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Statistics Slide 1 Central Tendency- Nominal Variable (1)

Recall that “marital status” [marital] is a nominal variable and the only central tendency measure available for a nominal level variable is a mode.Thus, average of “marital status” is an incorrect application of a statistic.

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Statistics Slide 2 Central Tendency- Nominal Variable (2)

This question asks the mode of “marital status” [marital], which is a correct application. Now, let’s look at how to find the mode for [marital] of GSS2002_PrejudiceAndAltruism.sav in SPSS.

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Statistics Slide 3

Central Tendency- Nominal Variable:Mode in SPSS (1)

In SPSS, you can obtain information about central tendency of variables of interest using “Frequencies” function. It can be implemented by clicking:

Analyze > Descriptive Statistics > Frequencies

In other words, first, click on Analyze in the menu bar of SPSS, then find and click on Descriptive Statistics on a pop-down submenu. Again, find and click on Frequencies on another pop-down submenu. Then, you will see a window shown in the next slide.

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Statistics Slide 4

Central Tendency- Nominal Variable:Mode in SPSS (2)

First, find the variable of interest (i.e., [marital]) in the left-hand side box. Use scroll bar on the right to find the variable. You can select the variable by clicking the variable. Also, you can select more than one variable by clicking variables while you press and hold Control key on your keyboard (Ctrl).

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Statistics Slide 5

Central Tendency- Nominal Variable:Mode in SPSS (3)

After selection of the variable, [marital], click on “Statistics” button to obtain more information than just frequency table. It will open a new window shown in the next slide.

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Statistics Slide 6

Central Tendency- Nominal Variable:Mode in SPSS (4)

The “Frequencies: Statistics” window provides various options for descriptive statistics. For now, we will focus on the “Central Tendency” box on the top of the right side. Since the variable [marital] is a nominal variable, only “mode” is a meaningful measure of central tendency. Select Mode by clicking the checkbox and click on “Continue” and “OK” buttons.

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Statistics Slide 7

Central Tendency- Nominal Variable:Mode in SPSS (5)

In the SPSS output, you will notice that the Mode of the variable [marital] is presented in the Statistics table. Since the corresponding category for the [marital] value of 1 is “married”, the mode of the variable [marital] is “married”. It is confirmed to be true by examining the frequency table of the same variable showing that the largest frequency category is 1 “married”.

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Statistics Slide 8 Central Tendency- Nominal Variable (3)

Thus, the right answer for this question is True.

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Statistics Slide 9 Central Tendency- Ordinal Variable (1)

We have to examine the level of measurement of this variable [fund] to decide whether the use of average is a correct application of a statistic. Recall that average can be used only for interval level variables.

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Statistics Slide 10 Central Tendency- Ordinal Variable (2)

Since there is an rank order between the categories (from fundamentalist to Liberal), the variable [fund] is an ordinal variable. Average of the variable [fund] is an incorrect application of a statistic.

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Statistics Slide 11 Central Tendency- Ordinal Variable (3)

If you click on “Show Correct Answer” button, the right answer for this question will blink shortly.

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Statistics Slide 12 Central Tendency- Ordinal Variable (4)

This question is about the median of the variable [fund], which is a correct application of a statistic for an ordinal level variable.

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Statistics Slide 13

Central Tendency- Ordinal Variable:Median in SPSS (1)

In SPSS, you can obtain information about central tendency of variables of interest using “Frequencies” function. It can be implemented by clicking:

Analyze > Descriptive Statistics > Frequencies

In other words, first, click on Analyze in the menu bar of SPSS, then find and click on Descriptive Statistics on a pop-down submenu. Again, find and click on Frequencies on another pop-down submenu. Then, you will see a window shown in the next slide.

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Statistics Slide 14

Central Tendency- Ordinal Variable:Median in SPSS (2)

First, find the variable of interest (i.e., [marital]) in the left-hand side box. Use scroll bar on the right to find the variable. You can select the variable by clicking the variable. Also, you can select more than one variable by clicking variables while you press and hold Control key on your keyboard (Ctrl).

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Statistics Slide 15

Central Tendency- Ordinal Variable:Median in SPSS (3)

After selection of the variable, [fund], click on “Statistics” button to obtain more information than just frequency table. It will open a new window shown in the next slide.

