Chapter 5

THE DATA COLLECTION AND STATISTICAL ANALYSIS

Major Tasks

    This practicum was the study of possible correlations between three behavioral (dependent) variables and four predictor (independent) variables. The behavioral variables were represented by the number of time-out incidents per school day, the total time spent in time-out by students each school day, and the number of times students had to be physically restrained during acting out incidents each school day. The predictor variables were represented by the barometric pressure at various times during each school day, the change in barometric pressure during various times each school day, the lunar synodic cycle, and the welfare check cycle. There were three major tasks before the writer. First was an accurate and complete collection of data. For the behavioral variables, this represented an accurate account of daily student behavior. For the predictor variables, it meant collection of barometric, lunar cycle, and welfare check distribution data.

    Once all data were collected, the second task required that it be properly sequenced, codified, and entered into a computer file. When all data were appropriately filed, a computer program was run to analyze the data in search of relationships. The Statistical Package for the Social Sciences X was the program used for this purpose, as it is commonly regarded as one of the most appropriate for these calculations. Runs were made on a DEC 20 mainframe computer.

    The final task, assuming that relationships were found, was to develop a plan which would include consideration of these relationships in future school programming, and to disseminate these findings to colleagues in other school environments for their consideration and use.

Sequence of Events

    During the 1984-85 school year this writer had a detailed record kept of all major disciplinary problems through a time-out log. Because the SELC utilizes time-out as punishment for all major disciplinary problems, use of the time-out log gave a good representation of daily disciplinary problems. Survey of the log gives the number of major disciplinary problems each school day, and the severity of the problems as indicated by the amount of time given for each offense. The log also indicates the number of times each day that students had to be physically restrained as an indicator of violent behavior.

    The writer obtained a copy of the Climatological Table from the National Oceanographic and Atmospheric Administration, showing barometric pressure for the Hartford, Connecticut area. This was used as the official record of this factor for each day studied. The barometric pressures at seven times for each day: 00:00, 02:00, 04:00, 06:00, 08:00, 10:00, 12:00, and 14:00 were recorded (Appendix A: 41).

    Phase of the moon for each date (using 00 for no moon through 28 or 29 for a full moon) was determined from charts in the World Almanac and Book of Facts, and recorded (Appendix B: 47).

    In addition, the writer obtained a copy of the dates that welfare checks were mailed in the Hartford area for the period covered by the study. The welfare check distribution schedule (Appendix C: 55) was calculated and prepared for entry using the days from check delivery (i.e. 00= day of check delivery, 07= seven days after check delivery.)

    During May and June, 1986 the writer caused all information needed for the study to be tabulated, properly ordered, and prepared for computer entry. Before the timeout data were entered, they were checked for accuracy by a review of all data from the original recording forms. Included in the tabulation of time-out data was the date, and the following information for each date: student attendance, the number of time-outs, the total time of the time-outs, and the number of violent restraints (Appendix D: 56, and Appendix E: 57). While attendance could be treated as an additional behavioral variable, it was used in this study to standardize the time-out data by number of pupils present.

    During July all data were entered in the computer in a special file created for that purpose (Appendix A: 41).

    During September and October computer runs were made to analyze the data. Frequency distributions were examined to check the validity of the data entry. The Statistical Package for the Social Sciences X (SPSSX) was run to construct scatterplots of predictor variables versus behavioral variable combinations. In order to more carefully determine certain possible relationships, several scatterplot ranges were adjusted (condensed) to make those scatterplots easier to read. At this point, it was noted that data on the behavioral variables had not reflected variation in attendance. The variables were corrected to reflect incidents per 150 attending students, and the scatterplots were reconstructed. These scatterplots should better represent the true variable of interest.

    The variables studied consisted of three groupings:

    1. Misbehavior (behavioral)

*A. Number of time?outs per day.

*B. Average time of time?outs per day.

