Using Microsoft Excel to Compute Confidence Interval of a population mean

CONFIDENCE: Confidence interval for a population mean

Classification: Microsoft Excel Data Analysis

The CONFIDENCE function calculates a value that you can use to create a confidence interval for the population mean based on the sample mean. This definition amounts to a mouthful, but in practice what the CONFIDENCE function does is straightforward.

Suppose that, based on a sample, you calculate that the mean salary for a chief financial officer for a particular industry equals $100,000. You might wonder how close this sample mean is to the actual population mean.

Specifically, you might want to know what range of salaries, working at a 95-percent confidence level, includes the population mean.

The CONFIDENCE function calculates the number that you use to create this interval using the syntax

=CONFIDENCE(alpha,standard_dev,size)

where alpha equals 1 minus the confidence level, standard_dev equals the standard deviation of the population, and size equals the number of values in your sample.

If the standard deviation for the population equals $20,000 and the sample size equals 100, use the formula

=CONFIDENCE(1-.95,20000,100)

The function returns the value $3920 (rounded to the nearest dollar). This interval suggests that if the average chief financial officer’s salary in your sample equals $100,000, there’s a 95-percent chance that the population mean of the chief financial officers’ salaries falls within the range $96,080 to $103,920.

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How to Analyze Multiple Responses in SPSS

How to analyze multiple responses in SPSS

Generating New Variables in SPSS: The Multiple Response Command

(Download SPSS File)

The table below shows part of a Health Issues survey questionnaire.

Question:

Thinking about health related matters, did any of the following happen to you in the last 1 Month?

	Response
Response	Yes	No
I was ill enough to go to the doctor
I sought counseling for mental problems
I had problems with infertility
I suffered from a drinking problem
I used illegal drugs
My child had to go to hospital
My partner had to go to hospital
A close friend died
My child suffered from drug or alcohol problems

The answers to such a set of questions are regarded as multiple responses, since the answer to each does not preclude an answer for the others; the responses are not mutually exclusive.

The answer to each of these questions is regarded, for the purpose of SPSS coding and data entry, as. a separate variable. That is, a column is set up for each of the items to which a respondent can answer Yes or No. In this instance, therefore, there are 9 columns of data; one containing either a 1 (= Yes) or 2 (= No) for each case according to whether they were ill enough to go to the doctor, another column containing 1 or 2 for each case indicating whether they had sought counseling for mental problems, and so on.

To code this in SPSS we use the code hlth1, hlth2, hlth3…hlth9

After coding and typing the respective labels, SPSS will look like the figure below:

Figure 1 - Variable View

The data view will look like the figure 2 below after data entry

Figure 2 - data view for multiple responses

With the data entered in this way, if we wanted to see the number of Yes responses for each of these variables we would have to generate 9 separate frequency tables and note the number of Yes responses in each.

An alternative, which also allows us to do further analysis, is to use the Multiple Response command. The Multiple Response command allows us to analyze a number of separate variables at the same time, and is best used in situations where the responses to a number of separate variables that have a similar coding scheme all ‘point to’ a single underlying variable.

In this example, we can consider each of the items in the question as all pointing to the state of a respondent’s health. They are particular operationalizations, each of which captures just one dimension of this complex variable. It is therefore interesting to summarize the responses to these items at once, and to be able to use the pattern of responses across these items in further analysis with other variables, which is exactly what the Multiple Response command allows us to do.

To use the Multiple Response command we initially have to set up a Multiple Response

Set. This procedure instructs SPSS to group together the responses across a range of variables.

Before doing this it is important to have noted the coding scheme for the items that will make up the Multiple Response Set. In this instance, the coding is 1  - 9 for the various health conditions. We note this because we need to tell SPSS which value (or range of values) is of interest to us. Here we are interested in all the Yes responses to each item.

Figure 3 - Define the Multiple Response variable sets

Transfer the Multiple variables to the right

Figure 4 - defining the variable categories

Since we have 2 responses (Yes, 1 and No, 2) we select categories 1 to 2.

Now that we have defined the multiple responses set we can analyze it. The ‘new’ variable that we have just created and called hlth_con does not appear on the Data Editor window with the existing variables, but is stored in SPSS’s memory, and is accessed only through the

Analyze/Multiple Response/Frequencies command. It won’t appear in the normal dialog boxes we are familiar with which present the variables in the data file in a source variable list.

It is also not saved with the data file and will disappear when the file is closed, so it is a good idea to perform all the analysis you plan to undertake using the multiple response set before finishing your current SPSS session.

The simplest analysis we can undertake on a multiple response set is to run a frequency  (Figure 5) on the new variable (Though you can also perform crosstabs

To analyze multiple frequencies

Figure 5 - Analyze Frequencies

The SPSS multiple frequencies command. Then Press OK