{'fraction_non_alphanumeric': 0.024573541691518548, 'fraction_numerical': 0.009960634617678635, 'mean_word_length': 4.6265100671140935, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On The Analysis of Blood Glucose Levels of Diabetic Patients

Paired observation tests (Paired t-test, Wilcoxon signed ranked test and Sign test) were employed to determine if there is any significant difference between fasting blood sugar and oral glucose tolerance tests of 47 diabetic patients. First, JarqueBera (JB) test was done to check for normality and it showed that not all the mean differences were normally distributed. Two sample t-test was used to check whether the level of change in blood glucose for fasting patients and patients who had glucose intake are the same. The fasting blood sugar test and oral glucose tolerance test were done hourly on two different occasions. The results revealed no difference between blood glucose testing on arrival and blood glucose testing after resting for one hour. The level of change in blood glucose after two hours for fasting patients was not the same with the level of change two hours after glucose administration. It was concluded that a single fasting blood glucose test is sufficient to diagnose diabetes on a visit to the laboratory while oral glucose tolerance test conducted hourly is necessary to monitor the blood to know when the glucose level is going high or low.


Introduction
Diabetes is a disease associated with high level of glucose (sugar) in the blood of the sufferer. It is very harmful to the body. Blood glucose testing involves measuring the levels of blood glucose after fasting and after glucose intake. Fasting blood sugar test is required to diagnose diabetes and Oral glucose tolerance test (OGTT), done after glucose intake, helps to monitor the glucose level in the blood of a patient. A hormone called insulin manages or regulates the glucose level in the body. When the body cannot produce enough insulin or when the insulin produced cannot work effectively owing to some other conditions, the blood sugar level rises causing diabetes. If it is too high or too low, medical attention will be needed.

Statistical tests such as Paired Observation tests
(including parametric and Non-parametric tests) are useful for ascertaining if there is any significant mean difference between the two measurements (before and after administration of glucose). Also, two sample t-test is useful for checking whether the level of change in fasting blood sugar after two hours is the same with the level of change after administration of glucose. In paired observation, we have Univariate case and Multivariate cases. In Univariate case, two samples obtained are correlated and must be dependent. The two samples are reduced to one by working the differences between the paired observations. Here, the assumptions are: X and Y have a bivariate normal distribution and, X and Y are correlated [1].
The approach used in controlling diabetes is the blood glucose testing. This test measures the concentration of glucose in the blood. Blood glucose testing consist of fasting blood glucose and glucose intake measurements. The fasting blood sugar is used to diagnose diabetes while glucose intake is conducted to measure the blood glucose level. Oral glucose tolerance test (OGTT) measures first and second stage insulin response to glucose. It compares the level of glucose in the blood before and after administering glucose. After testing the blood glucose level in the patient fasting, 75grams of glucose dissolved in water is given to the patient and another test conducted at one hour and two hours" interval. A glucometer (glucose meter) is used to measure blood glucose and the unit of measurement is mg/dl or mmol/l. Blood glucose level outside the normal range may be an indicator of a medical condition. If the blood sugar measured is greater than 140gm/dl two hours after, it means the person is prediabetic. If it is greater than 199mg/dl two hours after, it means the person has full blown diabetes. If the result is 139mg/dl, it is considered as normal. The purpose of testing blood glucose several times per day is to discover when the blood glucose level is going too low or too high. This will help the doctor to timely take steps to prevent the occurrence of low or high blood glucose levels. The test becomes a warning to those who fall into the category of prediabetic and full blown diabetes as it enables them to change their lifestyle and cut down the intake of foods that has the capacity to increase blood glucose level. It is also beneficial in the sense that it gives information on whether the body can tolerate glucose or not. [2]. The problem here is to ascertain whether the resting period of two hours is adequate or not and secondly, is the level of change after two hours for fasting glucose and the level of change two hours after glucose administration the same? The purpose of this study is to determine whether there is any significant difference between fasting blood sugar test and oral glucose tolerance test by performing a statistical analysis on blood glucose measurements obtained from the medical laboratory department of a University Teaching Hospital in Nigeria.
The specific objectives are to:

