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Statistical Techniques I EXST7005 Review

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Objectives n Develop an understanding and appreciation of Statistical Inference - particularly Hypothesis testing concepts. n Understand the role of Statistics in decision making processes n Develop procedures of basic statistical tests of Hypothesis and Estimations- develop an understanding of Statistical Methods. n Develop a framework of Statistical Notation and Terminology.

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Topics covered n What is the Scientific Method? n STATISTICS - the science and art of the development of the most effective methods of collecting, tabulating and interpreting quantitative data in such a manner that the fallibility of the conclusions and estimates may be assessed by means of inductive reasoning based on the mathematics of probability.

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n Frequency tables and relative cumulative frequencies. Our Z tables are cumulative frequencies in the tail of the Z distribution. n Central Tendency è Mostly we use means, but medians & modes have their applications. è We discussed Geometric and Harmonic means in addition to the common Arithmetic mean. Topics covered (continued)

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n MEASURES OF DISPERSION è Range, Interquartile range, variance and the standard deviation. We will most commonly use the variance and it's square root, the standard deviation. è Start with a corrected sum of squares and divide by N (population) or n-1 (sample). è n-1 is called the degrees of freedom è Coefficient of variation - used to compare variability for different variables.

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Topics covered (continued) n We also discussed Expected values and Bias under Measures of Dispersion.

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Topics covered (continued) Under transformations we mentioned the linear model, Yi = + i n We discussed the transformations of adding or subtracting a constant, multiplying or dividing by a constant. n We also discussed the logarithmic and inverse transformations that produce the geometric and harmonic means.

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Topics covered (continued) n The Gran Finale of transformations was the Z transformation! By now you know why.

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Topics covered (continued) n Probability distributions. n We discussed and worked with some simple probability distributions such as the binomial distribtuion and uniform distribution (both continuous and discrete). We then did a simple discussion of the Normal distribution. Remember, 67% between the limits ±1 , 95% between ±1.96 , etc.

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Topics covered (continued) n Then 74 grueling slides on the Z transformation! The highlights. è Reveiw the Z transformation. è Learn the Z tables (one sided, symmetric, area in the tails of the distribution). è Reading the Z tables (first digits on the left, second decimal at the top, probabilities in the body of the table).

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Topics covered (continued) n More Z tables, è The probability of a greater Z! When Z0 is positive or negative. Probability of a smaller Z for the same cases. è The probability of a greater or lesser absolute value of Z. è Then, just when it's making sense, work the tables backwards. Given a P, find the value of Z0.

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Topics covered (continued) n Then, find the probability of a greater of lesser Y value, requiring transformation before looking up values in the Z table. n Then transforming back to Y from Z.

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Topics covered (continued) n The distribution of SAMPLE MEANS! n Discuss the "derived population" of sample means. It's still a population (actually bigger than the parent population, Nn) è But it is associated with a particular sample size (n), And it's variance is different, 2 Y è And it's more nearly normally distributed than the original distribution (Central Limit Theorem).

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Topics covered (continued) n The concepts of reliability and accuracy were introduced. And an important new term, the "standard error", which was that standard deviation for the means ( Y).

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Topics covered (continued) n Hypothesis testing, at last. n Seven steps: è 1) H0, 2) H1, 3) Assume, 4) a=, 5) Draw a sample, 6) Calculate and compare the test statistic to the critical limits, 7) Conclusions. è Each with it's own concepts and terminology!! Null, alternative, assumptions, critical regions, "acceptance" (but not really accepting) & rejection, alpha & beta, confidence levels, etc. è Jargon (fail to reject, consistent with H0, etc.)

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Topics covered (continued) n Directional and non-directional alternatives n "Statistically significant" n And much, much more! 0 Region of "Acceptance" Upper Critical Region Lower Critical Region Z values

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Review n And then POWER. Or errors of two types (but only one at a time). n How does each error occur. How do you influence each error. n Everyone wants POWER, how do you get more of it?

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