Empirical Project 6 Working in Excel

Part 6.1 Looking for patterns in the survey data

Learning objectives for this part

  • explain how survey data is collected, and describe measures that can increase the reliability and validity of survey data
  • use column charts and box and whisker plots to compare distributions
  • calculate conditional means for one or more conditions, and compare them on a bar chart
  • use line charts to describe the behaviour of real-world variables over time.

First download the data used in the paper to understand how this information was collected. The dataset is publicly available and free of charge, but you will need to create a user account in order to access it.

  1. To learn about how Bloom et al. (2012) conducted their survey, read the sections ‘How Can Management Practices Be Measured?’ and ‘Validating the Management Data’ (pages 5–9) of their paper.

Now we will create some charts to summarize the data and make comparisons across countries, industries (manufacturing, healthcare, retail, and education), and firm characteristics.

  1. In ‘Manufacturing: 2004–2010 combined survey data (AMP)’, open the Excel document ‘AMP_graph_manufacturing.csv’. Use this data on manufacturing firms to do the following:
Country Overall management (mean) Monitoring management (mean) Targets management (mean) Incentives management (mean)
         
         

Figure 6.2a Mean of management scores.

Country Overall management (rank) Monitoring management (rank) Targets management (rank) Incentives management (rank)
         
         

Figure 6.2b Rank according to management scores.

To look at how management quality varies within countries, instead of just looking at the mean we can use column charts to visualize the entire distribution of scores (as in Empirical Project 1). To compare distributions, we have to use the same horizontal axis, so we will first need to make a frequency table for each distribution to be used. Also, since each country has a different number of observations, we will use percentages instead of frequencies as the vertical axis variable.

  1. For three countries of your choice and for the US, carry out the following:
Range of management score Frequency Percentage of firms (%)
1.00
1.20
4.80
5.00

Figure 6.3 Frequency table for overall management score.

Excel walk-through 6.1 Using Excel’s IF function

Follow the walk-through in the CORE video, or in Figure 6.4, to find out how to use Excel’s IF function.

Figure 6.4 How to use Excel’s IF function within another function.

The data

In this example, we will make a frequency table for the US data in Columns A to C. It’s a good idea to put all the tables in a separate place from the data.

Calculating frequencies for a particular country

We want to calculate the frequency but only for firms in the US. To do this, add an IF condition within the FREQUENCY function to tell Excel which data to use.

Calculating frequencies for a particular country

By putting the IF function inside the FREQUENCY function, Excel will only use the data that satisfies the condition we specified (firms in the US).

Calculating frequencies for a particular country

The formula that is completed in step 4 is: ‘(=FREQUENCY(IF(AMP_graph_manufacturing!N:N=”United States”,AMP_graph_manufacturing!A:A),Sheet2!A2:A22))’. After step 4, all the frequency values will be filled in.

Using frequencies to calculate percentages

The $ symbol before the row numbers in the formula tells Excel to keep these row numbers the same when copying the formula to other cells. We used it here because we are dividing the frequency value by the total number of observations (cells B2 to B22).

Excel walk-through 6.2 Overlaying one column chart over another

Figure 6.5 How to overlay one column chart over another.

The data

In this example, we use data for the US (Columns A to C) and Chile (Columns F to H), and plot a column chart of the percentages in Columns C and H (see the steps in Figure 6.4 for how to calculate these).

Plot a column chart

After step 3, the column chart will look like the one shown above.

Change the appearance of the columns

First, we will remove the gaps between the columns, and make the columns overlap (rather than being plotted side-by-side). After step 7, there will be a vertical axis on the left and right side of the chart.

Change the vertical axis values

In order to compare the distributions, make sure the left and right vertical axis have the same labels.

Change the horizontal axis values and series names

Now, change the horizontal axis values to match the data in our frequency tables.

Change the horizontal axis values and series names

After step 12, the horizontal axis value for the selected columns will change.

Change the horizontal axis values and series names

Now, we will change the series names to country names.

Change the horizontal axis values and series names

After step 14, the legend entry for that country will now be the country name.

Change the horizontal axis values and series names.

Since we have two vertical axes on our chart (one for each data series), we need to change the horizontal axis labels for both axes before Excel will update the chart.

Change the horizontal axis values and series names.

Finally, change the shading of the columns so we can see the distributions of both countries. After step 19, the distributions of both countries should be clearly visible.

Figure 6.6 Example of two overlapping distributions on the same column chart.

box and whisker plot
A graphic display of the range and quartiles of a distribution, where the first and third quartile form the ‘box’ and the maximum and minimum values form the ‘whiskers’.

Another way to visualize distributions is a box and whisker plot, which shows some parts of a distribution rather than the whole distribution. We can use box and whisker plots to compare particular aspects of distributions more easily than when looking at the entire distribution.

