Inductive reasoning moves from the specific to the general. Beginning with the evidence of specific facts, observations, or experiences, it moves to a general conclusion. Inductive conclusions are considered either reliable or unreliable instead of true or false. An inductive conclusion indicates probability, the degree to which the conclusion is likely to be true. Inductive reasoning is based on a sampling of facts. An inductive concluson is held to be reliable or unreliable in relation to the quantity and the quality of the evidence supporting it. Induction leads to new truths and can support statements about the unknown on the basis of what is known." (Wilson, Forensic Procedures for Boundary and Title Investigation, p. 51.)
Slothful induction" probably isn't the best phrase to describe what is the failure to see or concede the most likely inference from the evidence. The failure to infer is rarely due to laziness. It demonstrates an unwillingness to follow the evidence wherever it may lead due to stupidity, dogma, or vested interests. Usually it is a red flag that someone is not principally interested in the truth of a matter. And, because inductive arguments are at best probabilistic, not definitive, someone can always hold out against the preponderance of evidence. Nevertheless, there are times when it is appropriate to resist the inference of even a good inductive argument, namely, when there are countervailing reasons that support the contrary conclusion. For example, when new evidence appears against a well-established scientific theory, it can be appropriate to retain it until the evidence to the contrary is sufficiently strong. In such cases an ad hoc hypothesis may be introduced to explain how the established thesis may still be true in spite of the implications of this new inductive evidence.
The size of the sample is too small to support the conclusion. "[This] type of argument [goes] under varied terms for the fallacy like over-generalization, glittering generality, accident, converse accident, or secundum quid (neglect of qualifications). Typically, however, two types of fallacies are emphasized. One is an inductive fallacy that occurs in statistical reasoning from a selected sample to a wider population. The other has to do with overlooking qualifications to a defeasible generalization." (Douglas N. Walton, Argumentation Methods for Artificial Intelligence in Law, p. 39)
The sample used in an inductive inference is relevantly different from the population as a whole. Sample size does not overcome sample bias. "Sampling is a technique used by pollsters. It is a device for gathering information about an entire population from a small subset — a sample. A representative sample is one in which whatever features in the overall population deemed relevant to the issue at hand are represented in roughly the same proportions as these features are found in the population." (Johnson & Blair, Logical Self-Defense, p. 71.) [To Add: 2) Tautological Sampling 3) Tendentious Sampling]
In an analogy, two objects or events, A and B, are supposed to be similar. Then, it is argued that since A has property P, B must also have property P. An analogy is false when A and B are materially different such that B doesn't possess property P. 2) An imperfect analogy may succeed in predicting property P in B, but in B the property is possessed differently or only partially. So, analogies fail either by seeing an analogy where none exists, or by overestimating the value or significance of the analogy. However, determining whether an analogy is good, false, or imperfect is as much an art as a science. Accordingly, the examples provided below are not necessarily false or imperfect analogies. We leave that judgment to you. Furthermore, even a good analogy is not a proof and at most provides probabilistic or inductive evidence.
Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the "principle of total evidence". "In an induction, the total relevant information needs to be examined. The fallacy occurs when relevant evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the principle of total evidence." (Chhanda, Logic: Informal, Symbolic, and Inductive, p. 48.)