What is the difference between a grouped t test and a paired t test?

1. The applicable conditions are different

1. Group t-test.

It is suitable for the significance test of the difference between the mean of the two samples in the unpaired design or the group design;

A non-paired design or group design in which the trial units are completely randomized into two groups when a trial with only two treatments is performed, and then one treatment is randomly applied to both groups.

The test units of the two groups were independent of each other, and the obtained two samples were independent of each other and their contents were not necessarily equal.

Each set of data is approximately normally distributed.

or large samples), if the variance homogeneity is satisfied, the grouped t-test can be used.

2. The paired t-test is suitable for the significance test of the difference between the mean of the two samples in the paired design.

The following applies:

1) Comparison of the same sample receiving different treatments;

2) comparison of the same subject before and after treatment;

3) The subjects were paired with those with similar conditions, and two different treatments were given respectively, and the effects of the two treatments were observed.

Second, the test hypothesis is different.

1. The invalid hypothesis of the group t-test h0: 1= 2;

Alternative assumption h1: 1 does not equal 2.

2. Hypothesis testing of paired design data.

It can be seen as a comparison of the sample mean to the population mean d=0.

h0: d=0 (i.e., the overall mean of the difference is 0);

h1: d is not 0 (i.e., the overall mean of the difference is not 0).

Third, the calculation formula is different.

1. The formula for calculating the t-value of the group t-test:

2. The formula for calculating the t-value of the paired t-test:

Fourth, the inspection efficiency is different.

1. When the number of samples is the same, the group test of the measurement data is less efficient than the paired t-test.

2. When the number of sample cases is the same, the paired t-test has high efficiency; Because of the pairing method, some factors that have an impact on the experimental results (such as gender, weight, etc.) are matched, which eliminates the interference caused by these factors and reduces the error.

The paired t-test is a special case of the single-sample t-test. Paired t-test: It is the use of paired design methods to observe the following situations,1

The two paired subjects received two different treatments; 2.The same subject received two different treatments; 3.Comparison of results before and after treatment of the same subject (i.e., self-pairing); 4.

Two parts of the same subject are treated differently.

The grouped t-test, also known as the t-test of two independent samples, is suitable for comparing the means of two samples completely randomly. Subjects were randomly assigned to two treatment groups, and each group was randomized to receive one treatment.

Why do we need a t-test?

The t-test compares the mean of different data to see if there is a difference between the two sets of data. It can be divided into three types, namely single-sample t-test, paired-sample t-test, and independent sample t-test.

The independent-samples t-test is used to analyze the relationship between the distribution of qualitative and quantitative data. For example, researchers wanted to know if there was a significant difference in the average IQ between the two groups. The t-test only compares the difference between the two sets of data, and if there are three or more groups, ANOVA is used.

If there are only two groups, it is recommended to use the t-test with a small sample size (below 100) and ANOVA instead.

Data format: <>

The independent-samples t-test is a study of differences between two sets of data, such as differences in satisfaction between genders. The data format needs to have group x (e.g., gender) and analysis item y (e.g., satisfaction).

Sometimes there are only 2 columns in the data format and no groups, such as the experimental group and the control group. Then you need to transform the data, add a column of 'groups' by yourself, and then overlap the data to get the analysis item y, similar to the following figure:

spssau operation:

Paired t-test, which is used to compare the difference between paired quantitative data. For example, in two background cases (with and without ads); whether there is a significant difference in the purchase intention of the samples; The paired t-test is often used in experimental studies.

The format of the paired data is relatively special, including the paired t-test, or the paired chi-square, etc. For example, the difference between the data of the experimental group and the control group. As shown below:

spssau operation:

In the "General Methods" module, select the "Paired T-Test" method, put Pair 1 (Quantitative) in the upper analysis box, and Pair 2 (Quantitative) variables in the lower analysis box, and click "Start Analysis".

The single-sample t-test is used to analyze whether the quantitative data is significantly different from a certain number, such as a five-level scale, where a score of 3 represents a neutral attitude, and a single-sample t-test can be used to analyze whether the attitude of the sample is obviously not neutral; By default, the system uses a score of 0 for comparison.

Results of a single-sample t-test analysis.

t-test. It is to compare the differences between the two sets of data, whether there is statistical significance; The t-test is premised on the fact that both sets of data are from a normal distribution.

The variance of the data is uniform, and the independence is satisfied.

The independent sample t-test (i.e., independent samples if there is no correlation between the experimental treatment groups) is used to test the difference in data obtained by two groups of unrelated sample subjects.

The independent samples t-test statistic is:

S1 and S2 are two-sample variances.

n and n are two sample sizes.

The t-test compares the differences between the two sets of data to see if there is statistical significance; The premise of the t-test is that the two sets of data come from a normally distributed population, and the variance of the data is uniform, satisfying the independence.

The independent sample t-test (there is no correlation between the experimental treatment groups, the family search is the independent sample), which is used to test the difference in the data obtained by two groups of unrelated sample subjects.

The applicable conditions for the paired t-test are as follows:

1. Independence, the observed values are independent of each other and cannot affect each other.

2. Normality, each sample comes from a normally distributed population.

3. Homogeneity of variance, the variance of the population in which each sample is located is equal.

The t-test is to investigate whether there are significant differences between the two sets of data by comparing the means of different data. Paired Samples T-Test: Perform a mean comparison of paired samples, i.e., paired t-test.

A paired sample, or non-independent sample, actually has only one sample, but each individual in the sample is studied twice. The order of the samples is one-to-one.

The t-test is mainly classified.

The t-test can be divided into single population test, double population test, and paired sample test. The single-population t-test tests whether the difference between a sample mean and a known population mean is significant. When the population distribution is normally, if the population standard deviation is unknown and the sample size is less than 30, then the dispersion statistics between the sample mean and the population mean are t-distributed.

The t-test of the double population is to test whether the mean of the two samples is significantly different from the population they represent. The double-population t-test is divided into two situations, one is the independent sample t-test (there is no correlation between the experimental treatment groups, that is, independent samples), and the other is the paired sample t-test.

The results are as follows:

When the value of a statistic falls within the critical domain, the statistic is statistically significant, and the virtual hypothesis is rejected. When the value of a statistic falls in the receiving domain, the test is statistically insignificant, which does not reject the virtual hypothesis h0. Because, the reason for the staring of the results of the insignificant answer may be that the sample size is not enough to reject h0, and it is possible to make the first type of error.

Correct understanding of p-values.

and whether the difference was statistically significant. The smaller p is, it does not mean that the actual difference is greater, but that the more reason there is to sell and reject h0, the more reason there is to show that there is a difference between the two, and whether the difference is statistically significant and whether there is a professional practical significance is not exactly the same.

Most commonly usedt-test. The cases are:

1. Single-sample test: test a normal distribution.

Whether the mean of the population satisfies the null hypothesis.

, for example, to test whether the average height of a group of male military academy students meets the national standard of 170 centimeters.

2. Two-sample test: The null hypothesis is that the difference between the mean of the two normally distributed populations is a certain real number, for example, to test whether the average height of the two groups of people is equal. This test is often referred to as the Student's t-test.

But more strictly speaking, only when the variance of the two populations is equal, it is called the student t-test; Otherwise, it is sometimes referred to as the Welch test.