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May 19 - May 29, 2023
Mathematical statistics encompasses a scientific discipline that analyses variation,
Determinism implies that there is order and perfection in the universe …
saltational
eponymous
Malthus believed that populations would increase exponentially (2, 4, 8, 16, 32, etc.), whereas food supplies would increase mathematically (2, 4, 6, 8, 10, etc.).
sobriquet
In 1854, Nightingale’s lifelong friend, the Secretary at War Sidney Herbert (1810–61), approached her with an offer.
She was to care for the British troops fighting in the Crimean War, and was to take a group of 38 nurses with her.
Prior to this time, women had never been allowed to serve officially.
Once Nightingale arrived in the Crimea, she found herself amid utter chaos in the hospital at Scutari: there was no furniture, food, cooking utensils, blankets or beds; rats and fleas were constant problems. Though she was able to get basins of milkless tea from the hospital, the same basin was used by the soldiers for washing, eating and drinking. She was the only person with funds and the authority to rectify this bleak situation. She requested eating utensils, shirts, sheets, blankets, stuffed bags for mattresses, operating tables, screens and clean linen. She soon set up a laundry and a
...more
There was a complete lack of coordination among hospitals, and no standardized or consistent reporting. Each hospital used its own classification of disease, tabulated on different forms, making comparisons impossible. Even the number of deaths was not accurate: hundreds of men had been buried, but their deaths were not recorded.
astragalus
inveterate
Abraham de Moivre (1667–1754) wrote the Doctrine of Chance: or A Method of Calculating the Probabilities of Events in Play in 1718,
de Moivre’s book was also used as a gambler’s manual.
in 1685, due to Louis IV’s revocation of the Edict of Nantes. This ended toleration of Protestants in Catholic France, causing hundreds of thousands of them to flee.
the long-term regularity in random events, and is the ratio of the number of favourable occurrences of events to…
the probability of an event happening is the proportion of times that events of the same kind will appear in the long run.
how do we know how many times to flip a coin (or roll a die) in order for it to be an adequate test?
The way around this situation is the Relative Frequency Ratio, which is the ratio of the number of times that an event occurs in a series of experimental trials divided by the number of actual trials in the experiment performed.
Bayes’ theorem is a formula that shows how existing beliefs, formally expressed as probability distributions, are modified by new information.
Bayes’ theorem can be used in diagnostic testing by general practitioners or clinicians. These doctors often start out with a prior belief about whether a patient has a particular illness or disease (based on the knowledge about the patient’s symptoms or the prevalence of the disease in the community) and this knowledge will be modified or updated by the results of clinical tests.
The Binomial distribution is a discrete probability distribution and represents the probability of two outcomes, which may or may not occur. It describes the possible number of times that a particular event will occur in a sequence of observations. For example, it will give the probability of obtaining five tails when tossing ten coins.
The binomial distribution models experiments in which a repeated binary outcome is counted. Each binary outcome is called a “Bernoulli trial”. The binomial distribution (p + q)n is determined by the number of observations n, and the probability of occurrence, denoted by p + q (the two possible outcomes). This provides a model for various probabilities of outcomes that can occur. To determine the probability of each outcome, the binomial distribution has to be expanded by the number of observations – by raising p + q to the nth power.
probability distributions correspond to different types of variables. Discrete probability distributions, such as the binomial, use discrete data (such as “heads” or “tails” in a flip of a coin) while continuous distributions, such as the normal, use continuous data (height and weight).
To test an unbiased coin, the binomial distribution has to be expanded to accommodate the number of times the coin is flipped.
Expand the binomial distribution (p + q)n by raising p + q to the nth power
•p and q must add up to 1 (flipping a coin has 2 outcomes: p = ½ and q = ½) •n = the number of trials or flips (2 in this example) •...
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Suppose a coin is flipped 10 times and the result is 10 heads. The binomial distribution would account for the 10 different flips using the rules above. The chances of this would be ½10 (½ raised to the 10th power, which is 1/1024).
The Poisson distribution, discovered by Siméon-Denis Poisson (1781–1840), is a discrete probability distribution used to describe the occurrence of unlikely events in a large number of independent repeated trials. The Poisson is a good approximation to the binomial distribution when the probability is small and the number of trials is large.
The Normal distribution is a continuous distribution, and is related to the binomial.
It is also known as the normal curve, sometimes (inaccurately) referred to as the Gaussian distribution, and has long been used as a yardstick to compare other types of statistical distributions. It plays a vital role in modern statistics because it enables statisticians to interpret their data by using various statistical methods, which are quite often modelled on the normal distribution.
the “law of errors” (i.e. the normal curve)
The Central Limit Theorem The French mathematician and astronomer Pierre-Simon Laplace (1749–1827) was responsible for advancing probability as a tool for the reduction and measurement of uncertainty in data.
the sampling distribution of means gets closer and closer to the normal curve as the sample size increases, despite any departure from normality in the population distribution.
Norma is Latin for a T-square, first used by masons and carpenters in antiquity to make their work rectangular. From their use of the T-square, a right angle became known as a “normal angle”,
The word “normal” gained currency in the 19th century, firstly in the medical sphere. It was seen as the opposite of pathological,
for statisticians there are three kinds of averages: the arithmetical mean, the median and the mode.
Francis Galton wanted to find a faster way to establish an average, rather than going through the trouble of calculating the mean value. He introduced the word percentile, which is the point that divides a distribution into a lower percentage of cases and an upper percentage. Though Gauss first used the median in 1816, Galton introduced it into statistics.
the mode, quoted by Karl Pearson in 1894, is the value that occurs more frequently than any other.
The mode is a point of maximum frequency; it is used most often to look for typical cases.
to treat variation as a basic reality and to be wary of averages, which were, after all, abstract measures applicable to no single person and often largely irrelevant to individual cases.
perspicacity,
Stephen Jay Gould died in 2002, fully two decades after the initial diagnosis.
decennial
Stratified The investigator selects a specific characteristic in the sample that he or she thinks is important for the research and then divides the sample into non-overlapping groups or strata, such as age-groups, gender, geographical areas or political affiliation. This can be used with the other four sampling procedures.
fulcrum.
skewness
coefficient
