Statistics Software

Data Analysis using Statistics Software Such as SPSS, Minitab, MS-Excel, STATA, Eviews, etc. Stat-Soft

Cronbach’s Alpha Reliability Analysis of Measurement Scales

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Cronbach’s Alpha Reliability Analysis

Cronbach’s Alpha Reliability analysis is used to study the properties of measurement scales (Likert scale questionnaire) and the items (questions) that make them up. The reliability analysis method computes several commonly used measures of scale reliability. The reliability analysis also provides information about the relationships between individual items in the scale. The intraclass correlation coefficients can be used to compute the interrater reliability estimates.

Consider that you want to know if my questionnaire measures customer satisfaction in a useful way. For this purpose, you can use the reliability analysis to determine the extent to which the items (questions) in your questionnaire are correlated with each other. The overall index of the reliability or internal consistency of the scale as a whole can be obtained. You can also identify problematic items that should be removed (deleted) from the scale.

As an example open the data “satisf.save” already available in SPSS sample files. To check the reliability of Likert scale items follow the steps given below:

Cronbach's Alpha Reliability
Cronbach's Alpha Reliability Analysis Dialog box

Step 1: On the Menu bar of SPSS, Click Analyze > Scale > Reliability Analysis… option

Step 2: Select two more variables that you want to test and shift them from the left pan to the right pan of the reliability analysis dialogue box. Note, that multiple variables (items) can be selected by holding down the CTRL key and clicking the variable you want. Clicking the arrow button between the left and right pan will shift the variables to the item pan (right pan).

Step 3: Click on the “Statistics” Button to select some other statistics such as descriptives (for item, scale, and scale if item deleted), summaries (for means, variances, covariances, and correlations), inter-item (for correlations and covariances) and ANOVA table (for none, F-test, Friedman chi-square and Cochran chi-square) statistics etc.

Reliability Statistics

Click on the “Continue” button to save the current statistics options for analysis. Click the OK button in the Reliability Analysis dialogue box to get the analysis to be done on selected items. The output will be shown in SPSS output windows.

Reliability Analysis Output

The Cronbach’s Alpha Reliability ($\alpha$) is about 0.827, which is good enough. Note that, deleting the item “organization satisfaction” will increase the reliability of remaining items to 0.860.

A rule of thumb for interpreting alpha for dichotomous items (questions with two possible answers only) or Likert scale items (questions with 3, 5, 7, or 9, etc items) is:

  • If Cronbach’s Alpha is $\ge 0.9$, the internal consistency of scale is Excellent.
  • If Cronbach’s Alpha is $0.90 > \alpha \ge 0.8$, the internal consistency of scale is Good.
  • If Cronbach’s Alpha is $0.80 > \alpha \ge 0.7$, the internal consistency of scale is Acceptable.
  • If Cronbach’s Alpha is $0.70 > \alpha \ge 0.6$, the internal consistency of scale is Questionable.
  • If Cronbach’s Alpha is $0.60 > \alpha \ge 0.5$, the internal consistency of scale is Poor.
  • If Cronbach’s Alpha is $0.50 > \alpha $, the internal consistency of scale is Unacceptable.

However, the rules of thumb listed above should be used with caution since Cronbach’s Alpha reliability is sensitive to the number of items in a scale. A larger number of questions can result in a larger Alpha Reliability, while a smaller number of items may result in smaller $\alpha$.

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Operator order of precedence and Creating Formula in Excel

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Creating Formula in Excel

Creating customized (user-defined) formulas in Microsoft Excel is not too difficult. For creating formulas just combine the references of your data with the correct mathematical operator (such as -, +, /, *, and ^).

Operator Order of Precedence

The order of mathematical operations determines in which order the mathematical operations are carried out. If more than mathematical operators are used in the formula, there is a specific order (sequence) that Microsoft Excel will follow to perform (compute) these mathematical operations. However, to change the order of operations, brackets (parenthesis) are used in the Excel formula. The easy way to remember the order of operations (precedence) is to remember the acronym: BEDMAS (PEDMAS), that i.e.,

The Operator order of precedence (operations) is:

Bracket or Parenthesis
Exponents (^)
Division (/)
Multiplication (*)
Addition (+)
Subtraction (-)

Suppose, the following is the screenshot of an Excel sheet. The formula is also shown in the formula bar. As an example, addition (+), division (/), and multiplication (*) operators are used.

