There are loads of different methods and lots and lots of debate about which of them yield the most interesting results! By definition, though, none of the qualitative ones will give you a P value at the end. The mode of certainty is not the same
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Change - social change, historical change - is a complicated thing. Let's take a distant historical example, like the French Revolution because it's sometimes easier to see things when they are not right in front of you. I'm just going to tell you how I approach this, because it's only one way and there are lots of others! (Buffy has some really, really interesting thoughts on ethnography, which is a very different method but revelatory in terms of the way that it can get inside what's going on in a situation).
Now there is such a thing as quantitative history - researchers can go in and can analyse, say, correlations between the quality of the harvest, grain prices, and social disorder to try to pinpoint whether there was a relationship between these things. This is a method that would give you a figure for certainty about the correlation between grain price and riots.
But the trouble is it doesn't actually tell you much because the moving and shaking of the times: because the cause of the revolt might not just be 'hunger' because there is never, ever just raw 'hunger' that is uninterpreted in the social domain. All of our emotions and feelings are only interpretable within a social context. From this perspective, what starts to matter is the way in which those at the time understood and interpreted the hunger. If someone thinks their hunger is a personal punishment from God, for instance, they may be less likely to get up and revolt than if they think it's because an aristocrat up the road is sitting on a lot of grain and waiting for prices to increase.
So we begin to slot into much wider debates about how class structures are understood, how oppression is conceptualised etc. which are really shaped by a person's structural position in relation to power - and here's where things like race, gender, culture start to shape perception. The perspective of a peasant whose family is starving to death is unlikely to be the same as that of a grain merchant or an aristocrat landowner with grapes and a glass of wine in his hand! Women may occupy a different place with different possibilities to men. So position within wider power structures starts to matter - it's not something that you can 'edit' out as if there is just one viewpoint on events. If you tried to have a universal perspective that simply got rid of the ways in which these positions shape the understanding of events (which is part of what science tries to do with replication and repetition), you would lose a lot about what's really interesting. This is the basis of a lot of feminist arguments against conventional histories of the 'this happened then this happened then this happened' type. You lose a sense of the fact that not everyone agrees - the fact that you have interpretations that are particularly popular with one segment of the population and particularly unpopular with another.
On top of all that, you get particularly influential nodes where people come along and invent new ways of talking about what is happening that either dampen or ignite sentiment - so the way that the thought of Rousseau is used in the 1780s becomes very inflammatory (and contested) - and you could argue that a lot of the debates in the 1790s about which revolutionary faction should have power come down to claims about which is the most truly Rousseauvian!
So in this model, it's not that there is, at one level 'reality', and at another level 'language' or 'discourse' - reality is fundamentally the shared ways in which events are understood and discussed. And, at the same time, the limits of discussion are very much the limits of reality (and possible alternatives). So a lot of the historians and critics now take a topic and they investigate the many ways in which it was spoken about at the time, building up a kind of picture of the discourse which is also simultaneously a picture of events. (It's not that 'stuff happened' and 'was then understood' - the two are indivisible and simultaneous).
And of course, the historian's own work is shaped by the assumptions and discourses of their own time - so it's never objective or outside of its era.
Though I've given a historical example here, there's no reason the same techniques can't be applied to contemporary events. I just chose a distanced one because I think sometimes things are easier to see with historical perspective.
Hope this is helpful! 