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Descriptive Statistics - Assignment Example

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Statistical analysis of data provides objective and comparable means of understanding the trends seen in the sample and consequently in the population (Frankfort-Nachmias & Nachmias, 2008). The most basic type of statistical analysis is the use of statistics that are descriptive…
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Using Descriptive Statistics Statistical analysis of data provides objective and comparable means of understanding the trends seen in the sample and consequently in the population (Frankfort-Nachmias & Nachmias, 2008). The most basic type of statistical analysis is the use of statistics that are descriptive of the sample collected (Patten, 2005). These descriptive statistics help in understanding the most common and the most distinctive traits of the data collected, as well as helping in the use of other statistical techniques that can help in making estimates about the population (Patten, 2005).
For the data presented; the descriptive statistics help in understanding the extent of spread of scores, the aggregate score s of groups of participants, and the most representative scores in different groups(Frankfort-Nachmias & Nachmias, 2008). For the control group, it is evident that the scores on both variables – Depression and the number of candy bars eaten – are higher than the group receiving CBT. The control group had a Mean score of 5.3 and a Median and Modal score of 5 for candy bars eaten. The range of the scores was 4 and variance was 1.79 while Standard Deviation was 1.34. The CBT group had a Mean and Median score of 1.5 and Modal scores of 1 and 2. The range of the scores was 3, with a variance of 1.17 and a Standard deviation of 1.08. For the whole sample, the Mean was 3.40 and mode was 5 while median was 3.50 while range was 8, variance was 5.2 and Standard deviation was 2.28. For both the groups; the Mean, Median and Mode are quite close and this may be interpreted to mean that these groups are somewhat normally distributed, though the CBT group is a bimodal group with two adjacent modes. For all three measures of central tendency, the Control group had higher scores as compared to the CBT group. The control group also had higher scores on all measures of dispersion, showing that there was more variability in the control group’s scores than the CBT groups. The measures of variability were highest for the whole sample showing that all participants together had more variance in their scores.
The same trend was noticed for depression scores with CBT group scoring lower than the control group. The control group had a mean score of 72.2, a median of 74.5 and a mode of 72. The range of scores was 32 with a variance of 87.57 and a Standard deviation of 9.36. The mean score for the CBT group was 40.8, the median was 40 and the mode was 35. Although the control group had similar mean, mode and median showing a relatively normal distribution, the CBT group was more skewed towards the higher side. The range of scores for the CBT group was 26 with a variance of 59.96 and a standard deviation of 7.74. The CBT group again had less variability as compared to the control group. the mean for the whole sample was 56.75, median was 53.5 and mode was 35, showing that the sample data is indeed skewed(Patten, 2005).The higher mean and lower mode show that although many participants got lower than the median score on depression; there are some participants with very high scores. The range for the scores was 57, which was just short of the range for both groups put together. This shows that there was very little overlap in the dispersion of scores for the control group and the CBT group. The variance was 337.67 and standard deviation was 18.38. These measures are high since they consist of the scores taken from two groups that have provided very different scores, and so variability for the full sample is much higher than for either of the two groups.
This data provides us with a detailed picture about the differences in the scores of participants in the two groups, and about the distinctions in the manner in which the scores for these groups differ for the two variables. But this data only describes the sample and not the population. It is not possible to estimate what are the trends in the population based on these statistics (Frankfort-Nachmias & Nachmias, 2008).
References
Frankfort-Nachmias, C & Nachmias, D. (2008). Research methods in the social sciences (7th ed.). New York: Worth Publishers.
Patten, M. (2005). Understanding research methods: An overview of the essentials (5th ed.). Glendale: Pyrczak Publishing. Read More
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