# Hypothesis / Statsitical significance between continous variable and dependent binary variable

Sorry I am a stats newbie, I understood that I can use the search feature, I tried to search but I am afraid that I am not using the right terms and the results returned are not quite relevant to my question.

I have a set of data readings (50 cases), A is a number between [0,1] and B is {yes,no}. My hypothesis / I am trying to show that A does not affect the outcome of B based on my data. May I have some advice what are the right technique / test I should use? Thanks

• "Proving" that A does not affect B may be mighty hard. Most of statistics is oriented at providing evidence that there is an effect. – Nick Sabbe Apr 18 '13 at 15:29
• Is there any way I can set null hypothesis and NOT rejecting it? – drhanlau Apr 18 '13 at 15:30
• Not rejecting the null hypothesis is not a strong conclusion: it may just be proof that your dataset was too small to pick up the existing effect. – Nick Sabbe Apr 18 '13 at 15:33

Perhaps a visual would help. You may not need a named statistical test. If you use comparative boxplots with whiskers and notches (R), you can visually compare the distribution, median and 95% confidence intervals of the median side-by-side. If there is no significant relationship between the yes/no and the continuous variable, then the confidence intervals should overlap. Another option would be to use comparative density plots to demonstrate that the two distributions are essentially the same.

I think you're after logistic regressoin. This is the general idea of how to do it in R.

# generate some data
xy <- data.frame(A = runif(100, min = 0, max = 1), B = sample(c("yes", "no"), 100, replace = TRUE))
# logistic regression using a GLM
xy.mdl1 <- glm(B ~ A, data = xy, family = binomial)
summary(xy.mdl1)


This will give you the output. Plenty of information on the internet on how to interpret the results, or consult a local statistician.

Call:
glm(formula = B ~ A, family = binomial, data = xy)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.2766  -1.1768   0.0004   1.1716   1.2832

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    0.247      0.402    0.62     0.54
A             -0.497      0.700   -0.71     0.48

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 138.63  on 99  degrees of freedom
Residual deviance: 138.12  on 98  degrees of freedom
AIC: 142.1

Number of Fisher Scoring iterations: 3

• What I am trying to show here is that A has no effect on B. My understanding is if we use logistic regression, we are using A to classify B, which is not really what I want to do here. – drhanlau Apr 18 '13 at 15:27
• No, logistic regression is a reasonable way to go about this. However: at best it will give you evidence that knowledge of A does give you knowledge on B. – Nick Sabbe Apr 18 '13 at 15:31
• So in my paper how do I draw a conclusion that A has no effect or at least not much effect on B? – drhanlau Apr 18 '13 at 15:35
• If the odds ratios are approx. equal, you will state that you found no evidence of statistically significant differences. You can't prove that something doesn't exist. Look at an extreme - how do you prove there is NO diety? You can't, you can only offer evidence that he/she/it exists. – Roman Luštrik Apr 18 '13 at 18:23