Statistical Methods for Psychology

in which data can be represented graphically. Some of these methods are frequency distri-

butions, histograms, and stem-and-leaf displays, which we will discuss in turn. (I believe

strongly in making plots as simple as possible so as not to confuse the message with un-

necessary elements. However, if you want to see a remarkable example of how plotting

data can reveal important information you would not otherwise see, the video at

http://blog.ted.com/2007/06/hans_roslings_j_1.php is very impressive.)

Frequency Distributions

As a first step, we can make a frequency distributionof the data as a way of organizing

them in some sort of logical order. For our example, we would count the number of times

that each possible reaction time occurred. For example, the subject responded in 50/100

of a second 5 times and in 51/100 of a second 12 times. On one occasion he became flus-

tered and took 1.25 seconds (125/100 of a second) to respond. The frequency distribu-

tion for these data is presented in Table 2.2, which reports how often each reaction time

occurred.

From the distribution shown in Table 2.2, we can see a wide distribution of reaction

times, with times as low as 36/100 of a second and as high as 125/100 of a second. The data

tend to cluster around about 60/100, with most of the scores between 40/100 and 90/100.

This tendency was not apparent from the unorganized data shown in Table 2.1.

Section 2.1 Plotting Data 17

Table 2.1 Reaction time data from number identification experiment

Comparison

Stimuli* Reaction Times, in 100ths of a Second

40 41 47 38 40 37 38 47 45 61 54 67 49 43 52 39 46

lY 47 45 43 39 49 50 44 53 46 64 51 40 41 44 48 50 42

90 51 55 60 47 45 41 42 72 36 43 94 45 51 46 52

52 45 74 56 53 59 43 46 51 40 48 47 57 54 44 56 47

1N 62 44 53 48 50 58 52 57 66 49 59 56 71 76 54 71 104

44 67 45 79 46 57 58 47 73 67 46 57 52 61 72 104

73 83 55 59 51 65 61 64 63 86 42 65 62 62 51 62 72

3Y 55 58 46 67 56 52 46 62 51 51 61 60 75 53 59 56 50

43 58 67 52 56 80 53 72 62 59 47 62 53 52 46 60

73 47 63 63 56 66 72 58 60 69 74 51 49 69 51 60 52

3N 72 58 74 59 63 60 66 59 61 50 67 63 61 80 63 60 64

64 57 59 58 59 60 62 63 67 78 61 52 51 56 95 54

39 65 53 46 78 60 71 58 87 77 62 94 81 46 49 62 55

5Y 59 88 56 77 67 79 54 83 75 67 60 65 62 62 62 60 58

67 48 51 67 98 64 57 67 55 55 66 60 57 54 78 69

66 53 61 74 76 69 82 56 66 63 69 76 71 65 67 67 55

5N 65 58 64 65 81 69 69 63 68 70 80 68 63 74 61 85 125

59 61 74 76 62 83 58 72 65 61 95 58 64 66 66 72

*Y 5 Yes, test stimulus was included; N 5 No, it was not included 1, 3, and 5 refer to the number of digits in

the comparison stimuli

frequency
distribution