*C. Number of time?outs requiring physical restraint. adjusted for attendance


    2. Weather/Lunar Synodic Cycle (predictor)

A. Barometric pressure each day at 00:00, 04:00, 06:00, 08:00, 10:00, 12:00, and 14:00.

B. Amount of barometric pressure change between midnight and 6am, between midnight and noon, and between 8am and 2pm each day (Appendix B: 23 47).

C. Lunar synodic cycle as shown by days after new moon.


    3. Welfare check cycle (predictor) as shown by days after check delivery.

    An analysis was conducted of the relationship between each of the three behavior variables and four predictor variables. The analyses were conducted in two stages:

    1. Scatterplots for each of the relationships were prepared. This allowed a determination of possible relationships and their shape (linear or non-linear), and a statistical test for the presence of a linear relationship. The following combinations were examined:

A. the number of time-outs versus each predictor variable

B. the total minutes in time-out versus each predictor variable

C. the number of violent time-outs versus each predictor variable

    The Pearson product-moment correlation analysis was conducted and tested for statistical significance at the
.05 level.

    2. Explicit multivariate hypotheses were formulated for each behavioral variable and combination of two predictor variables. These hypotheses were tested with a series of two-factor analyses of variance.

    In order to prepare for this analysis, the predictor variables were first recoded from continuous to categorical variables as described in Table 1. This process made the predictors more readily understandable. Basically, those values of the predictor hypothesized to produce behavioral problems were given a "1" while other values were given a "0". An example of the resulting analysis is given subsequently.

Table 1

Regrouping of Predictor Variables

-
Values Hypothesized to Produce Behavioral  Problems
Other 
Values
Days From
Welfare Check
Delivery
0-3, 12-15
4-11
Lunar
Cycle
0-2, 13-16, 27-29
3-12, 17-26
Barometric
Pressure 
low- 29.7
29.71 - high
Barometric
Difference
low - 0
0 - high

    In Table 1, the significant categorical variables were defined as: the three days before and after the date of welfare check delivery; the four days around the full moon and around the new moon; barometric pressure below 29.7; and, barometric pressure drop.

Four hypotheses were tested. They stated the existence of a relationship between the predictor variables and the behavioral variables:

1. A drop in the barometric pressure is associated with an increase in behavioral problems.

2. Days around a new moon or a full moon are associated with an increase in behavioral problems.

3. Days around the issue of welfare checks are associated with behavioral problems.

4. There is a correlation between paired predictor variables and behavioral problems.
 

Participant Functions

The SELC principal coordinated all activities within the practicum. He saw that time?out activities were properly logged, and prepared those statistics in a usable form. He obtained climatological and welfare check data, and prepared that data for computer entry. When all information was ready, he caused the data to be entered in the computer file. Once all data was entered, he coordinated the analysis of the variables by computer.
 

Monitoring the Action

Due to the nature of this practicum, little monitoring action was required. The writer had to supervise collection of time-out data to assure its completeness and accuracy.

After the first computer run, he had to review the results to assure that the data had been entered correctly and
plotted in an appropriate way.
 

Rationale for the Implementation Design

The design of this practicum was dictated by accepted statistical procedures for the analysis of the relationship between variables.
 

The Results

This author approached the analysis of the data with the firm belief that a strong relationship exists between the behavioral and the predictor variables. In fact, the author was personally convinced that a causal relationship existed. It was with great surprise, therefore, when all of the statistical results indicated only three possible relationships existed between predictor and behavioral variables, at even the .05 level of significance.