Operator order of precedence

The formula in the screenshot performs the computation in the following order,

  • $E1/F1$ will be computed (the answer is 1.5),
  • the answer of $E1/F1$ will be multiplied by value of $G1$ (answer is $1.5*2 = 3$)
  • the answer of $E1/F1 * G1$ will be added to $D1$ (answer is 7)

Any operation(s) enclosed in brackets (parenthesis) will be carried out first followed by any exponents. After that, Excel will consider division or multiplication operations to be of equal importance. The operations are performed in the order they occur left to right in the formula. A similar sequence is also performed for addition and subtraction. Both (addition and subtraction) are considered equal in the order of operations. The operator that appears first will be computed first.

order of precedence bracket

For example, see the screenshot The sequence of operations is

  • The first bracket will be computed, that is, multiplication will be performed $(2 *2 = 4)$
  • E1 will be divided by the answer from the multiplication of $F1$ and $G1 (3/4 = 0.75)$
  • Lastly, $D1$ will be added to the answer $0.75 (4 + 0.75 = 4.75)$

Now check the sequence in the following screenshot

order of precedence bracket

For Creating formula in Excel, see the link Creating Excel Formula

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Creating Formulas in MS Excel and Changing Data

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Changing the data

Before Creating formulas in MS Excel, you need numeric data in different columns or rows of the Excel sheet. Suppose you want to enter a few numbers in a column. Before entering these numbers, you should confirm the cell reference where you need to enter the data. Let’s start by entering numbers in Microsoft Excel‘s cells $A1$ and $A2$. For this purpose follow the steps given below

  1. Click on the cell $A1$
  2. Type 3 from the keyboard
  3. Press the ENTER or DOWN ARROW key on the keyboard. You will be in Cell A2
  4. Now type say 2 from the keyboard and press the ENTER key

Suppose you want to add these numbers in Cell $C1$. You need to write a formula in cell $C1$. After writing the correct formula the content of Cell $C1$ will immediately change to adding two numbers typed in $A1$ and $A2$ and used in $C1$ as formula content.

excel-data-and-formula

Creating Formulas in MS Excel

In this section, we will learn about Creating Formulas in MS Excel. In Excel, each formula begins with an equal sign ($=$), see the picture below

Creating Formulas in MS Excel

Therefore, when creating formulas in Excel, ALWAYS start by typing the equal sign. The equal sign is typed in the Cell where you want the answer to appear. Like the image above, follow these steps

  1. Click on cell $C1$ with ARROW keys from the keyboard or with the mouse pointer.
  2. Type the equal sign in cell $C1$.
excel-data-and-formula

After typing the equal sign in step 2, you have two choices for adding cell references to the spreadsheet formula. Note that cell reference is the name of the cell you want to use in the formula. $A1$ and $A2$ are cell references of numbers 3 and 2, respectively.

  1. You can type these references in or,
  2. You can use an Excel feature called Pointing
excel-data-and-formula

Pointing allows you to click with your mouse on the cell that contains the data or approach a cell reference using the keyboard ARROW keys containing your data to add. This will add cell reference to the formula.

After typing an equal sign in cell C3 in step 2:

  1. Click on cell $A1$ with the mouse pointer to enter the cell reference into the formula
  2. Type a plus (+) sign. You can also use other operators such as for multiplication use you have to use the * symbol, for division/symbol, and for subtraction use $–$, etc.
  3. Click on cell $A2$ with the mouse pointer to enter the cell reference into the formula
  4. Press the ENTER key on the keyboard

The answer 5 should appear in cell $C1$.

Note if you have more than one row or column of data then you need to perform calculations on each row or column cell. It is often possible to copy the first formula to other cells. The easiest way is to copy formulas with the file handle.

See also Creating Formulas in Microsoft Excel

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