Correlation Methods Correlation and Covariance Matrices Fisher's z Transformation ( z r ) Pearson Product-Moment Correlation Coefficient (Pearson's r ) Spearman's Rank-Order Correlation Coefficient (Spearman's ρ) Kendall's Rank Correlation Coefficient (Kendall's τ) Correlation and Covariance Matrices You can generate a correlation or covariance matrix from numeric data columns, and have the choice of storing the computation results in an-autogenerated worksheet, or display the results in a table format whose values can be color coded. This method requires multiple numeric data columns whose values should be stored in a single worksheet. An example of a correlation matrix displayed as a color-coded table is shown below. Using Fisher's z Transformation ( z r ) This option is provided to allow transforming a skewed sampling distribution into a normalized format. The theoretical sampling distribution of the corre
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Definition Degree and type of relationship between any two or more quantities ( variables ) in which they vary together over a period ; for example, variation in the level of expenditure or savings with variation in the level of income . A positive correlation exists where the high values of one variable are associated with the high values of the other variable(s). A ' negative correlation ' means association of high values of one with the low values of the other(s). Correlation can vary from +1 to -1. Values close to +1 indicate a high-degree of positive correlation, and values close to -1 indicate a high degree of negative correlation. Values close to zero indicate poor correlation of either kind, and 0 indicates no correlation at all. While correlation is useful in discovering possible connections between variables, it does not prove or disprove any cause-and-effect (causal) relationships between them. See also regression Positive Co
Learning Objectives Create and interpret frequency polygons Create and interpret cumulative frequency polygons Create and interpret overlaid frequency polygons Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions . To create a frequency polygon, start just as for histograms , by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the
Histograms Histograms are similar to bar charts apart from the consideration of areas. In a bar chart, all of the bars are the same width and the only thing that matters is the height of the bar. In a histogram, the area is the important thing. Example : Draw a histogram for the following information. Frequency: Height (feet): (Number of pupils) Relative frequency: 0-2 0 0 2-4 1 1 4-5 4 8 5-6 8 16 6-8 2 2 (Ignore relative frequency for now). It is difficult to draw a bar chart for this information, because the class divisions for the height are not the same. The height is grouped 0-2, 2-4 etc, but not all of the groups are the same size. For example the 4-5 group is small
Introduction A graph refers to the plotting of different valves of the variables on a graph paper which gives the movement or a change in the variable over a period of time. Diagrams can present the data in an attractive style but still there is a method more reliable than this. Diagrams are often used for publicity purposes but are not of much use in statistical analysis. Hence graphic presentation is more effective and result oriented. Diagrams can present the data in an attractive style but still there is a method more reliable than this. Diagrams are often used for publicity purposes but are not of much use in statistical analysis. Hence graphic presentation is more effective and meaningful. According to A. L. Boddington, "The wandering of a line is more powerful in its effect on the mind than a tabulated statement; it shows what is happening and what is likely to take place, just as quickly as the eye is capable of working." Advantages o
Introduction Although tabulation is very good technique to present the data, but diagrams are an advanced technique to represent data. As a layman, one cannot understand the tabulated data easily but with only a single glance at the diagram, one gets complete picture of the data presented. According to M.J. Moroney, "diagrams register a meaningful impression almost before we think. Importance or utility of Diagrams Diagrams give a very clear picture of data. Even a layman can understand it very easily and in a short time. We can make comparison between different samples very easily. We don't have to use any statistical technique further to compare. This technique can be used universally at any place and at any time. This technique is used almost in all the subjects and other various fields. Diagrams have impressive value also. Tabulated data has not much impression as compared to Diagrams. A common man is impressed easily by good diagrams. This te
P r epa r ation of f r equency table: The pre m i se o f da t a i n t h e f o rm o f f reque n cy d i st r i b u t i on desc r i be s t h e bas i c pa t t e r n wh i c h t h e da t a assu m e s i n t h e m ass. F r e q u e n c y d i s tr i b ut i o n g i v e s a b ette r p i ctur e o f t h e p a t t e r n o f d a t a i f t h e nu m b er o f i t e m s i s l arge. I f t h e i de n t i t y o f t h e i n d i v i dua l s a b o ut w h o m a par t i cu l ar i n f o r m a t i o n i s taken, i s n o t r e l evan t t he n t h e f i r st s t e p o f c o nden s a t i o n i s t o d i v i d e t h e o bserve d r a ng e o f var i ab l e i n t o a su i t a b l e n u m b e r o f c l as s - i n t e r va l s an d t o r ec o r d t h e nu m ber o f o bserva t i o n s i n eac h c l ass . Le t u s c o ns i de r t h e we i gh t s i n k g o f 5 0 co l l eg e stude n t s. 42 62 46