The first apparent relationship (Table 2) was found between the Days from Welfare Check and the Minutes in Timeout. While it showed a correlation of .127 at a .045 level of significance, further examination of the scatterplot (Appendix F: 63) and its accompanying statistical data suggested this was attributed to a false positive (Type I) error due to high experiment-wise error rate. This interpretation was reached because:

1) A statistically significant result was not found for the same test when the variable was not corrected for attendance;

Table 2

Pearson Correlation Coefficients Showing
Relationship Between Behavioral and Predictor Variables

Behavioral Variables per 150 Students

Predictor 
Variables
Number of TO
Minutes of TO
Violent TO
Days from 
Welfare Check
.107
.127*
.074
Days from 
new Moon
-.093
-.073
-.050
Barometer 
at 00:00
.041
.025
.014
Barometer 
at 04:00
.054
.048
.046
Barometer 
at 06:00
.050
.042
.033
Barometer 
at 08:00
.060
.059
.042
Barometer 
at 10:00
.065
.060
.031
Barometer
at 12:00
.059
.055
.024
Barometer
at 14:00
.043
.038
-.005
Barometer
06:00-00:00
.017
.048
.053
Barometer 
12:00-00:00
.034
.051
.018
Barometer 
08:00-14:00
.051
-.064
-.144*
*Significant at .05 level

2) The size of the identified effects was too small to have practical value; and

3) The study ran 36 tests giving rise to the likelihood of a few "false positive" results.

    The second apparent relationship (Table 2) was found between the change in barometric pressure from 8am. until 2pm, and the number of violent time-outs. Because this relationship showing a correlation of -.138 at a level of significance of .034 seemed to indicate a true relationship, the scatterplot was redesigned (Appendix G: 64) to show a more detailed representation of the relationship through an expanded X axis and the elimination of rounding?off in the plotting of data points. The barometric change results were grouped into three categories. The first category represented the number of violent incidents when the barometric pressure dropped by .10 or more inches. The second category represented these incidents when the pressure dropped between .03 and .10 inches. And the third category represented a drop of less that .03 inches or a rise in pressure (Table 3).

    An analysis of Table 3 indicates almost one more violent time-out on days when barometric pressure dropped more than .10 inches. There is minimal difference when the drop was less, or when there was a barometric increase. While this is statistically significant the results raise the question of educational significance. Even if it is known that significant barometric pressure drops are associated with an increase in violent behavior, is one additional incident of this behavior sufficient to warrant major changes in a school's operational plan in anticipation of this increase. This author feels it is not. Consequently, this finding does not have educational significance.

Table 3

Analysis of Variance Between Grouped Barometric
Change and Violent Time-outs

Barometric
Change in Inches
Number of 
Days
Mean Violent
Time-outs
-.38 to -.10
46
2.51
-.10 to -.03
65
1.88
-.03 to +.21
67
1.64
F Probability = .0124

       The third apparent relationship was found during a two factor analysis of variance, when one pair of predictor variables showed a significant relationship with one behavior variable. This was found in an analysis comparing the welfare check cycle, the lunar synodic cycle, and the number of time-outs. The cell means of this analysis are shown in Table 4 below.

    In Table 4 the predictor variables of the period within a three day spread around the new and full moon and around a six day spread of the welfare check delivery schedule, are analyzed in respect to the behavior variable of the number of time-outs. It is interesting to note that the highest means occur when either one or the other of the predictor variables is present, and the lowest means occur when both predictor variables are either present or absent. Since these results contradict each other and are contrary to the hypothesized results, it is concluded that they are a result of a high experiment-wise error rate.

Table 4

The Relationship of Synodic Cycle, Welfare
Check Delivery, with Respect to
the Number of Time-outs
 

SYNODIC CYCLE

WELFARE
CHECK
DELIVERY
Within 3 Days  New/
Full Mooni
Other Days
Total
Within 3 days
 of Check 
 Delivery
21.64
26.38
25.74
Other Days
25.86
22.43
23.97
Total
25.00
24.69
24.79
Significance of Interaction =  .048

    The test of statistical significance applies to a single experiment. When many experiments are run in the same research, the probability rises that one or more individual experiments will produce statistically significant results by chance. This situation applies to the current study. Given that the findings were not in accordance with the hypothesis, it seems most likely that this significant finding was the result of a high experiment?wise error rate. It appears that a false positive result was obtained due to the result of conducting many tests.
 

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