Descriptive Statistics



When comparing experimental conditions, it is always a good idea to construct parallel box plots as shown below. (Note that although most boxplots represent the mean with a "+" sign, these boxplots computed with SPSS do not show the mean).



How this was done (from SPSS)

 

Generally speaking the time it took to name an aggressive word was
faster when the target word was preceded by a weapon word.
faster when the target word was preceded by a non-weapon word.
not affected by the type of the preceding word.
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The group names are defined as follows:
AN: Aggressive target word, nonweapon prime
AW: Aggressive target word, weapon prime
CN: Control target word (nonaggressive) and nonweapon prime
CW: Control target word (nonaggressive) and weapon prime

Notice that it took less time to name an aggressive target word when it was preceded by a weapon prime (AW) then when it was preceded by a non-weapon prime (AN). A comparison of the CW and CN conditions reveals no evidence of a weapon prime for the nonaggressive target words.

The presence of outside values (circles in the box plots) suggests that the distributions have slightly more scores in their tails than would be expected in a normal distribution. A histogram of the CW condition is shown below.

Such "heavy tailed" distributions are called
Mesokurtic
Leptokurtic
Platykurtic
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The means and standard deviations of the four conditions are shown below.

Descriptive Statistics
N Min Max Mean sd

AN

32

31.12

54.39

41.6395

5.1220

AW

32

28.56

52.95

40.9184

5.2845

CN

32

26.83

55.45

41.3356

6.0892

CW

32

28.89

54.92

41.4576

5.5310

How this was done (SPSS)


Since many inferential statistical procedures assume the data are normally distributed, Normal probability plots (also called Q-Q plots or Normal Quantile plots) are helpful tools to determine if the data is normally distributed. Basically these plots plot the sample quantiles from the data set against the quantiles of the normal distribution. If the data are from the same normal distribution, the data should fall along the line y=x.

The SPSS output is easily read because the green line is a reference line of where we would expect the data points to fall if the data were normally distributed. (the line y=x) Even though the data do not fall exactly on this line, the deviations are not extreme.

 

 

How this was done (SPSS)

Recall that the hypothesis is that a person can name an aggressive word more quickly if it is preceded by a weapon word than if the aggressive word is preceded by a neutral word. The first step in testing this hypothesis is to compute the difference between the mean naming time of aggressive words when preceded by a neutral word and the mean naming time of aggressive words when preceded by a weapon word separately for each subject. This difference score will be called the "aggressive-word priming effect." The hypothesis of this study would be supported if:
the mean aggressive-word priming effect is postive.
the mean aggressive-word priming effect is negative.
the standard deviation of the aggressive word priming effecy is greater than the mean.
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The statistics shown below were computed on the "aggressive-word priming effect" which is labeled "prime_agg."


As hypothesized, the mean aggressive-word priming effect is positive. However, this analysis fails to control for the possibility that "weapon words" prime non-aggressive as well as aggressive words. To control for this, compute the difference between (a) the mean naming time of non-aggressive words when preceded by a non-weapon word and (b) the mean naming time of non-aggressive words when preceded by a weapon word separately for each subject. This difference represents the how much preceding a non-aggressive word by a weapon word decreases the time it takes to name the nonagressive word and will be referred to as the "non-aggressive word priming effect." Finally, for each subject, subtract this "non-aggressive word priming effect" from the "aggressive-word priming effect" described above. This difference between priming effects will be called "prime difference" and labeled "prime_diff" in computer output. The hypothesis is that the mean prime difference will be positive.

Below is shown a histogram of prime difference scores.


Answer 1
Answer 2
Answer 3
Answer 4
Answer 5
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The distribution has a positive skew and a center that is slightly positive. As shown below, the mean is 0.8431 and the median is 0.579. Thus the hypothesis that weapon words prime aggressive words more than they prime non-aggressive words is supported. Of course, these descriptive statistics don't speak to whether this difference could have occurred by chance. The section on inferential statistics addresses that issue.