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Descriptive Statistics

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Statistics by Yesenia Frías Álvarez

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Descriptive Statistics

1. 1. Descriptive statistics It is used to analyze and represent the data that have been previously collected. It includes frequency counts, ranges (high and low scores or values), means, modes, median scores, and standard deviations Two important concepts to understand descripitive statistics are: Variables Distribution
2. 2. Descriptive statistics <ul><li>VARIABLES </li></ul><ul><li>Are the things we are going to take into account in our study, that is the different possibilities and the different aspectcs we will study. Each of those different aspects are variables. </li></ul><ul><li>There are 3 types </li></ul><ul><li>Nominal variables </li></ul><ul><li>Ordinal variables </li></ul><ul><li>Interval variables </li></ul>
3. 3. Descriptive statisticts <ul><li>NOMINAL VARIABLE </li></ul><ul><li>Used for categorize datas in groups </li></ul><ul><li>ORDINAL VARIABLE </li></ul><ul><li>It situates the data in a higher or lower group. </li></ul><ul><li>INTERVAL VARIABLE </li></ul><ul><li>Tells the real distance between the different data. </li></ul>
4. 4. Desciptive statistics <ul><li>Distribution </li></ul><ul><li>The line formed by connecting data points is called a frequency distribution. If the shape of the line is that of a bell the distribution is considered to be normal. The closer the line is to the shape of the bell, the more reliable is to generalization. </li></ul>
5. 5. Descriptive statistics <ul><li>Inferential statistics are used to draw conclusions and make predictions based on the descriptions of data. There are two basic methods: numerical and graphical. </li></ul>
6. 6. Two main methods <ul><li>NUMERICAL </li></ul><ul><li>We have to take into account things as mean and standard deviation. </li></ul><ul><li>The mean is the sum of all the scores divided by the number of scores. The formula is: μ = ΣX/N where μ is the population mean and N the size of the population. </li></ul>
7. 7. Two main methods <ul><li>GRAPHICAL </li></ul><ul><li>In order to expose your information graphically you need to create a stem and leaf display and a box plot. </li></ul><ul><li>STEM AND LEAF DISPLAY. </li></ul><ul><li>Is a graphical method for displayin data.It is similar to a histogram but is more precise. Data are shown vertically. </li></ul><ul><li>BOX PLOT </li></ul><ul><li>The box stretches from the lower hinge to the upper hinge and therefore contains the middle half of the scores in the distribution. </li></ul><ul><li>The median is shown as a line across the box. </li></ul>
8. 8. Inferential statistics <ul><li>Inferential statistics are used to draw conclusions and make predictions based on the descriptions of data. </li></ul><ul><li>Important terms to understand it are: </li></ul><ul><li>Experiments </li></ul><ul><li>Probability </li></ul><ul><li>Population </li></ul><ul><li>Sampling </li></ul><ul><li>Matching </li></ul>
9. 9. Experiments <ul><li>EXPERIMENT </li></ul><ul><li>To collect data of two or more groups to answer a question. Based on the analysis of the data develop a causal model of the population. </li></ul><ul><li>Two important concepts </li></ul><ul><li>Dependent variable : a variable which depends on the score of the another variable </li></ul><ul><li>Independent variable : a variable that determines the score a dependent varible </li></ul>
10. 10. Probability, population, sampling. <ul><li>PROBABILITY </li></ul><ul><li>Express the likelihood or degree of cetainty that a particular event will occur. </li></ul><ul><li>POPULATION </li></ul><ul><li>Is the group which is studied. </li></ul><ul><li>SAMPLING </li></ul><ul><li>Is the part of the population we take to symbolize and represent the wholle of the population. </li></ul>
11. 11. Matching <ul><li>MATCHING </li></ul><ul><li>Is a method used to gain precise results of a study. It is used when reserchers are aware of extrinsic variables </li></ul><ul><li>Two methods used to match groups are: </li></ul><ul><li>Precision Matching : Consist in generalize the result of a controled group to another group with the same characteristics. </li></ul><ul><li>Frequency distibution: Allows the comparison of a controled and an experimental group through relevant variables. </li></ul>
12. 12. TWO MAIN METHODS USED IN INFERENTIAL STATISTICS <ul><li>Estimation: A sample is used to stimate a parameter ( is a number measuring any of the aspects we study) and a confidence interval ( a range of values computed in such a way that that it contains the stimate parameter a bigh portion of the time) about the estimate is constructed. </li></ul><ul><li>Hypothesis: When doing an experiment we assume an hypothesis called null hypothesis. Data are colleted and the null hypothesis is compared with them. If the data are very different from the null hypothesis it is rejected, if not it is accepted. </li></ul>
13. 13. REGRESSION <ul><li>Is the tendency of an extreme meassurement to shows closer to a second meassurement. It is used to predict a meassure on the bases of another meassure. </li></ul>
14. 14. MODELS OF REGRESSION <ul><li>Sinple linear regression: We only work with an independent variable, so there is only two parameters. </li></ul><ul><li>It is expressed as: </li></ul>
15. 15. MODELS OF REGRESSION <ul><li>Multiple linear regression: there are several independet variables, so it has several parameters. </li></ul><ul><li>It is expressed as: </li></ul>