# ordinal logistic regression & t-test

I'm currently working on a statistics paper for practice (complete beginner here) and need to "test the hypothesis with a t-test". Unfortunately, most of my data is ordinal (because it's from WVS 6th wave), and I'm confronted with a lot of situations we didn't get to discuss in class.

I figured that an ordinal logistic regression is probably what I need and after using the following commands in R (V9 is ordinal, 1 highest and 4 is the lowest, V19 is a dummy variable with 1 and 2 and V242 stands for age, which I'm trying to use as a control variable):

m <- polr(V211.f ~ V9 + V242 + V19, data = finalvariables, Hess=TRUE)

summary(m)

ctable <- coef(summary(m))

p <- pnorm(abs(ctable[, "t value"]), lower.tail = FALSE) * 2
ctable <- cbind(ctable, "p value" = p)
ctable

ci <- confint(m)

exp(coef(m))

exp(cbind(OR = coef(m), ci))


This is what I get:

               Value  Std. Error    t value      p value
V9    0.45377983 0.090965416  4.9884874 6.085389e-07
V242 -0.03070772 0.004117975 -7.4569958 8.851753e-14
V19   0.06250584 0.164261954  0.3805254 7.035555e-01
1|2  -0.08301606 0.324161077 -0.2560951 7.978774e-01
2|3   2.78367366 0.355122209  7.8386358 4.554675e-15
3|4   4.48110377 0.477055113  9.3932622 5.817009e-21
4|5   5.87434596 0.776298722  7.5671205 3.815880e-14

OR     2.5 %   97.5 %
V9   1.574251 1.3182585 1.883566
V242 0.969759 0.9618787 0.977542
V19  1.064501 0.7713671 1.469292


Now, I'm not so much confused by the "value" or the OR (or at least I think I'm not) but I don't quite know what to do next (if I want to conduct a t-test?)... Also, is there anything I did, that maybe shouldn't be done?

I'd be very grateful for your help and please let me know if there's anything I need to specify. Thanks so much!

• Does WVS stand for World Values Survey? Just to clarify. – Mark White Jun 27 '17 at 15:00
• First you need to have a hypothesis. And then choose an appropriate test, which may not be a t-test. – Scortchi - Reinstate Monica Jun 27 '17 at 22:13
• Sorry about that, WVS is what we're mainly working with, I sometimes forget that it's actually "World Values Survey". About the hypothesis: What I'm mainly trying to do, is to show, that an increase of V9 and V19 would / will lead to an increase of V211. So my null hypothesis is the opposite, that it doesn't have such an effect or the complete opposite (in this case the value of V9 would be lower than 0?). Unfortunately V9 and V19 are correlated (kendalls tau: about 0.476), which is why I was thinking about not including V19 in the regression. – Amb Jun 28 '17 at 13:24
• Your regression coefficients act as your test in this case. You do not need to run any other analysis. You are testing that your regression coefficient is non-zero, thus there is a statistically significant relationship between your dependent variable and explanatory variables. For example, There is a statistically significant relationship between V211 and V9 with B=.454, t(n-p-1)=4.99, p<.001 – Steven M. Mortimer Jun 29 '17 at 18:52
• With regards to your comment on V9 and V19 being correlated: Correlated explanatory variables does not justify simply removing unless the correlation is very high. You should probably check variance inflation factors (VIF) of each variable before removing due to concerns about multicollinearity. – Steven M. Mortimer Jun 29 '17 at 18:52