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I have a relatively small language corpus (ca. 250000 tokens). There are two possible stems for a verb in the language: active and passive. Some of the verbs in the language occur only in passive stems (like deponent verbs in Latin, for example). There is also a number of verbs, of which there are only a few instances in the corpus. These instances happen to display passive forms. I would like to evaluate these passive-only verbs and to select real deponents out of them (e.g. if a verb has 0 active forms and 16 passive, then it is more likely to be a deponent, contrary to the verb which has, for example, 0 active forms and 2 passive).

What I have already done: 1) I gathered a small number of verbs which mostly have passive forms (more than 75%). Selecting verbs where the forms are 50-50 would lead to a lot of false positive results. The data looks like this:

VERB    N_ACTIVE N_PASSIVE PERCENTAGE_PASSIVE
Verb_1  3        16        0.84
Verb_2  2        20        0.9
....

2) Then I took the weighted average of this group. It turned out to be approximately 92%. 3) Then I assumed that the occurences of a verb were independent of each other, so having met n passive forms for a verb in my corpus I can assume that the probability of this is 0.92 ^ n.

The problem: I am not sure how I would test the significance of the difference between 0.92 ^ n for a given verb and the obtained average. I tried applying t-test, but it provides weird results, and I think that it is not best suited for this kind of study. I would be grateful if anyone could point the direction in which I should be thinking/reading.

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I assume these are your hypotheses:

H0: The verb is passive 92% of the time.

H1: The verb is passive 100% of the time.

You can't apply a t-test in this case; there's no t-statistic that can be generated. (Typically, when we apply a t-test, it's when we have some point estimate of a variable assumed normal minus the mean under the null hypothesis divided by the standard error, for example in the two-sample t-test or when we test hypothesis about simple linear regression.)

Instead, the p-value is simply 0.92^n, since the p-value is the probability that you get the data you have given the null hypothesis (which, in this case, is that the verb is passive 92% pf the time).

For a verb with two passive forms, the p-value is 0.92^2 = 0.8464, obviously insignificant.

For a verb with sixteen passive forms, the p-value is 0.92^16 = 0.26339, still not significant.

At alpha = 0.05, to conclude that a form is deponent, you need log 0.05 / log 0.92, or approximately 36 passive forms; at alpha = 0.1, you need 28.

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