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  1. 1. Statistical Analysis Research Writing WTUC March 19, 2007
  2. 2. Using Excel <ul><li>organizing data, i.e. basic data management, tabulation and graphics </li></ul>
  3. 3. The Excel Screen
  4. 4. Entering Data <ul><li>A new worksheet is a grid of rows and columns . The rows are labeled with numbers, and the columns are labeled with letters. Each intersection of a row and a column is a cell . Each cell has an address , which is the column letter and the row number. The arrow on the worksheet to the right points to cell A1, which is currently highlighted , indicating that it is an active cell . A cell must be active to enter information into it. To highlight (select) a cell, click on it. </li></ul><ul><li>To select more than one cell: </li></ul><ul><li>Click on a cell (e.g. A1), then hold the shift key while you click on another (e.g. D4) to select all cells between and including A1 and D4. </li></ul><ul><li>Click on a cell (e.g. A1) and drag the mouse across the desired range, unclicking on another cell (e.g. D4) to select all cells between and including A1 and D4. </li></ul><ul><li>To select several cells which are not adjacent, press &quot;control&quot; and click on the cells you want to select. Click a number or letter labeling a row or column to select that entire row or column. </li></ul><ul><li>One worksheet can have up to 256 columns and 65,536 rows, so it'll be a while before you run out of space. </li></ul>
  5. 5. <ul><li>To enter information into a cell, select the cell and begin typing. </li></ul><ul><li>Note that as you type information into the cell, the information you enter also displays in the formula bar. You can also enter information into the formula bar, and the information will appear in the selected cell. </li></ul><ul><li>When you have finished entering the label or value: </li></ul><ul><li>Press &quot;Enter&quot; to move to the next cell below (in this case, A2) </li></ul><ul><li>Press &quot;Tab&quot; to move to the next cell to the right (in this case, B1) </li></ul><ul><li>Click in any cell to select it </li></ul>
  6. 6. Entering Labels
  7. 7. Entering Values
  8. 8. Count <ul><li>Counts the number of cells that contain numbers and counts numbers within the list of arguments. Use COUNT to get the number of entries in a number field that is in a range or array of numbers. </li></ul><ul><li>COUNT ( value1 ,value2,...) </li></ul><ul><li>Value1, value2, ...    are 1 to 30 arguments that can contain or refer to a variety of different types of data, but only numbers are counted. </li></ul>
  9. 9. Note <ul><li>Arguments that are numbers, dates, or text representation of numbers are counted. </li></ul><ul><li>Logical values and text representations of numbers that you type directly into the list of arguments are counted. </li></ul><ul><li>Arguments that are error values or text that cannot be translated into numbers are ignored. </li></ul><ul><li>If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are ignored. </li></ul><ul><li>If you want to count logical values, text, or error values, use the COUNTA function. </li></ul>
  10. 10. Excel Functions: Sum, Average, Count <ul><li>A function is a special key word which can be entered into a cell in order to perform a process to some data which is appended within brackets. = FunctionName(Data) The data (or argument in proper terminology) often includes a range of cells. Excel automatically recognises the names of these functions provided that they are preceded by an equals sign and finish with brackets. </li></ul>
  11. 11. <ul><li>There is a function button on the toolbar which offers assistance and useful prompts when entering a function into a spreadsheet cell. Alternatively you can type the function directly into the formula bar. </li></ul>
  12. 12. <ul><li>SUM(), AVERAGE() and COUNT() are the most common functions and the easiest to understand. They each apply to a range of cells containing numbers (or blank but not text) and return either the arithmetic total of the numbers, the average value or the quantity of values in the range. </li></ul>
  13. 14. <ul><li>Cell C6 is currently empty. Both AVERAGE() and COUNT() would be affected by placing a zero value in the cell. Doing so would change last years values to 71 and 4 respectively. SUM() is unaffected. </li></ul><ul><li>The range need not be limited to a single column. For example the function = COUNT(B4:C7) would return 7. </li></ul><ul><li>These three functions only take numeric values into account. They ignore text and blank spaces which may be contained within the range. It is possible to use a variant of the Count function called COUNTA() which returns the number of cells in a range containing any numeric or text value. For example the function =COUNTA(A4:B9) would return 10. </li></ul>
