# t-test on ancient sacrificial victims' bones: which one?

#### ButtMike

##### New Member
I am trying to determine if the difference between the expected quantity and the actual quantity is significant using SPSS. I have been told I need to use a one-tailed t-test but I am having difficulty trying to ascertain which test is the appropriate test. My research involves quantities of bones to determine primary deposition (were they killed where they were found) or secondary deposition (were they killed elsewhere and relocated to where they were found?). We know the overall distribution of bones and in primary sites we expect the distribution of small bones of the hands and feet to be similarly distributed as the rest of the human skeleton. However, we find the representation of hand/foot bones to be very different from that expected quantity . It is obvious when you look at the raw numbers but I wish to analyze and prove the differences are significant. So... we have an expected quantity on which to base the comparison. We also have the actual quantity recovered. I am using the two numbers as variables in a variety of t-test analyses but I am getting no results, albeit likely due to my ignorance of the data needed to correctly run the tests. The one-sample t-test "cannot be computed because the sum of the caseweights is less than or equal 1". I don't know the term caseweights. The independent-samples t-test asks for a grouping variable but I know of no such grouping variable. The paired-samples t-test also gives the error message "cannot be computed because the sum of the caseweights is less than or equal 1".

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#### Karabiner

##### TS Contributor
It is obvious when you look at the raw numbers but I wish to analyze and prove the differences are significant.
If you eyeball data and find interesting patterns here and there (which should be expected if the data are complex enough), then statistical tests of signficance seem quite meaningless. The probabilities produced by the significance test would not reflect the fact that several other comparisons have already been made (and found uninteresting) by the researcher when looking at the data.

The paired-samples t-test also gives the error message "cannot be computed because the sum of the caseweights is less than or equal 1".
What do you wish to compare - you have several sites, and for each site you have the expected and the actual number of bones? How many sites were there?

With kind regards

Karabiner

#### ButtMike

##### New Member
Thank you Karabiner. You are completely correct in that the quantities by themselves show a pattern so far off the norm that it makes the use of statistics in this case seem rather meaningless. I simply wish to cover my bases as there are certain to be critiques coming from the audience. There are 6 sites so the degree of freedom would be 5. Two of those sites combined contained 2,132 total bones so I don't know if including the other four sites (a combined total of 60 bones) helps the discussion. A statistics professor at my University stated they should be part of the analysis so that is why I am including those four sites even though they provide only 3 percent of the bones found.
And, yes, I will be happy to only discuss the wide range of quantities found within this cave system without including a statistical analysis if that is the route you suggest to take. It'll save us a ton of unnecessary(?) workload.

#### gianmarco

##### TS Contributor
@ButtMike:
as an archaeologist myself, I am curious about your issue, and I would like to help. However, from your description, I couldn't wrap my head around your data (what they look like or are organized).
Should you provide some more detail, possibly providing a sample dataset, I would not mind to try and help you.

Best
Gm

#### ButtMike

##### New Member
@ButtMike:
as an archaeologist myself, I am curious about your issue, and I would like to help. However, from your description, I couldn't wrap my head around your data (what they look like or are organized).
Should you provide some more detail, possibly providing a sample dataset, I would not mind to try and help you.

Best
Gm
I have a collection of over 10,000 bones and bone fragments collected from a single cave in Belize, most coming from sacrificial victims. This cave is quite large and has eight chambers, six of which yielded bones. However, over 85% of the bones were located in two of the eight chambers. I am analyzing the 2,100 or so children's bones. We proposed in a paper released in this past December that one area within chamber 5 has evidence of secondary placement as there is a large stack of long bones. The movement of the bones within the cave are part of a ritual clearing of the floor. You may know this already but evidence of primary deposition is in the presence of small hand and foot bones. When people pick up skeletons to move them to another place there is a strong tendency to move only the big bones (femora, radii, humeri, etc.) while overlooking the small bones that slip into the cracks and fissures. In a dark cave environment with only torch light to guide the participants it makes perfect sense that the dim lighting would cause many oversights. As a result the areas of primary deposition would have a larger presence of small hand and foot bones (metatarsals, metacarpals, tarsals, carpals, and phalanges) and a lesser presence in areas of secondary deposition. In this case we have an expected quantity of primary deposition bones. Since 12% of all childrens bones are in chamber 5 and 84% are in chamber 8 we expect 12 percent of the hand/foot bones (and of every type of bone for that matter) to be in chamber 5 and 84% to be in chamber 8. The data is starkly different with 3% in chamber 5 and 96% in chamber 8. Here's the big question: "Is the 9% difference between what we expect and what we actually have in chamber 5 (and likewise with chamber 8) statistically significant?"
I was hoping to solidify my argument but the numbers speak for themselves. I will be presenting a poster at the SAAs this April and it isn't critical to have the statistics to support my claims but I am also publishing the discussion in May and that is where I would like to have the numerical support.

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#### gianmarco

##### TS Contributor
Hello,
thanks for taking the time to describe your previous and current research in detail.

To cut the long story short, I understand that your main goal is to understand (or back up statistically) if the underrepresentation of small bones is statistically testable.

