Friday the 13th accident statistics

Running Head: A STATISTICAL ANALYSIS OF AN OCCURRENCE ON FRIDAY 13TH

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A STATISTICAL ANALYSIS OF AN OCCURRENCE ON FRIDAY 13TH

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A Statistical Analysis of an Occurrence on Friday 13th

Marcelle

University

07/31/2016

A Statistical Analysis of an Occurrence on Friday 13th

SCENARIO 5:

Friday the 13th is considered as unlucky by many people. The belief is superstitious and this study was conducted to find out if in fact the theory is true. The involved parties are traffic accidents on Friday 13th and Traffic accidents on Friday the 6th within the months July and November of the year 1992. Data was collected on ten accidents which occurred on Friday 6th and Friday 13th in July and November in 1992. Analysis were carried out based on the accident data.

DATA:

The involved parties are traffic accidents on Friday 13th and Traffic accidents on Friday the 6th, the months July and November, the year 1992. The question that can be answered by this data is whether or not more accidents happens on what is termed as an unlucky day namely Friday the 13th in comparison to a regular day Friday the 6th. The respective accident data is given as follows:

ACCIDENT DATA

Friday the 6th

Friday the 13th

139246

138548

134012

132908

137055

136018

133732

131843

123552

121641

121139

118723

128293

125532

124631

120249

124609

122770

117584

117263

Mean number of accidents which occurred on Friday 6th and mean number of accidents which happened on Friday 13th were calculated and compared. It was observed that the mean number of accidents which occurred on Friday 6th was 128385 and the mean number of accidents which occurred on Friday 13th was 126550. That is, the mean number of accidents which happened on Friday 6th was in fact greater than the mean number of accidents which happened on Friday 13th. Since mean is a basic measure of central tendency, further study and analysis was required to arrive at a concrete inference.

ETHICAL ISSUES:

The data collected is on accidents that took place on Friday 6th and Friday 13th in July and November in 1992. Appropriate permission was obtained prior to collection of data from the relevant departments. This data was collected only from reliable sources. Proper care was taken to ensure that the identity and confidentiality of any of the accident victims was never compromised, as this was purely statistical reporting. The researchers adhered to Ethical standards 2.01, 8.02, 8.10, 8.14 and 8.15 of The Ethical Principles of Psychologist and Code of Conduct. Thus the ethical standard was fully maintained and the collection of the data did not violate any of the Ethical Codes. The Statistician should not have a misconceived notion about Friday 13th, otherwise bias factors can arise on all phases. One more important factor which has to be taken into account is a smaller alpha. When level of significance is kept lesser than 90% (and alpha > 0.01), precision and power of the test decreases and it is possible that we are misinterpreted about the results. The conduct of this research must also adhere and align with section 9.02, 9.03, also there should be no fabrication of data and if there are errors steps should be taken to ensure they are corrected as required in The Ethical Principles of Psychologist and Code of Conduct.

DATA ANALYSIS: Sample:

The sample size chosen is n1=n2=10. As is known, greater the sample size, lesser the margin of error and better the precision. The sample size chosen is very well informed as there were clear indications that the data was unbiased and representative of the population. Thus inference report of the study would be precise and satisfy the requirement for the problem in hand.

DATA ANALYSIS: Statistical Procedure

NORMALITY TEST:

STATISTICAL TEST:

A t test was performed to test the hypothesis. The test is a one tailed test. The sample size is <30 and hence Z cannot be used and hence t test was used. Normality condition was satisfied for the data. With the condition of normality been met, ‘t’ test for difference between independent sample means can be used. The t statistic for difference between two sample means is given by

Where is sp is the pooled standard deviation and

is the pooled standard error

t ~ t (n1+n2-2) degrees of freedom

Where is the sample mean of accidents which happened on Friday 6th

is the sample mean of accidents which happened on Friday 13th

is the sample variance (square of sample standard deviation) of

accidents which occurred on Friday 6th

is the sample variance (square of sample standard deviation) of

accidents which occurred on Friday 13th.

DATA ANALYSIS: Chance Factors:

Any study is definitely affected by clear chance factors and in this case factors which might have been responsible for the accidents could have happened because of rash driving, faulty vehicles, irresponsible driving, drunken driving, mistakes, or random issues etc., Hence a hypothesis test was conducted to analyze to prove or disprove if the accident data was merely by chance.

