You do not mention anything about sample size and so on, but if you predict that age is a risk factor for needlestick injury you can use logistic regression analysis.

You need one categorical dependent variable like needlestick injury no= 0/yes=1. The you need two or more continuous or categorical variable as independent variables. Code dichotomous variables 0 and 1 (like girl, boy). Measure continuous variable so that more of something is high e.g. age

You might consider providing more information about your sample/population. Generally, ANOVA is used to "determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups" subject to various assumptions:

• Each group sample is drawn from a normally distributed population
• All populations have a common variance
• All samples are drawn independently of each other
• Within each sample, the observations are sampled randomly and independently of each other

Read more on this: http://www.real-statistics.com/one-way-analysis-of-variance-anova/assumptions-anova/

You may do a logistic regression anlysis.