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Statistics Slide 16

Central Tendency- Ordinal Variable:Median in SPSS (4)

The “Frequencies: Statistics” window provides various options for descriptive statistics. For now, we will focus on the “Central Tendency” box on the top of the right side. Since the variable [fund] is an ordinal variable, “mode” and “median” are meaningful measures of central tendency. Select Median by clicking the checkbox and click on “Continue” and “OK” buttons.

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Statistics Slide 17

Central Tendency- Ordinal Variable:Median in SPSS (5)

In the SPSS output, the Median of the variable [fund] is shown in the Statistics table. Since the corresponding category for the [fund] value of 2 is “Moderate”, the median or middle score of the variable [fund] is “Moderate”. From the frequency table, you can see that 28.7 percent of the respondents are placed below the category “Moderate” and that 72.9 percent are accumulated up to and including the category “Moderate”. From this observation, we know that 50 percent is located somewhere within the “Moderate” category.

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Statistics Slide 18 Central Tendency- Ordinal Variable (5)

If you click on “Show Correct Answer” button, the right answer for this question will blink shortly.

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Statistics Slide 19 Central Tendency- Interval Variable (1)

Since age [age] is an interval level variable in this data set, the central tendency of it can be represented by mean, median, or mode.Let’s explore how to get mean of the variable [age] in SPSS.

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Statistics Slide 20

Central Tendency- Interval Variable:Mean, median, and mode in SPSS (1)

In SPSS, you can obtain information about central tendency of variables of interest using “Frequencies” function. It can be implemented by clicking:

Analyze > Descriptive Statistics > Frequencies

In other words, first, click on Analyze in the menu bar of SPSS, then find and click on Descriptive Statistics on a pop-down submenu. Again, find and click on Frequencies on another pop-down submenu. Then, you will see a window shown in the next slide.

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Statistics Slide 21

Central Tendency- Interval Variable:Mean, median, and mode in SPSS(2)

First, find the variable of interest (i.e., [age]) in the left-hand side box. Use scroll bar on the right to find the variable. You can select the variable by clicking the variable. Also, you can select more than one variable by clicking variables while you press and hold Control key on your keyboard (Ctrl).

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Statistics Slide 22

Central Tendency- Interval Variable:Mean, median, and mode in SPSS (3)

After selection of the variable, [age], click on “Statistics” button to obtain more information than just frequency table. It will open a new window shown in the next slide.

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Statistics Slide 23

Central Tendency- Interval Variable:Mean, median, and mode in SPSS (4)

The “Frequencies: Statistics” window provides various options for descriptive statistics. For now, we will focus on the “Central Tendency” box on the top of the right side. Since the variable [age] is an interval variable, any of “mean”, “mode”, and/or “median” are meaningful measures of central tendency. Select Mean by clicking the checkbox and click on “Continue” and “OK” buttons.

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Statistics Slide 24

Central Tendency- Ordinal Variable:Median in SPSS (5)

In the SPSS output, the mean, median, and mode of the variable [age] are shown in the Statistics table. In the table, you can see the mean of respondents’ age [age] was 46.58.You can also see that the age of a person right in the middle of the age distribution (i.e., median) was 45 and the modal age of the respondents in this data set was 33.

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Statistics Slide 25 The typical case for a variable

Measures of central tendency are also used to describe the “typical” score or value for a variable in the data set.

The typical case or respondent is described by the preferred measure of central tendency for the variable: Nominal/dichotomous variables: the mode Ordinal variables: the median Interval variables: the mean if not skewed

and the median if skewed

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Statistics Slide 26

Steps in solving central tendency problems - 1

The following is a guide to the decision process for answering central tendency homework problems.

If the problem asks about a specific measure of central tendency:

Is the level of measurement required for the statistic satisfied?

Incorrect application of a statistic

Yes

False

No

Is the correct value for the statistic reported?

True

Yes

No

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Statistics Slide 27

Steps in solving central tendency problems - 2

If the problem asks about the preferred measure of central tendency (typical score):

Is the variable nominal level?

Yes

False

No

Is the value of the mode correct?

True

Yes

Is the variable ordinal level?

Is the variable interval level?

Yes Yes

No No

Is the value for the median correct?

Is the variable badly skewed?

Is the value for the mean correct?

NoYes Yes

False

No

False

True

Yes

True

No

False

Note: to say one specific value is the mode, the distribution must not have multiple modes. If there is more than one mode, the answer to the problem will be false.