finite population

infinite population

Categorical variables

ordinal variable

Numeric variable

sample mean

Conditions: Unimodal symmetric distribution data, especially normal distribution data

Conditions: geometric data, especially lognormal data

Notice

Sort a set of observations from small to large, and the central observation is the median

The median is suitable for describing skewness or frequency distributions with no definite values ​​at both ends, and has strong applicability.

Sort a set of observations from small to large. The x%th observation is the xth percentile.

Applicable conditions

Most occurrences

It only makes sense when the amount of data is large

Also called full range, represented by R, it is the difference between the maximum value and the minimum value in a set of observed/measured values.

Range of individual differences in response: large range, large degree of variation; small range, small degree of variation

advantage

shortcoming

Reflects the range of the middle half of the observations/measurements

Advantages: simple calculation, stable than range

Disadvantages: Still does not take into account the variation of all observed/measured values, and is still not stable enough

It is mainly used to describe the variation characteristics of obviously skewed distribution data, and is often used in combination with statistical charts.

The greater the variance, the greater the variation

Advantages: Considers all variations in observed/measured values, relatively stable

Disadvantages: Dimensions (i.e. units) are changed and sometimes cannot be explained

When the unit of the mean is the same and the values ​​are similar, the standard deviation ↑ degree of variation ↑, the less representative the mean is.

Advantages: Taking into account the variation of all observed/measured values, the unit is the same as the original indicator, relatively stable

Also called dispersion coefficient, represented by CV

Outstanding advantages

Applicable conditions

rate (frequency indicator)

Compare

The denominator cannot be too small

Ratio and rate cannot be mixed

Calculation of consolidation rate (total rate)

Comparability

Sampling Error – Hypothesis Testing

Table number

title

line

number

Remark

title

graph domain

heading

legend

scale

unit

Histogram

Scatter plot

line graph

circle diagram

percentile chart

Parametric test

Non-parametric test

critical value method

p value method

confidence interval

simple judgment method

Graphical representation

Hypothesis testing method: P value

F test

Levene's test

The sample mean is distributed around the population mean

As n increases, the degree of variation decreases

Small variation range

Not necessarily equal to the overall mean

Indicates the size of the sample mean error and describes the reliability of the sample mean.

Standard error = standard deviation / square root sample size

An interval is used to estimate the range of the overall parameter according to a certain probability or credibility (1-α). This range is usually called the credible interval or confidence interval of the parameter. The pre-given probability (1-α) is called Credibility or confidence is often taken as 95% or 99%.

The closer the credibility is to 1, the higher the accuracy

The smaller the CL length, the higher the precision.