DATA ANALYSIS: Mean and Standard Deviation:

The mean and standard deviation of accidents which occurred on Friday 6th was

= 128,385 and s1=7259.2233 respectively. The mean and standard deviation of accidents which occurred on Friday 13th were =126,550 and s2 =7664.2818. There is greater variability in the data of accidents in Friday 13th data compared to Friday 6th data as the standard deviation of Friday 13th data was more than the accidents on Friday 6th.

Graphs and Histogram: The histogram and other charts are available in the attached Excel file

DATA ANALYSIS: Shape:

The minitab output graph of histogram fitted with the distribution curve shows that the shape of data is normal distribution. The t test was used after normality conditions were satisfied. The shape of the distribution is of much importance in Statistics. This is because, certain statistical tests can be used only when the distribution is normal. Most of the distributions attain a normal distribution when the sample size is large. ‘t’ test for difference between two sample means can be used only when normality is satisfied. Since the fitted curve follows normality, the mandatory condition for our analysis is satisfied. When the normality condition is satisfied, it shows that the data is well-modelled.

Average number of accidents on Friday 6th which is 128385 is greater than the average number of accidents on Friday 13th which is 126550. Average was calculated by summing the data and dividing by number of observations. =. This is done for both groups.

HYPOTHESIS: Whether One Mean is Higher and the Null Hypothesis and Alternative Hypothesis:

Average number of accidents on Friday 6th which is 128385 is greater than the average number of accidents on Friday 13th which is 126550. Symbolically, µ1 ≥ µ2.

HYPOTHESES:

Null hypothesis: The average number of accidents on Friday the 6ths are greater

than or equal to average number of accidents on Friday the 13ths.

Symbolically, µ1 ≥ µ2

Alternative hypothesis: Superstition of Friday the 13th as an unlucky day results in an

average number of accidents on Friday 13th to be greater than the

average number of accidents on other Fridays, such as Friday the

6ths. Symbolically, µ1<µ2.

Where µ1 is the mean number of accidents on Friday 6th and µ2 is the mean number of accidents on Friday 13th.

RESULTS: Valid:

The study conforms to face validity, criterion based validity, formative validity and sample validity. Also, there is scope to improve on face and sample validity.

RESULTS: Statistically Significant

CRITICAL VALUE APPROACH:

The calculated value of t is 0.5496 and at 95% confidence level the table value of t for one tailed test is 1.7341 at 18 degrees of freedom. Since the calculated value of t is lesser than the table value of t, we cannot reject the null hypothesis and we conclude that Friday the 13th cannot be blamed for the occurrence of accidents.

P VALUE APPROACH:

The p value of the test is 0.2979. Since the p value = 0.2979 > alpha = 0.05, we fail to reject the null hypothesis. Hence we conclude that Friday 13th is not unlucky.

INTERPRETATION:

The statistical analysis of data show that, Friday 13th is not unlucky and more traffic accidents do not occur on this day, as opposed to Friday 6th. Statistical analysis is a scientific way of approaching many things, and answering many questions, with evidence through numbers. Hence we may conclude with the data in hand, that Friday 13th is not unlucky as people believe and is not responsible for an increase in traffic accidents.

DATA ANALYSIS: Procedures

The first step of data analysis was to find the mean of the two data sets on Friday 6th and Friday 13th. We found out that mean number of accidents on Friday 13th was lesser than mean number of accidents on Friday 6th. In order to see if the difference was due to chance factors, a hypothesis test was conducted. Since n<30 with the data satisfying normality conditions, it was concluded that Friday 13th was just like any random day.

FURTHER STATISTICAL ANALYSIS:

Though the data suggests that Friday 13th was not unlucky, the study was based on a sample of size 10. The standard error and precision of any test is inversely proportional and hence it is better to collect more samples to make our inference strong. Also, an unlucky incident can be anything and not only accidents. These factors may also be considered to give a strong base to curb blind beliefs. Once the data is available, we may subject the data to ANOVA and see if Friday 13th is unluckier for any other types of bad accidents. This type of test would be more acceptable for the general public who think that Friday 13th is unlucky. Also, the inclusion of other factors will make the study more valid with respect to face and sample validity. The study will be complete with the above inclusions.

References

American Psychological Association. (2010). 2010 Amendments to the 2002 "Ethical principles of psychologists and code of conduct". American Psychologist, 5(5), 493-493. doi:10.1037/a0020168

http://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm

Lund, D. R., & Bennett, J. O. (2014). Student's solutions manual, Statistical reasoning for everyday life, fourth edition, Jeffrey O. Bennett, William L. Briggs, Mario F. Triola. Boston, MA: Pearson.

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