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# Statistics

## by Lorena Rodríguez on Jan 13, 2010

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## StatisticsPresentation Transcript

• STATISTICS Lorena Rafael Rodríguez
• Types of Statistics
• Descriptive: to describe the basic features of the data in a study.
• Inferential: to draw inferences about a population from a sample.
• Regression: includes any techniques for modeling and analyzing several variables.
• Descriptive
• With descriptive statistics you are simply describing what is or what the data shows.
• They provide simple summaries about the sample and the measures.
• Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
• Major characteristics
• Mean
• Median
• -If it is an odd number: the middle number.
• -If it is an even number:the mean of the two middle numbers.
• Mode: the most frequent value in a set
• The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range.
• Distribution is a summary of the frequency of individual values or ranges of values for a variable.
• One of the most common ways to describe a single variable is with a frequency distribution. The same frequency distribution can be depicted in a graph. This type of graph is often referred to as a histogram or bar chart.
• Inferential
• There are two main methods used in inferential statistics: estimation and hypothesis testing.
• Estimantion testing
• In estimation, the sample is used to estimate a parameter and a confidence interval about the estimate is constructed.
• Parameter is a numerical quantity measuring some aspect of a population of scores. For example, the mean is a measure of central tendency.
• Confidence interval: we can determine how confident we are that the population mean lies within a certain interval of a sample mean.
• Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter.
• Hypothesis testing
• In the most common use of hypothesis testing, a &quot;straw man“null is put forward and it is determined whether the data are strong enough to reject it.
• An experimenter starts with a hypothesis about a population parameter called the null hypothesis. Data are then collected and the viability of the null hypothesis is determined in light of the data.
• Formula
• The null hypothesis is that µ1 - µ2 = 0
• Thus, the null hypothesis concerns the parameter µ1 - µ2 and the null hypothesis is that the parameter equals zero
• The results
• If the data are very different from what would be expected under the assumption that the null hypothesis is true, then the null hypothesis is rejected.
• If the data are not greatly at variance with what would be expected under the assumption that the null hypothesis is true, then the null hypothesis is not rejected.
• Regression
• Regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
• Variables
• The independent variable ( X ) is typically the variable being manipulated or changed and the dependent variable ( Y ) is the observed result of the independent variable being manipulated.
• unknown parameters denoted as β
• A regression model relates Y to a function of X and β .