The Great Depression, which began in 1929, offers an example. A superficial acquaintance with the economic hardships of the era tempted one historian to write:
The Great Depression tested the fabric of American life as it had been seldom tested before or has since. It caused Americans to doubt their abilities and their values. It caused them to despair. But they weathered the test, and as a Nation, emerged stronger than ever, and we are all better today for their strength and their courage.
The first and last sentences of the above paragraph, despite some curious capitalization and syntax, are either supportable by data, or are emotive and constitute an interpretation of facts, and can thus be allowed. The middle two sentences, however, constitute assertions which would need to be supported by facts, and yet cannot be supported by facts.
In order to support his point, the author would need to produce evidence that (1) Americans doubted their abilities and values, (2) that the Great Depression caused this doubt, (3) that Americans despaired, and that (4) the Great Depression caused this despair. Such evidence cannot be found.
On the contrary, we can find evidence that, in the midst of hardship, despite hardship, and perhaps even because of hardship, Americans relied on their abilities and on their values. Such evidence would include the creativity and ingenuity which empowered people to survive these difficult years - creativity on a physical level, finding ways to make do with less than ideal supplies and materials, and creativity on a societal level, using the social structures of the time to offer material and emotional support to those who needed it. Americans continued to rely on their values, as evidenced by the continuance of societal norms based on cultural and moral tradition, and by continued eagerness with which they embraced the moral codes which directed individual choices and supported familial and social structures.
To be sure, individual exceptions can be found: those who perceived their abilities as insufficient, or those who doubted and even abandoned their values. But it would be necessary to show that these exceptions were measurably greater during the Great Depression than during other eras in history, and to show that such manifestations were caused by the Great Depression and didn't simply coincide with it. Even so, the number of exceptions would appear to be significant, and so the generalization would not stand.
Similarly with the notion that Americans despaired. Again, individual exceptions aside, as a categorical statement, we find insufficient supporting evidence. On the contrary, the resilience of the nation allowed for good humor, artistic creativity, and a form of hope or optimism in which people lived, loved, and worked, enjoying what could be enjoyed in the present, striving toward good moral character, forgiving their own failings and the failings of others, and establishing goals for the future. There was no general societal or national sense of despair.
What counts as evidence for all of the above? Evidence falls into different categories. Demographic and statistical evidence would count, offering information about everything from church attendance to divorce and suicide - with the usual caveat about the misuse and misinterpretation of statistics, per Mark Twain. Individual biographies, autobiographies, and memoirs - including oral histories and anecdotes - count as evidence. General histories of the era count, as do specific histories of a particular event, project, or series of developments: from accounts of agriculture to a chronicle of the development of the motion picture. Artifacts count as evidence: museums filled with machines, clothing, furniture, coins, etc., from the Great Depression.
Only a large amount of concrete specific evidence, and the analysis of this data, will confirm generalizations like those given above.