SPSS exercise 4.7

First describe both variables before carrying out the correlation analysis. Since there are no categorical variables here, it is a good idea to request a few descriptive statistics and histograms. A scatter plot is also important, because the correlation coefficient assumes a linear association (i.e., a straight line).

There is one impossible value: the scale score for parental attention must be between 1 and 9 but one respondent (number 87) has a scale score of 0. This value must be designated as missing. The histogram shows a clear non-linear association: the less parental attention received, the more hours spent chatting. It is therefore questionable whether the correlation coefficient is a suitable measure of association for the association between these two variables.

Statistics
		Scale score for parental attention	Number of hours spent chatting in the past seven days
N	Valid	92	93
	Missing	1	0
Mean		6,3776	4,26
Std. Deviation		1,91145	8,043
Skewness		-,976	5,657
Std. Error of Skewness		,251	,250
Minimum		1,02	0
Maximum		9,00	65

The result is significant, at p < .001. The correlation coefficient is -.52 in the sample, i.e. negative, as expected. The researcher's hunch therefore appears to be correct: the less parental attention received, the more hours spent chatting.

* Syntax from assignment a)
* Describe and process the variables.
FREQUENCIES VARIABLES=attention chatting
  /FORMAT=NOTABLE
  /STATISTICS=STDDEV MINIMUM MAXIMUM MEAN SKEWNESS SESKEW
  /HISTOGRAM NORMAL
  /ORDER=ANALYSIS.
* Missing value for attention score 0.
* Define Variable Properties.
* Attention
MISSING VALUES Attention(0.00.).
EXECUTE.
* Describe again.
FREQUENCIES VARIABLES=attention chatting
  /FORMAT=NOTABLE
  /STATISTICS=STDDEV MINIMUM MAXIMUM MEAN SKEWNESS SESKEW
  /HISTOGRAM NORMAL
  /ORDER=ANALYSIS.
* Scatter plot.
GRAPH
  /SCATTERPLOT(BIVAR)=attention WITH chatting
  /MISSING=LISTWISE.
* Correlation coefficient (unilateral and two-sided).
CORRELATIONS
  /VARIABLES=attention chatting
  /PRINT=ONETAIL NOSIG
  /MISSING=PAIRWISE.
CORRELATIONS
  /VARIABLES=attention chatting
  /PRINT=ONETAIL NOSIG
  /MISSING=PAIRWISE.

We have already carried out the checks; therefore we can calculate and test Spearman's correlation coefficient straight away.

The correlation coefficient is -.15, which is notably lower (closer to zero) than the correlation coefficient that we calculated in a. The correlation coefficient is not significant: p = .156

The researcher's hunch now appears not to be correct: in the population from which the sample was taken there is very probably no association between parental attention and time teenagers spend chatting.

* Assignment b.
* Spearman's correlation coefficient.
NONPAR CORR
  /VARIABLES=attention chatting
  /PRINT=SPEARMAN ONETAIL NOSIG
  /MISSING=PAIRWISE.
NONPAR CORR
  /VARIABLES=attention chatting
  /PRINT=SPEARMAN TWOTAIL NOSIG
  /MISSING=PAIRWISE.

With such a clearly skewed association, it is better not to use Pearson's product-moment correlation coefficient because it assumes a linear association. There are just a few teenagers in the sample who spend a lot of hours chatting (you can count the dots on the left-hand side of the scatter plot), but they do make the straight line running through the dot cluster fairly steep.

It is also better not to use this measure when the distributions are clearly not normal. This certainly seems to be the case here for the 'number of hours spent chatting' variable.

The correlation coefficient is not influenced by a few extremely high or low scores. Most of the teenagers gave attention scores of between 5 and 9; therefore the differences between them in terms of chatting carry more weight. Within this group, the differences do not coincide with the amount of attention, which is why the correlation coefficient is not significant.

In sum, it is better to use the correlation coefficient here, because the few extremely high scores on the chat variable would otherwise have too great an effect on the results. There could easily have been fewer extreme cases of this kind in a different sample.

It is probable that a larger sample would produce a significant result, but that does not really help us.

If you had left out the four extreme values for the chat variable from the beginning, the Pearson's correlation coefficient would have been much lower (-.23), and still significant (p = .017).