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BJP Data related to claims 4 and 5 These statistics describe only residents of the biggest cities, 37% of the total population. Big cities and tiny towns have different culture, different police forces, and different patterns of crime. Although extrapolating data from big cities to the whole country is terrible analysis, I can't be sure that RAINN actually did this. The source is called out in RAINN's sources, and the numbers approximately match

NCVS Data related to claim 1 Data from the National Crime Victimization Survey (NCVS) lumps rape and sexual assault together, and defines sexual assault as:

A wide range of victimizations, separate from rape or attempted rape. These crimes include attacks or attempted attacks generally involving unwanted sexual contact between victim and offender. Sexual assaults may or may not involve force and include such things as grabbing or fondling. Sexual assault also includes verbal threats.

RAINN takes these two together and reports it in their infographic simply as "rape." This seems seriously misleading; Forcible rape is far more heinous than grabbing or fondling.

BJP Data related to claims 4 and 5 These statistics describe only residents of the biggest cities, 37% of the total population. Big cities and tiny towns have different culture, different police forces, and different patterns of crime. Although extrapolating data from big cities to the whole country is terrible analysis, I can't be sure that RAINN actually did this. The source is called out in RAINN's sources, and the numbers approximately match, but that is not conclusive.

The analysis RAINN is doing appears to stitch together data from a variety of different sources. They list their sources, but do not include any indication of how they picked and processed their data. Although this is better than the average completely unsourced infographic, it is still frustratingly opaque.

Claim 1: 31% of rapes are reported to police.

The 2015 National Crime Victimization Survey (NCVS) is an annual survey that asks people if they have been victimized by various crimes, including rape and sexual assault. It is conducted annually by the Bureau of Justice Statistics (BJS). The NCVS reports numbers about rape and sexual assault. The infographic reports the same numbers but talks only about rape. I find this misleading.

In 2014 and 2015 33.6% and 32.5% of rape/sexual assault incidents were reported to police. RAINN's statistics are taken from an average of several years of data. I think these numbers are close enough to assume that RAINN is faithfully reporting the results of their averaging.

This government report presents data on felony defendants in America's 75 largest counties. These counties contain large cities accounting for 37% of the total population, and are not nationally representative.

In 2009 in the 75 largest urban counties there were 412 felony rape defendants, of which 68% were convicted of something, 57% (235) were convicted of a felony, the rest a misdemeanor. The infographic claims that of the 11 cases referred to a prosecutor, 7 of them will result in a felony conviction. The two sources have a similar felony conviction rate; The difference could be explained by rounding errors in the 7 and 11. (Source: Table 21)

According to the same source, 89% of convicted rapists are incarcerated. (Source: Table 24)

https://www.bjs.gov/content/pub/pdf/fdluc09.pdf

This "answer" is too long for a comment, and is definitely incomplete. It is meant to supplement @BradC's answer, which is currently marked as a work in progress.

The analysis RAINN is doing appears to stitch together data from a variety of different sources. They list their sources, but do not include any indication of how they picked and processed their data. Although this is better than the average completely unsourced infographic, it is still frustratingly opaque. When the question was first posted, I spent a few frustrating hours researching this, and came to some of the same conclusions that @BradC did. I also found the following.

NCVS Data related to claim 1

Data from the National Crime Victimization Survey (NCVS) lumps rape and sexual assault together, and defines sexual assault as:

A wide range of victimizations, separate from rape or attempted rape. These crimes include attacks or attempted attacks generally involving unwanted sexual contact between victim and offender. Sexual assaults may or may not involve force and include such things as grabbing or fondling. Sexual assault also includes verbal threats.

RAINN takes these two together and reports it in their infographic simply as "rape." This seems seriously misleading; Rape includes things far more heinous than grabbing or fondling. I find it baffling that the NCVS does not report these separately.

