1.Design

2. Collect information

3. Organize information

4. Analyze data

homogeneous

Mutations

variable

type of data

overall

sample

parameter

Statistics

A quantitative measure that describes the likelihood of a random event occurring.

It is customary to call an event with P ≤ 0.05 a small probability event, which means that it is very unlikely to occur in a random sampling.

Frequency table creation steps

Uses of frequency distribution tables and histograms

average

degree of variation

Classification

Rate

composition ratio

relative comparison (ratio)

mortality rate

case fatality rate

Incidence

Prevalence

1. Don’t confuse composition ratio with rate

2. When using relative numbers, the denominator should not be too small.

3. Calculate the total rate correctly

4. Pay attention to the comparability of data

5. Sampling error exists in sample rate or composition ratio

Applicable conditions: 1. The indicator is a quantitative indicator and obeys the normal distribution 2. Small sample

Used to test whether the population mean μ represented by the sample mean X is different from the known population mean μ₀

Applicable conditions: 1. The indicator is a quantitative variable value 2. Each pair of difference values ​​d obeys the normal distribution 3. Small sample

The essence is the one-sample t test comparing the difference sample mean d with the known population mean μᵈ=0

Applicable conditions: 1. The indicator is a quantitative variable value 2. There are two groups of samples, and the two groups of samples are independent 3. The two populations from which the two samples come respectively obey the normal distribution 4. The population of the two normally distributed populations The variances are equal (homogeneous variances) 5. Small sample

The two sample sizes n₁ and n₂ can be equal or different, and should be as equal as possible.

If F≥Fα/2, then P≤α, reject H₀ and accept H₁, it can be recognized that the variances of the two populations are not equal; otherwise, the variances of the two populations are considered to be homogeneous.

The basic steps

Difficulty: Calculation of divisions and combinations

q test (SNK method)

2×2 (2 groups of observation objects, opposing 2 types of results)

The χ² value reflects the degree of agreement between the actual frequency and the theoretical frequency.

Applicable conditions: 1. When n≥40 and all T≥5, use the basic formula of χ² test or the special formula of χ² test for four-table data; 2. When n≥40 and 1≤T<5, use the correction formula of the four-table data χ² test; 3. When n<40 or T<1, use Fisher's exact probability method (exact probability method) with four tables of data.

Suitable for data whose sample size is not very large

1.b c≥40, basic formula 2.b c＜40, correction formula

Basic steps: 1. Establish a test hypothesis and determine the test level 2. Compile the rank sum (sum of ranks) and combine the rank sum statistic 3. Determine the P value and make an inference

The difference between a sample statistic and a population parameter caused by sampling

⑴Individual differences exist, that is, each X– is different from one another ⑵The error of random sampling, that is, X– is different from μ

Standard deviation reflects the variation between sample means

σₓ₋=σ/√n, sₓ₋=s/√n

The smaller the standard error, the more accurate the estimate is.

refers to estimating population parameters from sample statistics

Estimation method

Applicable conditions: 1. Large sample, n≥50 2. σ is known

Function: Reflect the sampling error distribution rules or sampling distribution rules of the sample mean of a large sample

z=X–-μ/σ√n

Applicable conditions: 1. Small sample, n<50 2. Unknown σ (in quantitative variables)

The greater the degree of freedom ν, the closer the t distribution curve is to the standard normal distribution curve.

(X–-1.96σₓ₋, X– 1.96σₓ₋)

(1) Establish hypotheses and determine test levels

(2) Select test methods and calculate test statistics

(3) Make statistical inferences based on P value

Notice!

Also known as the significance level, represented by α, it is the probability value of the predetermined rejection region. In practice, α=0.05 or α=0.01 is generally used.

μ is a position parameter that describes the mean level of the normal distribution

σ is a shape parameter that describes the degree of variation of the normal distribution.

①The area under the curve is the probability

②The total area under the curve is 1 or 100%

③All normal curves have the same area within the range of any multiple of the same standard deviation around μ

μ=0，σ=1

Standardized Transformation of Random Variables

1. As a reference index for clinically determining normality and abnormality

2. Can be used to evaluate children’s developmental level

1. Determine a homogeneous reference population

2. Select a sufficient number of reference samples

3. Control detection errors

4. Select single and bilateral cutoffs

5. Choose an appropriate percentage range

6. Select the method for calculating the reference value range

(Mean > Variance)