As shown in Figure 6.7, the ‘box’ consists of the first quartile (value corresponding to the bottom 25 per cent, or 25th percentile, of all values), the median, and the third quartile (75th percentile). The ‘whiskers’ are the minimum and maximum values. (In Excel, the ‘whiskers’ may not be the actual maximum or minimum, since any values larger than 1.5 times the width of the box are considered outliers and are shown as separate points.)

Figure 6.7 Example of a box and whisker plot.
(Note: In Excel, the mean value is shown by X. In general, the median may not be in the centre of the box, and can differ greatly from the mean. Using the data shown in Figure 6.7 for a variable from the dataset, the mean and median are very similar.)

  1. Using the same countries you chose in Question 3:

Excel walk-through 6.3 Drawing box and whisker plots

Follow the walk-through in the CORE video, or in Figure 6.8, to find out how to draw a box and whisker plot in Excel.

Figure 6.8 How to create box and whisker plots.

The data

In this example, we will use data for the US (Column A) and Chile (Column B). To create a box and whisker plot of more than one variable, each variable needs to be in a separate column. You will need to filter, then copy and paste the required data into a new tab in Excel.

Create box and whisker plots

After step 3, your box and whisker plot will look like the one above. The plots are ordered according to the columns in Excel, so the first plot corresponds to Column A, the second plot corresponds to Column B, and so on.

Add a chart legend

First, we will add a legend to indicate to which country each plot corresponds.

Change the legend entries

Now, we will change the labels in the legend. If your legend is already correctly labelled, skip Steps 6–9.

Change the legend entries

After changing the name of the data series, the label in the legend will change.

Change the legend entries

After step 9, your data should now be correctly labelled in the chart legend.

Remove the outliers (optional)

Excel shows any observations that are greater than 1.5 times the box width (in absolute value) separately as outliers. If your chart is too cluttered with outliers, you can remove them to make your chart more readable.

From the manufacturing data, firms in the US seem to be managed better (on average) than firms in other countries. To investigate whether this is the case in other sectors, we will use data gathered on hospitals and schools.

  1. Using the data for hospitals and schools (AMP_graph_public.csv):

Part 6.2 Do management practices differ between countries?

Learning objectives for this part

  • calculate conditional means for one or more conditions, and compare them on a bar chart
  • construct confidence intervals and use them to assess differences between groups.

Using the management survey data collected by Bloom et al. (2012), we can compare average management scores across countries and industries. When we find differences between groups in the survey, we are interested in what that tells us about the true differences in management practices between the countries.

confidence interval
A range of values centred around the sample mean value, with a corresponding percentage (usually 90%, 95%, or 99%). When we use a sample to calculate a 95% confidence interval, there is a probability of 0.95 that we will get an interval containing the true value of interest.

In Empirical Project 2, we used p‑values to assess differences between groups. A p‑value tells us how unusual it would be to observe the differences between groups that we did, assuming our hypothesis is correct (and additional model assumptions about the data hold). If the p-value is small, we might then conclude that the data is not compatible with our assumptions (e.g. that the two groups were drawn from populations with the same mean), and that there is a real difference between the underlying populations. Now we will use another method that helps us to allow for random variation when we interpret data, called a confidence interval.

When we work with data we usually have only a small sample from the entire population of interest. For example, the World Management Survey collects information from a selection of all the firms in a particular country. If we calculate the average management score for the sample, we have an estimate of the average management score across all firms in the country (the ‘true value’) but it may not be a very accurate estimate—especially if the sample is small and management scores vary a lot between firms.

A 95% confidence interval is a range of possible values within which the true value might lie. It is estimated from the mean and standard deviation of the data. As in the process of calculating p-values, we use a standard method that gives a good estimate provided that certain statistical conditions are satisfied. We cannot be certain that the true value lies in the range; we might have the bad luck to pick an atypical sample, in which case our estimate of the confidence interval would be atypical too. But we can say that when we use this method, there is a 95% probability that we will find an interval that contains the true value. One way to interpret this is to say that if we were able to repeat the process of sampling and calculating confidence intervals many times, roughly 95% of these confidence intervals would contain the true value.

As the name suggests, confidence intervals tell us how much confidence we can place in our estimates, or in other words, how precisely the sample mean is estimated. The confidence interval gives us a margin of error for our estimate of the true value. If the data varies a lot, the 95% confidence interval may be quite wide. If we have plenty of data, and the standard deviation is low, the estimate will be more precise and the 95% interval will be narrow.

Rule of thumb for comparing means

When comparing two distributions, if neither mean is in the 95% confidence interval for the other mean, the p-value for the difference in means is less than 5%.