Claim 4: 64% of prosecutions lead to a felony conviction (7 of 11)

This government report presents data on felony defendants in America's 75 largest counties. These counties contain large cities accounting for 37% of the total population, and are not nationally representative.

In 2009 in the 75 largest urban counties there were 412 felony rape defendants, of which 68% were convicted of something, 57% (235) were convicted of a felony, the rest a misdemeanor. The infographic claims that of the 11 cases referred to a prosecutor, 7 of them will result in a felony conviction. The two sources have a similar felony conviction rate; The difference could be explained by rounding errors in the 7 and 11 or it could be that RAINN took the average of several years of data. (Source: Table 21)

Claim 5: 85% of felony convictions are incarcerated (6 of 7)

According to the same source, 89% of convicted rapists are incarcerated. (Source: Table 24) This is very similar to the numbers presented by RAINN.

BJP Data related to claims 4 and 5 These statistics describe only residents of the biggest cities, 37% of the total population. Big cities and tiny towns have different culture, different police forces, and different patterns of crime. Although extrapolating data from big cities to the whole country is terrible analysis, I can't be sure that RAINN actually did this. The source is called out in RAINN's sources, and the numbers approximately match

NCVS Data related to claim 1 Data from the National Crime Victimization Survey (NCVS) lumps rape and sexual assault together, and defines sexual assault as:

A wide range of victimizations, separate from rape or attempted rape. These crimes include attacks or attempted attacks generally involving unwanted sexual contact between victim and offender. Sexual assaults may or may not involve force and include such things as grabbing or fondling. Sexual assault also includes verbal threats.

RAINN takes these two together and reports it in their infographic simply as "rape." This seems seriously misleading; Forcible rape is far more heinous than grabbing or fondling.

Lack of a conclusion

After looking at all of this data, I still do not know what to think. The data sources RAINN looked through are credible and authoritative, but the sources use a variety of definitions, methodologies and sample populations. The infographic was an attempt to weave these threads of evidence into a clear cut story. After reviewing the evidence, I still believe the broad strokes of the story, but I am skeptical of details and specifics. I believe that a distressingly low number of rapes end in incarceration, but the final number could be very different from 6 out of 1000.

The 2016 National Crime Victimization Survey (NCVS) is an annual survey that asks people if they have been victimized by various crimes, including rape and sexual assault. It is conducted annually by the Bureau of Justice Statistics (BJS). The NCVS reports numbers about rape and sexual assault. The infographic reports the same numbers but talks only about rape. I find this misleading.

The

The analysis RAINN is doing appears to stitch together data from a variety of different sources. They list their sources, but do not include any indication of how they picked and processed their data. Although this is better than the average completely unsourced infographic, it is still frustratingly opaque.

Claim 1: 31% of rapes are reported to police.

The 2015 National Crime Victimization Survey (NCVS) is an annual survey that asks people if they have been victimized by various crimes, including rape and sexual assault. It is conducted annually by the Bureau of Justice Statistics (BJS). The NCVS reports numbers about rape and sexual assault. The infographic reports the same numbers but talks only about rape. I find this misleading.

In 2014 and 2015 33.6% and 32.5% of rape/sexual assault incidents were reported to police. RAINN's statistics are taken from an average of several years of data. I think these numbers are close enough to assume that RAINN is faithfully reporting the results of their averaging.

This government report presents data on felony defendants in America's 75 largest counties. These counties contain large cities accounting for 37% of the total population, and are not nationally representative.

In 2009 in the 75 largest urban counties there were 412 felony rape defendants, of which 68% were convicted of something, 57% (235) were convicted of a felony, the rest a misdemeanor. The infographic claims that of the 11 cases referred to a prosecutor, 7 of them will result in a felony conviction. The two sources have a similar felony conviction rate; The difference could be explained by rounding errors in the 7 and 11. (Source: Table 21)

According to the same source, 89% of convicted rapists are incarcerated. (Source: Table 24)

https://www.bjs.gov/content/pub/pdf/fdluc09.pdf