Microbiological Procedures MICR 3053
Weber State University
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This 2 page Class Notes was uploaded by Alexandra Senger on Wednesday October 28, 2015. The Class Notes belongs to MICR 3053 at Weber State University taught by William Lorowitz in Fall. Since its upload, it has received 12 views. For similar materials see /class/230780/micr-3053-weber-state-university in Microbiology at Weber State University.
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Date Created: 10/28/15
Statistics Background Statistics is a mathematical eld that allows us to summarize and analyze data The two major subdivisions are descriptive statistics and inferential statistics In descriptive statistics the main goal is data reduction That is large amounts of data are summarized typically with graphs or tables and by calculating measures of central tendency and variability Although these summaries are convenient for simplifying data and making patterns more obvious it should be recognized that much of the detail is lost during summarizing Descriptive statistics are employed when the whole population can be sampled When the whole population cannot be sampled the typical situation a sample or several is withdrawn om the population and inferences about the population are made om the characteristics of the sample Thus it is assumed that a sample is a good representative of the population However this is not always the case and statistics also allows us to decrease our uncertainty about drawing conclusions om incomplete data Measures of Central Tendency A distribution is created when data variables are arranged in order om highest to lowest typically represented graphically as a frequency distribution plotting the value of the variable versus the equency of that value s occurrence It was shown quite a long time ago that if the number of data points is very large the distribution usually becomes a normal or Gaussian distribution the bell shaped curve Researchers can learn a lot om these plots including the shape of the distribution the range of values and the most common value Measures of central tendency that is the values that the distribution seems to cluster around are some of the most commonly calculated statistics The mean is one of the most used statistics in all manners of research It is the arithmetic average of values calculated as the sum of all values divided by the number of values Although the mean provides a simple summary of a distribution it doesn t indicate anything about the range of values The distribution may have a very tight distribution around the mean or may be so spread out that a peak is hard to identify Another shortcoming of the mean is that it is sensitive to extreme values A single outlying data point can skew the distribution so that the mean no longer represents the peak of the curve Because of this other descriptors of the central tendency may actually be more use il The mode is the mo st equently occurring value It s where the distribution displays a peak or peaks in the case of a multimodal distribution It is the only descriptor of central tendency possible with nominal data Nominal data classi es items into mutually exclusive groups and can only be classi ed as equal or not equal for example male or female The median is the midpoint of the distribution with half of the values on either side of it Another way to say this is that the median represents the 50Lb percentile The median can tell us about the shape of the distribution In a normal distribution the mean and median and mode are the same If the distribution is skewed the mean is closer to the mode than is the median The median is usually the best measure of central tendency in a skewed distribution for example the salaries in the NBA where a few people earn much much more than the others The Central Limit Theorem The Central Limit Theorem states that the means of independently drawn random samples will be approximately normally distributed if the sample size is large enough In other words even if a distribution is not normal the distribution of the means will be Means calculated om observation sets containing thirty sample values is considered large enough to produce a normal distribution of means om nonnormally distributed data but 10 sample values per observation set may be enough in many cases The mean of a sampling distribution of the means is considered the same as the population mean and is often called the expected value When we calculate a mean om random samples drawn om a population we expect that mean to be the same as the population mean The dispersion standard deviation of the sampling distribution of the means is called the standard error because it is drawn om a sampling distribution rather than a data distribution It represents how con dent we should be that a sample mean represents the population mean The standard error is equivalent to the population standard deviation divided by the square root of the number of samples in each observation set The standard error is smaller than the population standard deviation so distribution of the means has less dispersion than the distribution of the population Thus a sampling distribution of the means can provide more accurate inferences about a population than a distribution om a large pool of data In practice sampling distributions of the mean are usually not constructed but knowledge of the Central Limit Theorem increases our con dence when making an inference based on a single sampling We know that if we take several sets of samples om a population they would have a normal distribution So a mean om a single set of samples taken om a population represents one mean in a normal distribution Based on the Central Limit Theorem it is possible to calculate the probability that a sample or predicted outcome is signi cantly different om the population mean but that s a discussion for another time Hypothesis Testing We know that a hypothesis is a testable prediction that is consistent with speci c observations With testing it is possible to show that a hypothesis is false but not true At best we re ise to reject a hypothesis based on current data but recognize that as yet unexamined conditions may show the hypothesis to be false sometime in the lture In statistical hypothesis testing it is common to reduce the question at hand to two outcomes eg A and B are the same A and B are not the same We can state these outcomes as the null hypothesis H or the hypothesis of no difference and the alternative hypothesis H Two of the most common statistical tests used for determining if a signi cant difference exists between two or more samples is the t test and AN OVA analysis of variance The ttest is a power il and robust test for determining if two populations have different means when samples are independent and random and the measured variable is continuous and normally distributed AN OVA is more appropriate and less error prone than running multiple t tests when there are more than two samples to compare In ANOVA there are two types of variance to consider error variance withingroups variance and treatment variance betweengroups variance When samples are independent and random the withingroups variance should be the same Therefore any difference between the variances of the measurements would be due to the treatment ANOVA can indicate a difference between the treatments but additional tests are necessary to nd which treatments are signi cantly different A level of signi cance must be selected for statistical hypothesis testing designated as an alpha level An alpha value of 005 is the level usually selected as it offers a good compromise to avoid Type I rejecting a null hypothesis that is true or Type II not rejecting a null hypothesis that is false errors
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