Review of works on glucose test
Glucose, the simplest form of sugar, is the body"s major source of energy while, glucose test measures the amount of glucose in the blood. A hormone called Insulin regulates blood glucose level in the body.
According to Martel (2012) [3], Diabetes occurs when the body does not produce enough insulin thereby causing the blood glucose to rise, or when the body cannot use the insulin produced effectively. If diabetes is left untreated, the high blood glucose level will cause damages in the organs. People with diabetes normally go for blood glucose test to determine whether their condition is being managed well or not. A high blood glucose level is an indication of poor management of the diabetes. Blood glucose testing provides information that helps the physician to make decisions on diet and medication dosage.
Saudek et al (2006) [4], states that since there is increasing rate of diabetes, there is need to learn how to successfully control blood glucose level as this, leads to significant reduction in mortality due to diabetes, where assessing glycaemia in diabetes is challenging.
According to Haller et al. (2004) [5], blood glucose testing helps in administration of medication e.g., deciding the dosage to take. It also tells when the blood glucose level is high or low. An important benefit of blood sugar testing is that diabetic patients are sensitized to read and interpret their results thus, enabling them to take proper actions to improve control of the disease. People on insulin therapy or other medications should test their blood glucose level regularly so as to know when their blood glucose level is going too low or too high. Fasting blood sugar test is used to diagnose diabetes while Oral glucose tolerance test is conducted to measure blood glucose level. People with diabetes always have their blood sugar level higher than those without diabetes. According to American Diabetes Association (2006) [6], the normal level of blood glucose in diagnosis ranges from 126mg/dl to 140mg/dl.

Review of works on Paired Observation Tests
Given two random samples from two populations, we call the data paired if the j th measurement of the first sample is paired with the k th measurement of the second sample. Paired data or observations can be analyzed using parametric and non-parametric methods. Conover (1999) [7], states that parametric test involves population distribution that has a particular form and also involves hypothesis about the population parameters, while non-parametric test does not make assumptions about the underlying distribution. Non-parametric tests use approximate solutions to a particular problem, while parametric tests use particular solutions to approximate problems. Hollander and Wolfe (1973) [8], posits that parametric test depends on distributional assumptions while nonparametric test do not require any strict distributional assumptions. They analyze ranks of a variable instead of using the original values.
Paired ttest is a parametric statistical method used to compare two population means that emanate from two samples that are correlated. According to Zaiontz (2013) [9], paired ttest is used to test for the differences in mean of two samples which are dependent on one another. In this case, the null hypothesis is such that the mean difference is equal to zero. Paired ttest involves comparing two means for information where every person who participated in one sample also participated in the other sample.
The difference scores are created for every individual, and we compare mean differences between the results with the mean difference for the population [10,11].
. . n, it is required that Z i are independent. For v i and u i , ranking can then be applied and differences taken.
Also, the distribution of Z i "s is symmetric. The hypothesis, H 0 can be stated as "the distribution of difference scores in the population is symmetric about zero" [9]. The Wilcoxon signed rank test is used to test if the median of a symmetric population is zero. Firstly, the data is ranked without regarding the sign. Secondly, we attach the signs of the main observation to their corresponding ranks [12]. The test can also be applied in the comparison of two dependent or correlated data in which the measurements are ordinal and for samples that are matched or measurements that are repeated on a single sample to check whether the rank in their population mean differ or not [13,14]. Sign test can also be used to check if a binomial distribution has equal chance of success and failure.
In this case, the differences of the paired values, using the signs of the individual differences, are taken. Then, the binomial distribution table is used for the test assuming probability, p = 0.5 when the sign is positive and q = 0.5 when the sign is negative [16]. Here, the null hypothesis is "the number of positive differences is approximately equal to the number of negative differences". Lucky and Bright (2012) [18] [20] also used the Wilcoxon Signed-Rank Test to study the aggressive reactions of turkeys housed in pens towards unfamiliar turkey brought into the pen.
They found that the median difference between the number of pecks per test in the small pen and in the large pen was significantly greater than zero.

Jarque -Bera (JB) test
The JB test is based on the classical measures of skewness and kurtosis. It is a "goodnessof -fit" test used to check whether the sample data has the skewness and kurtosis matching the normal distribution. The JB statistic has a chi squared distribution with two degrees of freedom   2 2  [21].
The JB statistic [22] is given as: where, 1  is the skewness, 2  is the kurtosis and n is the where, d is the difference in each observation, s is the standard deviation. Equation (3.1) was used to test whether the differences obtain are normally distributed or not.

Hypothesis:
H 0 : Data follows a standard normal distribution.

Paired Observations Tests
In this section, we describe parametric and nonparametric methods used in the study. The methods are Paired t test, Wilcoxon Signed Rank Test and Sign Test for paired samples.

