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Confidence intervals (CI) can be described in terms of confidence levels as a range of values defined by the confidence level within which the population parameter is estimated to fall, which in other words could be referred to as a margin of error. While Confidence level is the likelihood, expressed as a percentage or a probability, that a specified interval will contain the population parameter (Frankfort-Nachmias and Leon-Guerrero, 2018). In this week’s discussion on confidence intervals analysis, a continuous variable named “prestg10” with label “Rs occupational prestige score (2010)” was selected.
- For 100 random sle at 95% confidence interval (Valid cases here is 3)
- For 100 random sle at 90% confidence interval (Valid number here is 3)
- For 400 random sle at 95% confidence interval (Valid number here is 12)
- For 400 random sle at 90% confidence interval (Valid number here is 12)
In each of 95% confidence interval, the lower and upper bound of the confidence interval for mean shows more confident that the true value in the Rs occupational prestige score (2010) is represented in the interval while the 90% confidence interval represented less. However, 95% is less specific measure than a 90% confidence interval as it captures a broader range of values. It seems more acceptable to use a 90% confidence interval in other to extend the result to the general score.
Effects of levels of confidence and sle size
The effect of the different levels of confidence concerning sle size is that when the sle size increase, the width of confidence intervals decreases because it decreases the standard error (Frankfort-Nachmias, and Leon-Guerrero, 2018, Wagner, 2016, Attia, 2005). The 100 and 400 random sles give 8.888 and 4.485 standard error, respectively; in other words, the standard error gets lower as the sle size increases. (See the graphics).
Confidence intervals are underutilized
Confidence intervals are considered underutilized when researchers fail to include CI whenever a sle statistic such as a mean or difference in means is presented as an estimate of the corresponding parameter (Sim, and Reid, 1999). Also, for not making CI part of the results of hypothesis tests, to showcase the level of confidence that the CI matched to the level of statistical significance for the hypothesis test (Sim, and Reid, 1999).
Implications of using or not using CI
The information provided by CIs could be used to assess the importance of study findings (Sim and Reid, 1999). For exle, market research is good at providing information to reduce risk. So, CI would help the researcher with the provision of knowledge and understanding, which would allow the readers to value the alternatives and make better decisions effectively. However, when CI is not in use, researchers can only report a number, and he/she might not be specific enough then to provide a range of data in which he/she is over-representing the precision of the results (Attia, 2005). So, interpretation of confidence level based on the analysis shows that the test looks significant because the range of data used does not include 0 or minus value. Otherwise, the test will not be not significant, I mean, if 0 is included within the range of the lower and upper bound (Frankfort-Nachmias and Leon-Guerrero, 2018).
Attia, A. (2005). Why should researchers report the confidence interval in modern research? Middle East Fertility Society Journal, Vol. 10, Issue 1, Pp. 78-81
Frankfort-Nachmias, C., #038; Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.
Sim, J. #038; Reid, N. (1999). Statistical Inference by Confidence Intervals: Issues of Interpretation and Utilization. Physical Therapy, Vol. 79, Issue 2, Pp. 186â€“195.
Wagner, W. E. (2016). Using IBMÂ® SPSSÂ® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
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