Data Analysis for Health Care Decisions

Question :

Perform descriptive statistics and create a histogram for selected variables in a dataset.

The dataset contains the following variables:

Utilization(average number of patient days per month)

Satisfaction (patient satisfaction scores percentile rank).

Readmissions (readmission rate per month).

Nursing home administration has the objectives of higher utilization, higher patient satisfaction, and lower readmissions, and they need to make a decision on whether to retain the department manager based on average performance over the past 70 months.

Answer :

Mean is the average of the data and used to describe the sample with a single value that represents the center of the data. The mean used as a standard measure of the center of the distribution of the data.

Median is the Middle value of the data and used to measure the center value when there are many outliers. It is the value that splits the dataset in half.  

Mode is the value that occurs most frequently in a set of observations. 

Range is the difference between the largest and smallest data values in a sample. It is used to understand the amount of dispersion roughly in the data. A large range value indicates greater dispersion in the data and vice-versa.

Standard deviation is used to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data.

Variance means how widely the observations vary. 

Standard Error or standard error of the mean is used to determine how precisely the sample mean estimates the population mean. A smaller value of the standard error indicates a more precise estimate of the population mean and vice versa.

Skewness measures the measures the degree of asymmetry among the observations. 

o Normal Skewness (symmetrical): measure is 0; distribution is symmetric around its mean 

o Positive Skewness: measure is positive; long right tail, more higher values

o Negative Skewness: measure is negative; long left tail, more lower values

Kurtosis measures the peakness or flatness of the distribution of the observations.

o Mesokurtic: a normal distribution with a kurtosis of 0 the observations follow the normal distribution perfectly

o Leptokurtic: positive kurtosis (peaked-curve), a distribution that has a positive kurtosis value indicates that the distribution has heavier tails and a sharper peak than the normal distribution.

o Platykurtic: negative kurtosis (flatted-curve), a distribution with a negative kurtosis value indicates that the distribution has lighter tails and a flatter peak than the normal distribution.

Mean: On an average the department manager was there in approximately 70 patient days per month.

Median: The Middle most value the director manager’s average number of patient days per month is approximately 68 units.

So the Central value of the average number of patient days per month is around 68-70 units if both mean and median is considered.

Minimum & Maximum the average number of patient days per month for the director manager was approximately 21 & 117.

Sample Variance The director manager’s average number of patient days per month varies 468.2515 square units.

Standard Deviation: The director manager’s average number of patient days per month has a spread of 21.63912 from its mean 70.

Range The difference between the director manager’s highest and lowest average number of patient days per month is around 96.04878

So, we can consider any of the above measures as the spread of the director manager’s average number of patient days per month.

Skewness: The coefficient of Skewness is 0.239966. i.e. the distribution of the director manager’s average number of patient days per month is positively skewed or right skewed and have higher values towards it’s right side.  

Kurtosis: The coefficient of Kurtosis is -0.36956 i.e. the distribution of the director manager’s average number of patient days per month is Platykurtic or the distribution has the distribution has lighter tails and a flatter peak than the normal distribution.

From the above Histogram and the based on the interpretations of the descriptive statistics we can say that the distribution of the director manager’s average number of patient days per month does not resembles the Normal Distribution fully as it is unsymmetrical (slightly positively skewed). 

The Highest number of occurrences of the average Number of the director manager’s patient days per month is in the class of (57.4162857034269 - 69.4223830272379). [See the frequency table in the excel for reference]

Mean: On an average the Patient satisfaction score for the department manager was approximately 49.35714 percentile rank.

Median: The Middle most value the director manager’s Patient satisfaction score percale rank is approximately 51.5 units.

Mode the highest number of occurrences of the patient satisfaction scores for the director manager is 96 percentile rank. 

The Maximum & Minimum Patient satisfaction score received by the director manager is 100 & 3 respectively.

Sample Variance The director manager’s patient satisfaction scores varies 955.5663 square units.

Standard Deviation: The director manager’s patient satisfaction scores have a spread of 30.91223 from its mean 49.35714.

Range The difference between highest and lowest patient satisfaction scores received by the director manager is around 97.

So, we can consider any of the above measures as the spread of the director manager’s average number of patient days per month.

Skewness: The coefficient of Skewness is 0.119794 i.e. the distribution of the director manager’s Patient Satisfaction score is positively skewed or right skewed and have higher values towards its right side.  

Decision for the Management:

Nursing home administration was to decide whether to retain the department manager based on the past data of 70 months. Their objective includes: 

Higher utilization i.e. positively Skewed distribution or more higher values towards the right of the data and low spread of the data. The mode of the data has to be closer to the Maximum value. 

Based on the above interpretations: The distribution is positively skewed but the spread is high. So, wiser to not retain him/her as he is not that consistent.

Higher patient satisfaction i.e. positively Skewed distribution or more higher values of the data and low spread of the data. The mode of the data has to be closer to the Maximum value.

Based on the above interpretations: The distribution is positively skewed the spread is also high. Moreover he got a lowest rating of 3 which is not good for any organization (1 bad rating can ruin 100s of good ratings). Better to not retain him/her.

Lower readmissions i.e. negatively Skewed distribution or more lower values of the data and low spread of the data. The mode of the data has to be closer to the Minimum value.

Based on the above interpretations: It is negatively skewed and the spread is low and the mode is nearer to the minimum value. So Based on it we can retain him.