SPSS exercise 2.6

The WatchAndListenSurvey.sav database contains a number of variables that measure use of the media, including those variables that measure how many seconds people have watched a particular channel. This was measured by placing a 'viewing meter' on the televisions of the respondents - which recorded exactly how long each channel was watched. The variables 'totchannel1', 'totchannel2' and 'totchannel3' refer to the three channels that together form the public broadcast channels in the Netherlands.

a. From the variables 'totchannel1', 'totchannel2' and 'totchannel3', make a new variable, 'totchannelps' (total number of seconds spent watching the public service channels). Drag and drop the syntax into the answer field.

COMPUTE totchannelps=totchannel1+totchannel2+totchannel3.
EXECUTE.

b. In general, we do not say how long we watched a particular channel in terms of seconds. From the new variable, 'totchannelps', make a new variable: 'totminps' (total number of minutes spent watching public broadcast channels). Drag and drop the syntax into the answer field.

COMPUTE totminps=totchannelps/60.
EXECUTE.

c. Calculate the most suitable measure of central tendency with the help of frequencies, BUT without printing out the whole frequency table. Drag and drop the syntax into the answer field.

FREQUENCIES VARIABLES=totminps
  /FORMAT=NOTABLE
  /STATISTICS=MEAN
  /ORDER=ANALYSIS.

Given that the level of measurement is ratio, the most suitable measure of central tendency is the mean.

d. What conclusion can you draw? When giving your answer, you must include the following: the 'content' of the variable, the units of analysis, the correct number for the measure of central tendency (round off to two decimals), and the interpretation of the measure of central tendency.

When asking “how many minutes a person spend watching public broadcast channels”, watched on average, the mean score is 466.56.

The content of the variable is the number of minutes spent watching public broadcast channels.

The units of are analysis are people.

The correct value of the measure of central tendency is 466.56.

The respondents watch the public broadcast channels for 466.56 minutes on average.

e. What is the standard deviation of the new variable, 'totminps'? Round it off to two decimal places.

485.15

f. What is the meaning of the standard deviation?

The greater the standard deviation, the more the values differ from each other, and the fewer values that equal the mean there are.

The standard deviation is 485.15 minutes. That means that the mean deviation from the mean (466.56 minutes) is 485.15 minutes. There is therefore a wide dispersion. It also means there are many 'extreme' values.

Hints

1 Creating a new variable based on multiple existing variables When you want to convert two or more variables into one variable, use the Compute function in SPSS. Compute is SPSS's 'calculator'; it can be used to add, subtract and multiply variables, etc. Compute can only be used when the level of measurement of the variable is at least ordinal.

In the Transform menu, click Compute. This will open a screen: 'Compute variable'. In the 'Target variable' field, enter the name of the new variable that you want to create. You now need to define the formula for calculating the values of the new variable. The 'numeric expression' field now contains the formula. You can do this by typing or using the mouse to select the variables and symbols. When you have finished, click OK.
2 Measures of central tendency and measures of dispersion selection chart

	Measure of central tendency	Mode	Median	Mean
	Measure of dispersion		Interquartile range	Standard deviation, Variance
1. Select	1.1 Specifics	What occurs most frequently?	What is the median value?	What is the balance point of the distribution?
	1.2 Minimum level of measurement	Nominal	Ordinal	Interval
	1.3 Shape of the distribution	Usable with every distribution shape	Usable with every distribution shape	Not optimal for very skewed distributions
2. Calculate		Analyze-> Descriptive Statistics -> Frequencies -> Statistics	Analyze-> Descriptive Statistics -> Frequencies -> Statistics	Analyze-> Descriptive Statistics -> Frequencies -> Statistics
3. Check		Unusable with a distribution with many peaks, e.g. in the case of an ungrouped interval variable.		The greater the difference between the mode, median, and the mean, the more skewed the distribution.
4. Conclude		General:  1. Give your reasons for selecting the measure of central tendency and measure of dispersion (see Select and Check). 2. Use the value of the measure of dispersion to comment on the accuracy of the calculated measure of central tendency: the smaller the distribution, the better the centre typifies the distribution.
		Mode: "The most common value of variable X is A.".	Median: "The median value of variable X is A" or "Half of the units of analysis have A or less on variable X, and half of the units of analysis have A or more on variable X." Interquartile range: "The mean deviation from variable X compared to the median is A" or "The middle half of the observations lies between (first quartile limit) and (third quartile limit).	Mean: "The units have an average A on variable X." Standard deviation, Variance "The mean deviation in relation to the mean."

3 What do we mean by the standard deviation, the variance, and the interquartile range? The standard deviation, the variance, and the interquartile range are all measures of dispersion. A measure of dispersion is a number that shows how far apart the results are from each other and/or from the mean. One number therefore serves to demonstrate the usefulness of the mean.

The standard deviation is the most commonly used measure of dispersion. It is calculated by extracting the root from the variance. The greater the standard deviation, the more the values differ from each other, and the fewer values that equal the mean there are. Analyse -> Descriptive Statistics -> Frequencies -> Statistics -> Std.deviation

Quartile: a quarter of the observations are below the first quartile; three-quarters of the observations are below the third quartile. The interquartile range is calculated as follows: the third quartile (percentile 75) minus the first quartile (percentile 25), divided by 2. Analyse -> Descriptive Statistics -> Frequencies -> Statistics -> Quartiles