This rule of thumb is handy when looking at charts. If two 95% confidence intervals don’t overlap, we can say immediately that the observed difference between the means for the two groups is unlikely to have arisen by chance alone (given that our hypothesis that there were no differences in the populations from which these groups were drawn and that our other assumptions about the data, such as random sampling, are correct). For a more definite conclusion, we can calculate the actual p-value (see Empirical Project 2) or construct a confidence interval for the difference in means. (This method involves more mathematics so we will discuss that in Empirical Project 8.)

It is possible to calculate a confidence interval for any probability: however wide the 95% confidence interval, a 99% confidence interval would be wider, and an 80% one would be narrower. 95% is a common choice: it gives us quite a high degree of confidence, and to go higher tends to lead to very wide intervals. We will use 95% confidence intervals throughout this project.

To sum up: A confidence interval is a range of values centred around the sample mean value, with a corresponding percentage (usually 90%, 95%, or 99%). When we use a sample to calculate a 95% confidence interval, there is a probability of 0.95 that we will get an interval containing the true value of interest.

We will now build on the results from the Bloom et al. (2012) paper by using 95% confidence intervals to make comparisons between the mean overall management score for different countries and types of firms. The confidence interval for the population mean (mean management score for that country) is centred around the sample mean. To determine the width of the interval, we use the standard deviation and number of firms.

  1. First look at manufacturing firms in different countries. Using the manufacturing data (AMP_graph_manufacturing.csv) for three countries of your choice and for the US:
Country Mean Standard deviation Number of firms
       
       

Figure 6.9 Summary table for manufacturing firms.

Excel walk-through 6.4 Creating confidence intervals and adding them to a chart

Figure 6.10 How to create confidence intervals and add them to a chart.

Calculate the width of the confidence interval

In this example we will use data for the US and Chile (shown in Columns A and B). To calculate the width of the 95% confidence interval (distance from the mean to one end of the interval), we first need to calculate the standard deviation and number of observations for each country. The 0.05 in the CONFIDENCE.T function is 1 − 0.95 (our specified probability).

Plot a bar chart

After completing step 4, your bar chart will look similar to the one above.

Add confidence intervals to the chart

The ‘error bars’ option in Excel plots confidence intervals. We will use the calculated width values from step 1 to determine the size of the error bars.

Add confidence intervals to the chart

The positive error value determines the right end of the interval (the value above the mean). The negative value determines the left end of the interval (the value below the mean). Confidence intervals are symmetric, so we use the same values for both.

The finished chart

After completing step 9, your chart will look similar to the one above. You can also add horizontal and vertical axis titles and a chart title.

  1. Using the data for hospitals or schools (AMP_graph_public.csv), using all available countries:
  1. Look at the width of your confidence intervals and the corresponding standard deviation and number of observations for each one. Explain whether or not the relationship between them is what you would expect.

Part 6.3 What factors affect the quality of management?

Learning objectives for this part

  • calculate conditional means for one or more conditions, and compare them on a bar chart
  • construct confidence intervals and use them to assess differences between groups
  • evaluate the usefulness and limitations of survey data for determining causality.

Besides documenting and comparing management practices across industries and countries, another purpose of the World Management Survey was to investigate factors that affect management quality.

One possible factor affecting differences in management is firm ownership. To look at the data for this factor in the healthcare and education sectors, we will focus on broad groups (public vs privately-owned firms), and for manufacturing firms we will focus on different kinds of private ownership.

  1. Using the data for hospitals and schools (AMP_graph_public.csv):

Besides ownership type, management practices may vary depending on firm size, though it is difficult to predict what the relationship between these variables might be. Larger firms have more employees and could be more difficult to manage well, but may also attract more experienced managers. We will look at the conditional means for manufacturing firms, depending on whether they are above or below the median number of employees (calculated from the data), and see if there is a clear relationship.

  1. Using the data for manufacturing firms (AMP_graph_manufacturing.csv):

Excel walk-through 6.5 Using Excel’s IF function

Figure 6.11 How to use Excel’s IF function.

The data

This is what the manufacturing data looks like. We will create a new variable in Column T, according to the log employment values in Column E. We have labelled our new column ‘size’ (cell T1).

Create a new variable

After completing step 2, you will have a variable for firm size. We used the IF function to fill the cells in Column T with the word ‘Smaller’ if log employment is smaller than 5.8, otherwise the cell is filled with the word ‘Larger’.

So far we have looked at associations between firm characteristics and management practices, but have not made any causal statements. We will now discuss the difficulties with making causal statements using this data and examine how we might determine the direction of causation.

  1. For each of the following variables, explain how it could affect management practices, and then explain how management practices could affect it:
  1. One way to establish the direction of causation is through a randomized field experiment. Read the discussion on pages 22–23 of the Bloom et al. paper (the section ‘Experimental Evidence on Management Quality and Firm Performance’) about one such experiment that was conducted in Indian textile factories.