Statistical Significance: Descriptive Statistics + Excel Data Sheet (Essay Sample)

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[Professor’s Name]
Assignment #1 - QUA1206
[Date of Submission]
Statistical Significance
Introduction
Statistical significance or statistical importance is used to refer to a population effect or relation that is not zero (SPSS Inc., 2010). For instance, in testing the null hypothesis that there is no relationship between two variables, the level of statistical significance is predefined. This refers to the level of risk at which the null hypothesis will be rejected. Usually, a 5% level of significance is chosen, which implies that there is a 5 in 100 chance that the relationship between the two variables does not exist.
In testing whether or not a significant relationship exists between two variables, the confidence intervals can be used. In using the confidence intervals, the number line technique is employed. This involves plotting the confidence intervals for the groups on the same graph and assessing whether the intervals overlap. Overlapping intervals are indicative that there are no significant differences between the groups. Thus, this paper makes use of the number line technique to explore group differences in anxiety scores between males and females.
Calculating the Confidence Intervals
In computing the confidence intervals, the population is assumed to be large, N = 1,000,000. The sample size, on the other hand, is n = 103, which is very small. In this case, since n/N is less than 0.05, the finite population correction factor does not apply (Black, 2009). Thus, as outlined in Levine (2011), the confidence intervals are computed using the following formula:


Descriptive Statistics
In order to effectively conduct the confidence interval analysis to compare mean differences in anxiety scores between males and females, it is necessary to describe the data in terms of the composition groups. The descriptive statistics for each of the groups is as presented in table 1.
Table 1
A summary of the descriptive statistics for anxiety scores between the males and females
GenderMeanStandard DeviationCountMedianModeMinimumMaximumFemale74.3816.425279.0482.2710.0097.58Male74.3018.095178.2484.690.0695.97 On average, females have a slightly higher anxiety score (M = 74.38, SD = 16.42) than males (M = 74.30, SD = 18.09). The huge standard deviation in anxiety scores for males indicates a higher variability in these scores than in the anxiety scores for females.
95% Confidence Intervals
In computing the 95% confidence interval, the statistical significance is 5% (α = .05). Thus, the critical Z statistic is obtained by looking up the probability (1 – 0.05/2) = .975 from the normal distribution tables. The critical Z statistic (Zα/2) is obtained as 1.96. Thus, the 95% confidence intervals around the mean for each gender are obtained as:




In order to determine whether or not the observed mean differences in anxiety scores between males and females is significant, a comparison is made between these confidence intervals. This is done by using a number line as shown in figure 1.
Figure 1. A number line showing the 95% confidence intervals for anxiety scores
As it can visually be observed, the number lines are overlapping. This implies that the observed mean difference in anxiety scores is not statistically significant at the 5% level of significance. Thus, it is tenable to say that the mean level of anxiety is the same between males and females.
90% Confidence Intervals
In this case, the level of statistical significance is set at 10%, that is, α = .1. Thus, the critical Z statistic is obtained by looking up the probability (1 - 0.01/2) = 0.95 from the normal distribution tables. This yields the critical Zα/2 = 1.64. The 90% confidence intervals around the mean for each gender are obtained as follows:
A number line is used to compare the confidence intervals and to determine whether the observed mean difference in anxiety scores between males and females is statistically significant. The number line for the 90% confidence...