I have learned about the 4 areas of Statistical methods: Descriptive statistics, probability, statistical inferences and statistical techniques. I have learned about population, sample, random sample, survey, census, data, numerical and categorical data, data set. The data set is the collection of all the data taken from a sample. So a statistic is a number that summarizes the data collected from a sample. And statistics are based on sample data, non on population data. When data is collected from an entire population, we have a census. I also learned to distinguish between mean or average, median, mode, standard deviation which represents the typical distance from any point in the data set to the center. It’s roughly the average distance from the center. I also learned how to calculate the standard deviation, understand its properties (s can never be a negative number; the smallest possible value for the standard deviation is 0; it has the same units as the original data. I also learned about the connection of probability to statistics. There are two conceptual approaches in the study of probability, objective and subjective probability. I learned about P(A or B) and P(A and B). I also learned about conditional probability as expressed in the probability of A given B = P(A and B)/P(A). A probability tree is also defined.
Probability is about uncertainty and outcomes. Life itself can be interpreted as a sequence of unpredictable events. Probability can be used to help predict the likelihood of certain events occurring. By collecting data which can be summarized and interpreted with statistics, one may get a better idea of the salaries of the NBA and NFL athletes. Since every probability is a number or percentage between 0% and 100%, one can have an idea of weather report predicting an 80% chance of rain. If I get this report, I will most likely wear a raincoat to work or school. At least, I will have an umbrella. If I have all the salaries of NBA team San Antonio Spurs, I could calculate the mean, median and mode of all the athletes’ salaries. Another real-life example is that of stock brokers. They use probability in their decision-making every day. They wonder whether a given stock goes up or down, whether to buy or sell or inform their clients. Statistics are also present in the news reports and NFL games. In fact, most NFL coaches have dedicated staff who monitor the statistics of games. Then, broadcasters report them to us, fans and viewers. A new website is trying to start trading players. ProTrade.com starts as a fantasy player trading. The premises of the site are each player’s stats.
I learned about regression, correlation and the tests associated with them. b1 and bo are the coefficients or parameters of the equation. t-test is used to test the significance of each coefficient. f-test is used to test the significance of the equation as a whole. Y is the dependent variable where is X represents the independent variable. Formulas to calculate b1 and r are given. Regression analysis is the process of estimating a functional relationship, or of using statistical methods to obtain an equation between random variable y and non-random variable(s) X(s). And Correlation analysis involves measuring the direction and strength of the relationship between two random variables. This measurement takes a numerical form called the correlation coefficient. Correlation coefficient is between -1 and 1 (inclusive). This is very important in the reporting of data in a research.
I also worked on some problems to find the sum of cross deviations from the two means SSxy, b1 and bo (Ybar –b1 Xbar), write the estimated equation, calculate the standard error of the estimate b1 (Sb1), state the null hypothesis and the alternative hypothesis for b1, calculated t, state the rejection rule, find the point estimate of the variance S2 which is the mean square error (SSE), calculate F etc. I also learned about calculated t in regards to the rejection rule. If calculated t is larger than table t (alpha)/2, n-2, or calculated t is less than negative table t(alpha)/2, n-2, reject the Ho. Finally, I also learned about simple linear regression analysis, multiple regression and model building.
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