その結果(けっか)As a result

These expressions are similar in that both are used at the beginning of a sentence and can express the outcome of a situation, but they differ in nuance. そこで is relatively vague about the connection between the two events, like the English 'as such' or 'accordingly', while その結果 more specifically conveys that a situation or condition results from the previously mentioned cause.

その結果 and したがって are similar in that both express a result or consequence with a relatively formal tone. その結果 emphasizes the resulting situation or condition, similar to the English 'as a result of that', while したがって implies a logical conclusion, which may or may not necessarily be a 'resulting' situation.

Both expressions use 結果 to express a resulting situation or condition, like the English 'as a result', but differ in how they connect to the cause. その結果 is used at the beginning of a sentence and points back to something just mentioned, while 結果・の結果 is used in mid-sentence and connects directly to an explicitly mentioned cause, either by attaching to a verb or to a noun with の.

ために and その結果 both express a cause/effect relationship, but in different ways. ために is used within a sentence following a noun, verb, or adjective, and can mean either 'due to (A)' or 'in order to (A)'. その結果 comes at the beginning of a sentence and always means 'as a result of that', referring back to the previous statement.

These expressions are similar in that both are used at the beginning of a sentence to express the effect of a cause mentioned just previously. そのため(に) implies a direct, logical cause, like the English 'due to that', while その結果 focuses on the ultimate condition or situation brought about by the cause, like 'as a result of that'. そのため(に) can also express 'for the purpose of (A)', which is a nuance その結果 cannot have.