Paired ttest:
The t-statistic is given as: (CI) for the mean difference include zero [17,23]. In other words, if t calculated is less than the t tabulated, we reject H 0 otherwise we accept the null hypothesis.

Assumptions of paired t-test
The test can only be performed with the matched pairs of sample. The differences of the paired sample must be normally distributed and the data must be continuous.

Wilcoxon Signed Ranked Test
Wilcoxon signed ranked test is useful in cases involving symmetric continuous distribution. In using it, we assume that the mean is equal to the median.
The null hypothesis is where R is the Wilcoxon signed rank If R calculated is less than or equal to tabulated R, we reject 0  at 0.05 level of significance [17].

Assumptions of Wilcoxon Signed Rank test
The difference between the two data values of a pair is continuous and symmetric. The two samples need to be dependent observations of the cases and the data are measured on an ordinal or interval scale.
x denotes the Sign test statistic [17].

Assumptions of Sign Test
The observation can be independent. It can be identically distributed and the measurement scale is at least ordinal.
Our interest was to determine whether the binomial distribution has equal chance of success and failure hence, we compared the outcome between fasting blood glucose test () i  and oral glucose tolerance test ( i  ); using  at 99%, 95% and 90% confidence level respectively.

Two sample t-test
Two sample t-test is a statistical method used to evaluate whether the means of two independent populations differ or not, the observation from one sample are not related to the observation from the other sample. The two sample t-test uses the sample standard deviations to estimate the variance, σ 2 for each population [24][25][26]. Reject the null hypothesis if the p-value is less than 0.05.
We compare the level of change in    l is the fourth difference (d 4 )

Assumptions of two sample t-test
The data are continuous, they follow normal distribution and variances of the two populations are equal. The two samples are independent and both are simple random samples from their respective population.

Definition and measurement of variables
The fasting variables were taken on two different occasions after the initial value, X 1 at one-hour and two-hour interval each. The glucose intake variables were also taking on two occasions at one-hour interval each. Paired Observation tests were used to check whether it is possible to take the recording on three occasions. For the fasting variables we denote the variables with x 1 , x 2 , and x 3 .
where, X 1 = blood glucose test on arrival.
X 2 = blood glucose after resting for one hour.

Results
The aim of this work is to determine whether there is any significant difference between fasting blood sugar test and oral glucose tolerance test. given in the following subsections.

Jarque-Bera (JB) test Result
This test was used to test for normality of the data set differences stated in Section 3.1, for the fasting and glucose intake variables. The results are shown in Table 1.

Paired Observations Tests Results
Since the fasting variables are taking on two different occasions, we tested whether it is necessary to take the measurement at one-hour interval before administering glucose to the patient. Tables 2 to 4 summarizes the data set differences test results using the Paired t-test, Wilcoxon signed rank test and Sign test at 99%, 95% and 90% confidence intervals, respectively.

Discussion
These results suggest that it is not necessary to take the blood glucose measurements every one hour rather, it should be taken every two hours since there was no difference between blood glucose tested on arrival and one hour after resting, as shown by the results of paired ttest and Wilcoxon signed rank test at all three levels of significance (99%, 95% and 90%) respectively. This implies that conducting fasting blood glucose test three different times on a visit, is not necessary as it amounts to a waste of time, money and resources. Furthermore, d 2 to d 6 in Tables 2 to 4, have p-values (p = 0.00) less than 0.05 for all the three paired-observation tests, indicating that there is significant difference between the variables. The change in blood sugar level after glucose intake is significant. The blood sugar level increased progressively after administering glucose at one-hour and two-hour intervals. This shows that a measurement in one hour or two after administering glucose is sufficient to give the diagnosis. There was significant difference between the change in blood sugar level after two hours for fasting glucose test and after one hour of glucose administration for the Oral glucose tolerance test. As a result, it is necessary to measure glucose level at hourly intervals after administering glucose to help monitor when the blood glucose level is too high or too low.

Conclusion
Based on the above results, it was concluded that a single fasting blood glucose test is sufficient to diagnose diabetes on a visit to the laboratory while oral glucose tolerance test conducted hourly is necessary to monitor the blood to know when the glucose level is going high or low.

Appendix B
The differences data set for the fasting and glucose intake variables Minitab 18 result output of Skewness and Kurtosis (See JB"s computation in T-Test of mean difference = 0 (vs not = 0): T-Value = 3.87 P-Value = 0.000