Describe How Distributions Relate to Statistical Research (Essay Sample)

Statistics project
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Abstract
Experiments are key towards invention in modern society. Research in medical field has led to alleviation of human suffering through discovery of drugs. Data analysis and presentation depends on distribution and it gives useful information and suggests conclusion that can be used in decision-making. In this paper different aspects of statics has been covered including discrete and continuous random` data distribution with their probabilities. It is therefore important to have concrete knowledge on statistics to enable one set up experiments and chose best analysis methods that can lead to best results and better conclusion.
Introduction
Data distribution refers to arrangement of values of a variable showing their observed or theoretical frequency of occurrence. Graphical methods are often used for organization and presentation of data to display useful information. Discrete data are variables with can be quantified and it takes certain values from a finite set. The variables are obtained by counting; an example is the number of men who were sampled for measurement of weight and fat in our case. The value for discrete variable is given as a whole number and not fractions. Continuous data are variables whose values can be obtained by measuring and can take any value between two specified values; examples are the weights and body fat content for 252 men sampled. Discrete and continuous data are regarded as random variables if the values were obtained from a random experiment/phenomenon (Bohrnstedt and Knoke, 1994).
Types of distributions
The discrete probability distribution includes binomial, hypergeometrical, multibinomial and poisson probability distribution. Continuous probability distribution comprises normal, student’s t distribution, Chi-square and F-distribution. Binomial distribution is used to summarize the independent number of observations in the group that represent one of two outcomes. Binomial distribution measure the probabilities of successes over a given number of trials. In binomial distribution number of observation are fixed and each observation must be independent. Each observation represents one of two outcomes with equal outcome having equal probability. Poisson distribution is used to present outcomes that can be classified as successes or failure. The number of successes that occur in specified region is known and the probability that a success will occur is proportional to the size of the region. The probability that a success will occur in extremely small region is virtually zero.
Multinomial probability distribution is a multinomial experiment characterized by, repeated trials, each trial have discrete number of possible outcomes and the probability of any outcome is constant. The trials are independent; an outcome of one trial does not affect outcome of other trials. Hypergeometric distribution measures the probability of a specified number of successes in n trials without replacement. In hypergeometric experiments, a sample size n is selected randomly without replacement from a population of N items. In population, k items can be classified as successes and N-k items can be classified as failures.
Normal distribution applies when all outcomes have equal chance of occurring. Normal probability distribution is defined by probability density function whose graph depends on mean and standard deviation. The mean determines the center of graph whereas standard deviation determines the height and width of graph. Small standard deviation results in tall and narrow graph whereas bigger standard deviation makes graph shorter and wider. Normal curve area is equal to one and the probability that normal random variable equals to any particular value is zero. F-distribution arises from a test between two observed samples if they have variance. T- distribution is used to estimate population parameters when sample size is small and the population variance is unknown. The chi-square distribution curve has an area of 1.The area under the curve between o and a particular chi-square value is the cumulate probability associated with that chi-square value (Wardlaw, 2000).
Influence of discrete and continuous probabilities on data analysis.
Random discrete variable gives discrete probability distribution. It can be presented in table whereby each value of a random variable is related with its probability of occurrence. Since the discrete random variable has countable number of possible values, probability mass function of and individual variable can be obtained. For example, the probability that given named person will be picked for measuring weight is 0.0039 (1/252). Each individual has equal chance of being chosen, has mass probability mass function that describes the probability of random variable to be below certain point. The probability mass function of all variables adds to 1(in our case we add probalities o...