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Unformatted text preview: Statistical Techniques I EXST7005 Start here Frequency Tables Objective  Hypothesis testing Background A probability will be involved  we need to cover frequency distributions in general and probability distributions in particular A transformation will also be involved  we need cover transformations We will test primarily means, but also variances we will need to cover these statistics Course Progression Constructing a FREQUENCY Table DIVIDE the population into a number of classes or groups based on the characteristics studied. Categories are often quantitative, but not necessarily DETERMINE the number of observations in eac class (i.e. the frequency of occurrence of observations in each clas CONSTRUCT the table with both classes and frequencies. The frequencies may also be relative (i.e. percentages) or cumulative. EXAMPLE Construct a frequency table for a population of fish age groups. N = 10 Y = age of fish in years 8, 4, 4, 0, 1, 5, 6, 5, 3, 4 These values are placed into discrete age groups (0 to 8) FREQUENCY TABLE Class value Frequency (f.) cumulative frequency (c.f.) 1 1 1 1 2 2 2 3 1 3 4 3 6 5 2 8 6 1 9 7 9 8 1 10 SUM 10 Define the additional terms FREQUENCY TOTAL the total number of observations. The sum of the class frequencies FREQUENCY (f) the number of observations in each class CUMULATIVE FREQUENCY (c.f.) The sum o all class frequencies up to and including the class in question. Implies an order or rank, so this is usually done only with QUANTITATIVE VARIABLES Define the additional terms (continued) RELATIVE FREQUENCY (r.f.) the ratio of the class frequencies to the total frequency. These always sum to 1.0 r.f. * 100% gives the percentage frequency (sum to 100%) RELATIVE CUMULATIVE FREQUENCY (r.c.f. the sum of the r.f. up to and including the class question (for QUANTITATIVE VARIABLES). Class value frequency cumulative frequency relative frequency (r.f.) relative cumulative frequency (r.c.f) 1 1 0.1 0.1 1 1 2 0.1 0.2 2 2 0.0 0.2 3 1 3 0.1 0.3 4 3 6 0.3 0.6 5 2 8 0.2 0.8 6 1 9 0.1 0.9 7 9 0.0 0.9 8 1 10 0.1 1.0 SUM 10 1.0 FREQUENCY TABLE A SAS example (#1) from Freund & Wilson (1997) Table 1.1 ***************************************; *** Data from Freund & Wilson, 1997 ***; *** TABLE 1.1  HOUSES DATA ***; ***************************************; OPTIONS NOCENTER NODATE LS=78 PS=61; DATA ONE; INFILE CARDS MISSOVER; TITLE1 'Analysis of house sale price data'; TITLE2 'Table 1.1 from Freund & Wilson, 1997'; INPUT OBS QUALITY $ EXTERIOR $ DSQF SP; SP_INT = INT(SP / 10); CARDS; RUN; The program: Part 1  the DATA step 1 POOR FRAME 0.816 19.000 2 POOR FRAME 0.907 19.800 3...
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 Fall '08
 Wang,J

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