# QQ Summary Statistics

### Description

This function calculates a set of summary statistics for the QQ
plot of two samples of data. The summaries are useful for determining
if the two samples are from the same distribution. If
`standardize==TRUE`

, the empirical CDF is used instead of the
empirical-QQ plot. The later retains the scale of the variable.

### Usage

1 |

### Arguments

`x` |
The first sample. |

`y` |
The second sample. |

`standardize` |
A logical flag for whether the statistics should be standardized by the empirical cumulative distribution functions of the two samples. |

`summary.func` |
A user provided function to summarize the
difference between the two distributions. The function should
expect a vector of the differences as an argument and return summary
statistic. For example, the |

### Value

`meandiff` |
The mean difference between the QQ plots of the two samples. |

`mediandiff` |
The median difference between the QQ plots of the two samples. |

`maxdiff` |
The maximum difference between the QQ plots of the two samples. |

`summarydiff` |
If the user provides a |

`summary.func` |
If the user provides a |

### Author(s)

Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, http://sekhon.berkeley.edu/.

### References

Sekhon, Jasjeet S. 2011. "Multivariate and Propensity Score
Matching Software with Automated Balance Optimization.”
*Journal of Statistical Software* 42(7): 1-52.
http://www.jstatsoft.org/v42/i07/

Diamond, Alexis and Jasjeet S. Sekhon. Forthcoming. "Genetic Matching for
Estimating Causal Effects: A General Multivariate Matching Method for
Achieving Balance in Observational Studies.” *Review of Economics and Statistics*.
http://sekhon.berkeley.edu/papers/GenMatch.pdf

### See Also

Also see `ks.boot`

,
`balanceUV`

, `Match`

,
`GenMatch`

,
`MatchBalance`

,
`GerberGreenImai`

, `lalonde`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | ```
#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
#
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)
#
# Do we have balance on 1975 income after matching?
#
qqout <- qqstats(lalonde$re75[rr$index.treated], lalonde$re75[rr$index.control])
print(qqout)
``` |