How many tests do I need to run? My hypothesis is that the wording of a particular yes-no question affects whether people will answer "Yes" or "No", such that Wording 1 is more likely to be answered "Yes" than "No", and Wording 2 is more likely to be answered "No" than "Yes".
Here are the results of a survey:





Yes
No




Wording 1
70
30


Wording 2
20
80




What test(s) should I run to analyse these results? It seems to me that I could run a binomial test for each of the wordings to determine whether the results for that wording are likely to have occurred by chance. But do I need to use a further test (perhaps chi-squared) to determine whether there's a significant difference between the results for Wording 1 and the results for Wording 2? If not, I'm struggling to see how I can attribute the difference between the results to the difference between the wordings.
 A: A viable answer is contained in the comments and the answer by C8H10N4O2.
For hypothesis 1, a chi-square test of association (or independence) can be applied to the contingency table.
For a 2 x 2 table, a significant result can also be interpreted as suggesting that the two rows are significantly different.
In R,
Input =("
           Yes  No
Wording.1  70   30
Wording.2  20   80
")

Matrix = as.matrix(read.table(textConnection(Input), header=TRUE, row.names=1))
 
Matrix
 
chisq.test(Matrix)

   ### Pearson's Chi-squared test with Yates' continuity correction
   ### 
   ### X-squared = 48.505, df = 1, p-value = 3.294e-12

For hypotheses 2 and 3, a binominal test can be applied to each row of the table.
 Matrix[1,]

   ### Yes  No 
   ###  70  30 

binom.test(Matrix[1,])

   ### Exact binomial test
   ###
   ### number of successes = 70, number of trials = 100, p-value = 7.85e-05

Since you have dichotomous results, here of Yes and No, an intuitive way to present the results are to present or plot the proportion of Yes results in each row.
prop.table(Matrix, margin=1)

   ###            Yes  No
   ### Wording.1  0.7  0.3
   ### Wording.2  0.2  0.8

In addition, for a 2 x 2 table, the phi statistic could be used to present the effect size.  This is similar to the r statistic in correlation.
library(DescTools) 

Phi(Matrix)

   ### 0.503

Whether or not the differences in the proportion of Yes answers across rows --- or the magnitude of the phi statistic --- is meaningful, is up to the judgement of the analyst.
A: It's best to show the outcome of testing Wording and Answer for independence. A Chi-squared test would probably work well for that. The 70/30/20/80 contingency table shown in the question will end up with a tiny p-value, so it will be safe to say the variables are not independent.
Follow that up with something like an odds ratio to show just how more likely Wording 2 is to get a "No" than Wording 1 (or in the other direction, how much more likely Wording 1 is to get a "Yes" than Wording 2).
