◆ descriptive statistical analysis
Concept: statistical analysis method described refers to the application of the classification, tabulation, graphics and general data indicators (to mean, variance, etc.) to summarize data distribution method.
The inferential statistical analysis method is through random sampling, to promote the application of statistical methods to data obtained from the sample to the conclusion that the overall data analysis needs to keep out the cold sample data to generalize information, and integration on abstract statistics,
To obtain the composite indicator reflects the sample data. These indicators called statistics. Descriptive statistics feature data can be divided into two categories: one represents the center position data,
The mean, median, and other public, those indicating the degree of dispersion of data, such as variance, standard deviation, range, etc. are used to measure the degree of off-center subject in the qualitative observations described knowledge,
Sometimes we need to refer to these principles into some groups according to some or classes, such that each observation must only fall into a class. For a given class, the number of cases falling within this class called frequency, the ratio of the number of cases falling into the total number of cases of the class and is referred to as the relative frequency.
Frequency analysis will be described mainly by the frequency distribution of data distribution table, bar charts, pie and bar charts, and a variety of central tendency and dispersion statistics trends.
◆ description of central tendency
The concept: central tendency refers to the tendency to move closer to a set of data center value. Statistics describing the location of the center of data distribution statistics called position.
For continuous variables and ordinal variable, and specification data of central tendency are the mean , median, mode, 5% trimmed mean,
For qualitative data, index data describing the central tendency of the mode only.
In the SPSS variables into three levels, which is a variable scale, ordinal variable, nominal variables.
◆ mean
Concept: mean generally refers to the arithmetic mean of the data. The effects of extreme values of the mean data vulnerable.
◆ 5% trimmed mean
Concept: The observed values sorted in ascending order, mean excluding both ends of the off portion of the digital data in the sorted sequence is referred calculated trimmed mean to avoid the influence of extreme values.
◆ Geometric Mean
Concept: Geometric Mean, also known as the geometric mean. It is the product obtained after the N-th power to open the sample data obtained even by a computer and requires the presence of the average multiplicative relation between the observed value,
And even a product of the respective observations must have practical significance, it is mainly used the relative number of columns, the number of samples required him and comparison arithmetic mean, geometric mean narrow range of applications.
◆ median
Concept: the observed value of the ascending order, at the intermediate position called the median value.
The median is less affected by extreme values, the data has a maximum and minimum value, the mean and median are often more representative of the central tendency of the data.
◆ 众数
Concept: The mode is the highest number of observations in value appears, reflecting the central tendency of this set of observations. Impact from extreme value. There may be described in multiple modes of discrete trends.
◆ poor
Concept: difference between maximum and minimum values of the observed data reflects fluctuation data. This difference is called the whole distance or poor, vulnerable to the effects of extreme values.
◆ variance and standard deviation
Concept: standard deviation is a measure of the observed value deviates from the average size, corresponding to an average deviation may be directly described in the data of degree of deviation from the mean.
◆ standard error of the mean
Concept: mean standard error of the mean measure of the difference between the different samples.
If the difference between the two sample mean and standard error of the ratio is less than -2 or greater than 2, it can be concluded two significant differences in the mean, and thus concluded that the two samples from two different overall.
◆ coefficient of variation
Concept: When comparing two sets of discrete data size level, if the measured dimension much difference observation, or the dimension data is not the same, then direct comparison of the two standard deviation is not appropriate, eliminate the need to measure the amount of scale and Gang influence of the coefficient of variation can eliminate these effects.
◆ quantile
Concept: P% quantile means such that at least P% less than or equal to the data value, and such that at least (100-P)% of the data is greater than or equal to this value.
Data in ascending order.
Minimum quartile as bottom quartile, referred to as Q1, all observations have observed value less than 1/4 of the lower four digits, observed 3/4 is greater than the lower digit, a middle point position quartile is the median. The largest quartile called upper quartile, denoted by Q3
Often the minimum statistical data, the lower quartile, median, upper quartile and maximum number of five called summary data. These five values can be seen that substantially the center of the degree of dispersion and distribution of data. The box plot is a graphical representation of the number five.
◆ shape distribution
Concept: when α> 0, the distribution is forward biased and skewed to the right, and the right tail distribution pattern, a long profile front left and right tail tip,
α <0, left side and negative distribution, and distribution pattern in the left tail, the profile has a long left tail peak top-right, α = 0, symmetrical distribution,
Either negative skewness, the greater the degree of skewness represented by the largest absolute skew, the skew degree smaller the contrary, the closer a shape symmetrical distribution.