  14. 15. The Excel FREQUENCY function <ul><li>This useful function can analyze a series of values and summarize them into a number of specified ranges. For example the heights of some children can be grouped in to four categories of [Less than 150cm]; [151 - 160cm]; [161 - 170cm]; [More than 170cm]. </li></ul>
  15. 16. <ul><li>FREQUENCY() is an unusual array function and it works differently to most other normal functions. It can not simply be typed into a cell or even entered properly using the Excel Function Wizard. </li></ul><ul><li>Note that this function does not analyse values into categories e.g. household expenditure into groups such as gas, electricity, water, rates etc. To perform this kind of analysis an Advanced Filter may be appropriate. </li></ul>
  16. 17. <ul><li>The frequency function has two arguments - the first is the range of cells containing values to be analysed; the second is the range of cells containing the upper values of each group banding. e.g. =FREQUENCY(A3:A120, B6:B10) </li></ul><ul><li>The second argument (the group upper limits) will exclude any values which exceed the highest category or banding. The function allows you to take account of this and extend the range of analysis to an additional category which contains all values that exceed the specified upper limit. </li></ul>
  17. 18. A step by step example of how to use the FREQUENCY function:
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  20. 21. Calculating the Mean and Standard Deviation with Excel <ul><li>1. Enter the scores in one of the columns on the Excel spreadsheet (see the example below). After the data has been entered, place the cursor where you wish to have the mean (average) appear and click the mouse button. Now move the cursor to the Function Wizard ( fx ) button and click on it. </li></ul>
  21. 22. 2. A dialog box will appear. Click on Statistical from the left section of the box and AVERAGE on the right section. After you have made those two selections, click on Next> at the bottom of the dialog box .
  22. 24. The mean (average) for the list will appear in the cell you selected.
  23. 25. 5. Place the cursor where you wish to have the standard deviation appear and click the mouse button. Now move the cursor to the Function Wizard ( fx ) button and click on it.
  24. 26. 6. A dialog box will appear. Click on Statistical from the left section of the box and STDEV (for a sample) on the right section (Note: If your data is from a population, click on STDEVP) . After you have made your selections, click on Next> at the bottom of the dialog box.
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  26. 29. Variance and the Standard Deviation with the Excel
  27. 30. Descriptive Statistics <ul><li>The Data Analysis ToolPak has a Descriptive Statistics tool that provides you with an easy way to calculate summary statistics for a set of sample data. Summary statistics includes Mean, Standard Error, Median, Mode, Standard Deviation, Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum, and Count. This tool eliminates the need to type indivividual functions to find each of these results. Excel includes elaborate and customisable toolbars, for example the &quot;standard&quot; toolbar shown here: </li></ul>
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  29. 32. <ul><li>Interpretation and application </li></ul><ul><li>A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean. </li></ul><ul><li>For example, each of the three data sets (0, 0, 14, 14), (0, 6, 8, 14) and (6, 6, 8, 8) has a mean of 7. Their standard deviations are 7, 5, and 1, respectively. The third set has a much smaller standard deviation than the other two because its values are all close to 7. In a loose sense, the standard deviation tells us how far from the mean the data points tend to be. It will have the same units as the data points themselves. If, for instance, the data set (0, 6, 8, 14) represents the ages of four siblings, the standard deviation is 5 years . </li></ul>
  30. 33. <ul><li>As another example, the data set (1000, 1006, 1008, 1014) may represent the distances traveled by four athletes in 3 minutes, measured in meters. It has a mean of 1007 meters, and a standard deviation of 5 meters . </li></ul><ul><li>In the age example above, a standard deviation of 5 may be considered large; in the distance example above, 5 may be considered small (small to the mathematician, not so small to the athletes). </li></ul>
  31. 34. <ul><li>Standard deviation may serve as a measure of uncertainty. In physical science for example, the reported standard deviation of a group of repeated measurements should give the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance: if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then we consider the measurements as contradicting the prediction. This makes sense since they fall outside the range of values that could reasonably be expected to occur if the prediction were correct and the standard deviation appropriately quantified. See prediction interval . </li></ul>
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