or design. But the 5 percent stuck, and so we credit Fisher. (At the same time, Fisher denied that his pipe smoking was associated with an increased risk for cancer despite contrary evidence. So maybe he wasn t such a smarty pants after all.) One more point. Statistical significance is often misinterpreted as the likelihood that something happened by chance. Well, not exactly. It actually reflects whether we can reject the null hypothesis the idea that nothing happened. But that s a bit complicated. So let s get back to football and see what regression can tell us about statistical significance. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 7

8 Thinking about Variables Click on the NFL data sheet. Consider the column headers as variables. Yards gained, points, etc. those are variables (or, things that vary or change). Further, one of those variables means the most to us: Wins. (We re bottom-line oriented here, and we want more wins.) So the Wins category is the focus of our attention. Everything depends on wins. Thus, we will consider Wins to be our (drum roll, please!) dependent variable. (Some call this the criterion variable.) The abbreviation for a dependent variable is DV. Everything else is a potential influence on wins. Thus, we consider them independent variables. (Some call these the predictor variables.) The abbreviation for an independent variable is IV. Here s a visual way to remember the difference between an independent variable (IV) and the dependent variable (DV), drawing from the medical shorthand for intravenous: IV. The IV: Something that influences the patient (to get better, we hope!) The DV: The thing we care about in this case, the patient Further, this picture gives us the order. The IV comes first. It goes into the patient to deliver medicine and fluids. And if the IV works, the result is the patient gets better. Now, let s translate that to the X and Y language of regression. 1. The IV (independent variable) comes first. X comes first in the alphabet. So X = the IV. 2. The DV (dependent variable) comes second. Y comes after X. So Y = the DV. Now, let s get Excel to do some regression. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 8

9 Linear Regression in the NFL. On the NFL data sheet, click on the Data tab. On the far right, choose the Data Analysis option. When you do, you trigger this box. Scroll down until you get to regression. Click on OK to trigger the box below. The dependent variable goes in the Y box (in this case, wins) The independent variables go in the X box (in this case, everything but wins) Include the labels in the data you select and check this box The statistics can take up space, so use the default of a new worksheet These are useful but too complicated to explain here, so leave unchecked Click in the Input Y Range box and select the dependent variable cells (the Wins column, including the column label). Click in the Input X Range box and select the independent variable cells (everything else with numbers, including the column labels Yds Gain, Pts Score, Takeaway, Giveaway, Yds Allow, and Pts Allow). Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 9

10 The result looks like this. (Some column widths have been expanded for readability.) This figure describes how well the regression model does in predicting the DV. But that s a bit misleading here because of the data chosen. Excel is giving us scientific notation here. The E-12 means move the decimal point 12 places to the left. Thus, E-12 is , which in nonscientific terms is a small number. Suffice to say, it s less than These coefficients would be useful in creating an algorithm (remember line and slope from algebra?) but are less useful for us here. Suffice to say they re low. This is also an important statistic for regression but not what we re trying to achieve here. (FYI, these also are low.) Here s what we re most interested in: P-value or probability value. The section is enlarged here: Let s interpret P-value on the next page. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 10

11 Interpreting P-value Ignore the Intercept line because that has to do with line and slope. Look instead at each of the p- value scores, compressed here to three decimal points. P-value Intercept Yds Gain Pts Score Takeaway Giveaway Yds Allow Pts Allow p <.05 Two variables have P-values less than 0.05 (or, 5 in 100 or 5 percent): Pts Score is 0.005, or 5 in 1,000. Pts Allow is We can never have 0 probability, so this would be expressed as p <.001, or less than 1 in 1,000. How to interpret this? Remember that the P-value addresses the null hypothesis. The null hypothesis is the opposite of our guess. Our hypothesis is that Points Scored and Points Allowed have something to do with Wins. (Otherwise, we would not have included the data, eh?) The null hypothesis is the opposite that Points Scored and Points Allowed have little to do with wins. The fact that our P-value is below 0.05 means there is a less than a 5 percent chance the null hypothesis is true. Thus, we reject the null hypothesis and accept our working hypotheses. All the other variables are greater than It does not matter how much larger. All that matters is none of the other factors are statistically significant meaning, we cannot reject the null hypothesis. How to apply this? Sports commentators who want to assert that fumbles and interceptions giveaways (bad) or takeaways (good) result in wins cannot do so from this data because the P-values are not less than The association could just be by chance. Basic Statistical Analysis in Excel, NICAR 15, Norm Lewis / Page 11