Statnote 2: describing the normal

If a sample of measurements comes from a population that is normally distributed, we can use several statistics to describe our sample, such as the mean, SD, and CV. In addition, we can determine how atypical an individual measurement has to be before we would consider it not to be a member of a specific population. Furthermore, we can use our sample to make inferences about the population from which the sample is drawn including making estimates of the population mean and fitting confidence intervals to a sample mean.

The use of data analysis methods: basic concepts for optometrists

This article explains first, the reasons why a knowledge of statistics is necessary and describes the role that statistics plays in an experimental investigation. Second, the normal distribution is introduced which describes the natural variability shown by many measurements in optometry and vision sciences. Third, the application of the normal distribution to some common statistical problems including how to determine whether an individual observation is a typical member of a population and how to determine the confidence interval for a sample mean is described.

Development and validaton of an indicator to compare antibiotic usage in secondary care in England

The use of antibiotics was investigated in twelve acute hospitals in England. Data was collected electronically and by questionnaire for the financial years 2001/2, 2002/3 and 2003/4. Hospitals were selected on the basis of their Medicines Management Self-Assessment Scores (MMAS) and included a cohort of three hospitals with integrated electronic prescribing systems. The total sample size was 6.65% of English NHS activity for 2001/2 based on Finished Consultant Episode (FCE) numbers. Data collected included all antibiotics dispensed (ATC category J01), hospital activity FCE's and beddays, Medicines Management Self-assessment scores, Antibiotic Medicines Management scores (AMS), Primary Care Trust (PCT) of origin of referral populations, PCT antibiotic prescribing rates, Index of Multiple Deprivation for each PCT. The DDD/FCE (Defined Daily Dose/FCE) was found to correlate with the DDD 100beddays (r = 0.74 pmean 4.16 DDD/FCE in 2001/2 to 4.35 DDD/FCE in 2003/4. Antibiotic use in the electronic prescribing cohort was found to be lower, than the sample mean at 3.48 DDD/FCE in 2001/2 and 3.34 DDD/FCE in 2003/4. The MMAS and AMS were found to correlate (r = 0.74 pmean IMD 2000 for each hospital's referral population and the hospital antibiotic prescribing rate.

Vertical and horizontal scope economies in the regulated US electricity power industry

This paper investigates vertical economies between generation and distribution of electric power, and horizontal economies between different types of power generation in the U.S. electric utility industry. Our quadratic cost function model includes three generation output measures (hydro, nuclear and fossil fuels), which allows us to analyze the effect that generation mix has on vertical economies. Our results provide (sample mean) estimates of vertical economies of 8.1% and horizontal economies of 5.4%. An extensive sensitivity analysis is used to show how the scope measures vary across alternative model specifications and firm types. © 2012 Blackwell Publishing Ltd and the Editorial Board of The Journal of Industrial Economics.

Mean reversion in the short horizon returns of UK portfolios

This paper will show that short horizon stock returns for UK portfolios are more predictable than suggested by sample autocorrelation co-efficients. Four capitalisation based portfolios are constructed for the period 1976–1991. It is shown that the first order autocorrelation coefficient of monthly returns can explain no more than 10% of the variation in monthly portfolio returns. Monthly autocorrelation coefficients assume that each weekly return of the previous month contains the same amount of information. However, this will not be the case if short horizon returns contain predictable components which dissipate rapidly. In this case, the return of the most recent week would say a lot more about the future monthly portfolio return than other weeks. This suggests that when predicting future monthly portfolio returns more weight should be given to the most recent weeks of the previous month, because, the most recent weekly returns provide the most information about the subsequent months' performance. We construct a model which exploits the mean reverting characteristics of monthly portfolio returns. Using this model we forecast future monthly portfolio returns. When compared to forecasts that utilise the autocorrelation statistic the model which exploits the mean reverting characteristics of monthlyportfolio returns can forecast future returns better than the autocorrelation statistic, both in and out of sample.