In this section, parametric tests (based on a Normal distribution) and non parametric tests are discussed. In addition, there are sections on power analysis, sensitivity / specificity, errors, repeatability / reproducibility, bias / accuracy and multiple observer analysis.

**Null Hypothesis:** No difference between study groups

**Alternate Hypothesis:** There is a difference between the study groups

**Outcome Measure:** Variable used to test the hypotheses

**Test Statistic:** Calculation used to determine statistical significance

**P Value:** Probability statement is incorrect

**Statistically Significant:** p < 5 %

**Parametric Test:** Assumes Normal distribution

**Tests for Normality:
**

- Quantile-Quantile plots

*qqnorm(data)*

*qqline(data)*

- Shapiro-Wilk test

*shapiro.test(data)*

- Kolmogorov-Smirnov test

*ks.test(data,”pnorm”,mean=mean(data),sd=sd(data))*

**t-test:**

*t.test(data~group)*

*t.test(data1,data2,paired=FALSE)*

**Non Parametric Test:** Not Normal distribution

Data | Sample Size | Test |
---|---|---|

Continuous | > 50 | Normal |

< 50 Normal | t-Test | |

Not Normal | Wilcoxon | |

Ordinal | Wilcoxon | |

Nominal | Chi Squared |

**α:** Probability of incorrectly rejecting the null hypothesis (false positive)

**β:** Probability of incorrectly accepting the null hypothesis (false negative)

**Power:** Probability of correctly rejecting the null hypothesis (**Power = 1 – β)**

**Chi-square test:**

The prerequisites are:

**Random sample****Sufficient sample size**of the observations**Independence**at least 5 in 2 by 2 tables or at least 5 in 80% of larger tables, but no cells with an expected count of 0.**Expected cell count**

*data<-matrix(c(a,b,c,d),nrow=2)*

*chisq.test(data,correct=TRUE)*

*chisq.test(data,correct=TRUE)$expected *(for expected frequencies)

It is recommended to use Yates’ continuity correction (correct=TRUE), if the expected cell count is less than 10 . When the expected cell count is less than 5, the Chi Square test should not be used and the Fisher exact test is recommended.

**Wilxocon test:** Non parametric singed rank test for continuous data

*wilcox.test(data)*

**Power analysis**

- Difference desired to detect
- Spread of data
- Significance level (α)
- Test statistic (power)

*power.t.test(sd=s,delta=d,sig.level=0.05,power=0.8)*

**Errors:**

**Type 1:** Null hypothesis is incorrectly rejected (false positive; significance level (α)

**Type 2: **Null hypothesis is incorrectly accepted (false negative; statistical power)

**Errors are related to:**

- Difference desired to detect
- Spread of data
- Significance level (α)
- Test statistic (power)

In general:

Athroscopy Positive | Arthroscopy Negative | ||
---|---|---|---|

a + c | b + d | a + b + c + d | |

MRI Positive | a | b | a + b |

MRI Negative | c | d | c + d |

True Positive:

False Positive:

False Negative:

True Negative:

**Positive Predictive Value** is the probability that a person who is test positive has the condition:

**Negative Predictive Value** is the probability that a person who is test negative does not have the condition:

**Sensitivity,** or true positive rate, is the probability that a person who has the condition tests positive:

**Specificity**, or true negative rate is the probability that a person who does not have the condition tests negative:

**Accuracy** is the probability a test result is correct:

Or in the JGR / R console using the epiR 1 package:

*library(epiR)*

*mat<-matrix(c(a,c,b,d),ncol=2) *{enter values}

*epi.tests(mat)*

* Disease + Disease – Total*

*Test + a b *

*Test – c d *

*Total *

*Point estimates and 95 % CIs:*

*———————————————————*

*Apparent prevalence *

*True prevalence *

*Sensitivity *

*Specificity *

*Positive predictive value *

*Negative predictive value *

*Positive likelihood ratio *

*Negative likelihood ratio *

*———————————————————*

**Bias**

**Selection bias**; reduced by**randomisation****Confounding bias**; reduced by**stratification****Observational bias**; reduced by**blinding**

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1. Stevenson M, Nunes T, Heuer C, Marshall J, Sanchez J, Thornton R, et al. epiR: Tools for the Analysis of Epidemiological Data [Internet]. 2015. (R package). Available from: http://cran.r-project.org/package=epiR
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