The central tendency of a set of data refers to the tendency to move closer to a center value. Statistics describing the location of the data distribution center called the ruling position of the amount referred to position statistics. For the continuous variables (or scale variable) and sequencing variables, trends in the data center and specification are the mean, median, mode, mean the end of 5%. For qualitative data (in nominal terms), and specification data center trends, only the mode.
Generally it refers to the mean data arithmetic mean (arithmetic mean) is the main trend of data center metrics, the largest use of indicators also practical problems. We have examined the variable set n measured values, they are not referred to as x1, x2, ..., xn, is an arithmetic mean as follows.
The observed values are arranged in ascending order of large, average after excluding both end portions of the score values calculated sorted out, it referred to as the mean end.
Thus calculated mean avoiding the effects of extreme values.
The observations of the ascending order, at the intermediate position called the median value.
Smaller median influenced by extreme values, the data has a maximum or minimum value, the mean and median are often more representative of the central tendency of the data.
The mode is the most frequently observed value of the value appears, this reaction the central tendency of the set of observations.
The standard error of the mean is a measure of the difference between the mean of the different samples.
When two groups of discrete data size level, if the measured dimension much difference data, or the data is not the same dimension, then direct comparison of the two standard deviation is not appropriate, eliminate the need to first measurement scale and a dimensionless influences. Coefficient of variation of these effects can be eliminated, provided the sample mean, the sample standard deviation s, then the coefficient of variation is calculated as follows
Quantile, also known as percentile, a position indicator. p% quantile means such that at least p% of the data is less than or equal to this value, and such that at least (100-p)% of the data is greater than or equal to this value.
All of the cases, less than a quarter of observations at four points, observed value is greater than three quarters of the lower quartile. Quartile center position is the median. The largest quartile called upper quartile, denoted by Q.
Profile has a long tail to the right, left spike, a> 0, the distribution is negatively skewed or left side, i.e., on the left tail distribution pattern, FIG. 3-10 (b), the distribution has a long left tail, the tip of the wind-right, a = 0, symmetrically distributed. Regardless of positive, which negative skew, the larger the absolute value indicates a larger degree of skewness of the side branches, whereas the smaller the degree of deflection, the more nearly symmetrical profile shape.
Many statistical process also provides an output descriptive statistical indicators.
SPSS custom table module can also generate most of the descriptive statistical indicators.
The most commonly used are listed first of four processes, i.e. frequency, Description, Discovery and cross table.
To determine whether the variable is normally distributed
Analysis selected in SPSS - descriptive statistics - frequency, the frequency of occurrence in the dialog box shown in FIG 3-12. 3.1 has been introduced in front of the frequency table, we here do not show the form. In Figure 3-12, the table shows the frequency not checked.
In SPSS, select an analysis - descriptive statistics - explore, get Figure 3-18 is exploring dialog box, the meaning of the relevant element is as follows.
(1) a list of the dependent variable D: the need to analyze the variables selection box, if necessary to change the classification of different amounts of detailed analysis, the classification criteria will have provided the list of factors.
(2) a list of factors F: Set variable analysis group variables set, where the variables are always selected categorical variables.
(3) Case denoted C: If the observed value of the information marked on the required graphics rendering, need to take some variables into the selected callout box.
(4) Statistics S: Descriptive statistics of the output.
(5) Draw T: This option will be selected and the corresponding output pattern is provided
(6) Option O: setting missing value processing method
Descriptive Statistics index number of applications in addition, may also be applied a bar chart, pie chart, Pareto chart, histogram, box plot, leaf statistical graphics board of FIG.
In the analysis - Descriptive statistics - explore options for drawing under the sub-menu, you can draw box plots, stem and leaf plots, histograms and test data normality of QQ plot.
Graphical depiction of the shape data - bar, pie, Pareto
Three kinds of statistical data can be quantified using the pattern described: a histogram, FIG stem and box FIGS.
Histogram first continuous data into a plurality of consecutive sections, and then calculates the observed value falls relative frequency or frequencies of the respective sections.
From the histogram distribution of the observed data can be intuitively
FIG stem quantitative variables describing a graphical manner, except that it can give information on the distribution of the histogram analysis, it also is possible to restore most of the original data information.
FIG box is a summary of the number of five (the minimum value, the first quartile, median, third quartile, maximum) of the graphical representation.
Normalized data includes data processing and chemokines with processing two dimensionless. Data processing with chemotactic nature of the data mainly to solve different problems.
After the standardization process, you can ensure that the data subject to standard normal distribution.