Relationship between type 1 error and type 2 error?

In statistics, there are two types of errors for hypothesis tests: Type 1 error and Type 2 error.

Type 1 error is when the null hypothesis is rejected, but actually true. It is often called alpha. An example of Type 1 error would be a "false positive" for a disease.

Type 2 error is when the null hypothesis is not rejected, but actually false. It is often called beta. An example of Type 2 error would be a "false negative" for a disease.

Type 1 error and Type 2 error have an inverse relationship. The larger the Type 1 error is, the smaller the Type 2 error is. The smaller the Type 2 error is, the larger the Type 2 error is.

Type 1 error and Type 2 error both can be reduced if the sample size is increased.