Now, it could be I am wrong or I am actually missing something, but what would I do (or what I would recommend if I was a reviewer) is to tabulate the number of bones per bone type that you actually observe along with those you would expect if the bodies were in primary deposition (i.e., if they were complete).

In other words, you may want to build a cross-tabulation with two columns, one representing the observed bones count, the other the expected bone counts. You should put in the rows each bone type you are interested in (e.g., femora, radii, humeri, etc etc). This would allow you to run a chi-square test of your observed vs expected counts, and should allow you to "gauge" to what extent (if any) some of your bone types are underrepresented.

As for software, I recall that the free PAST program can perform chisq test using two columns as described above (observed vs expected): see this PDF, pag 83 (https://folk.uio.no/ohammer/past/past3manual.pdf).

Hope this helps

EDIT:
of course the above assumes that you have an idea of how many individuals are represented (at least, in terms of MNI) in your assemblage.

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#### ButtMike

##### New Member
I hadn't considered the chi-square. This will be my goal this week. Let's see where it takes me. We have determined the overall subadult MNI at a very conservative 53. We will use this as the starting point and take it from there. I own SPSS so no worries. Thanks for the advice as it makes sense. (Wait... statistics make sense?)
I dislike emoticons yet I use them from time to time. Thank you very much Gianmarco. This is what I needed.

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#### gianmarco

##### TS Contributor
Hello. I am glad that makes sense.
Are you on ResearchGate or Academia? I would like to keep myself update about that interesting piece of research.

#### ButtMike

##### New Member
Hello. I am glad that makes sense.
Are you on ResearchGate or Academia? I would like to keep myself update about that interesting piece of research.
I am on both but I prefer Academia as it seems to be the choice of more archaeological academics. You can find me by searching either site for "buttmike". This nickname has a long story and it is not meant to be offensive. haha My name is Michael Prout. Look at our recent publication titled "Paleodemographics of Child Sacrifice at Midnight Terror Cave" to get an idea of the types if research I am doing at the CSULA Mesoamerican Archaeology Lab. Cheers!

#### ButtMike

##### New Member
I am on both but I prefer Academia as it seems to be the choice of more archaeological academics. You can find me by searching either site for "buttmike". This nickname has a long story and it is not meant to be offensive. haha My name is Michael Prout. Look at our recent publication titled "Paleodemographics of Child Sacrifice at Midnight Terror Cave" to get an idea of the types if research I am doing at the CSULA Mesoamerican Archaeology Lab. Cheers!
Gianmarco, I am trying to set up the data in SPSS and I have become confused. I know the overall bone totals for each type of bone, the expected totals, and the observed totals. When I attempt to enter this info into the crosstabs function I first select "Weight cases" in the Data tab. Should this number be the entire bone total of the specific type of bone (i.e hand and foot bones or epiphyses or metaphyses)? After entering those Frequencies I select the Analyze tab, then Descriptive Statistics, then Crosstabs where I enter the Expected category into the Column box and Observed category in the Row box. I chose the Chi-square test along with the Phi and Cramer's V option in the Statistics button and both the Observed/Expected Counts. I did not choose any option in the Percentages (Row, Column, or Total). The problem is that the operation produces a different Expected number. Any suggestions? I am attaching screenshots showing my selections as my descriptions suffer in comparison.
Hello. I am glad that makes sense.
Are you on ResearchGate or Academia? I would like to keep myself update about that interesting piece of research.
Gianmarco, I am trying to set up the data in SPSS and I have become confused. I know the overall bone totals for each type of bone, the expected totals, and the observed totals. When I attempt to enter this info into the crosstabs function I first select "Weight cases" in the Data tab. Should this number be the entire bone total of the specific type of bone (i.e hand and foot bones or epiphyses or metaphyses)? After entering those Frequencies I select the Analyze tab, then Descriptive Statistics, then Crosstabs where I enter the Expected category into the Column box and Observed category in the Row box. I chose the Chi-square test along with the Phi and Cramer's V option in the Statistics button and both the Observed/Expected Counts. I did not choose any option in the Percentages (Row, Column, or Total). The problem is that the operation produces a different Expected number. Any suggestions? I am attaching screenshots showing my selections as my descriptions suffer in comparison.

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#### j58

##### Active Member
Thankfully, I don't know much about SPSS, but I do know something about chi-squared tests. If your hypothesis is that the distribution of small bones differs from the theoretical version, then I think you only need 6 numbers: the observed and expected number of small bones in chambers 5, 8, and all others. Spoiler alert: based on what you've written, the p-value will be indistinguisible from 0.

#### gianmarco

##### TS Contributor
@ButtMike: are you sure you entered the dataset in the proper way? I have used SPSS in the past, and I recall that it is quite "tricky" to properly arrange data to get cross-tabulation. It requires the so-called "long form". I do not have SPSS right now, but I recall you should first define your data format in a separate facility, and then run the analysis. Your data should have three columns: two for the categories, one for the frequencies. Why don't you try the PAST program I was referring to earlier, which is quite popular among scientists (archaeologists included) and with a spreadsheet-like interface.

Hope this helps
Gm

#### ButtMike

##### New Member
Thankfully, I don't know much about SPSS, but I do know something about chi-squared tests. If your hypothesis is that the distribution of small bones differs from the theoretical version, then I think you only need 6 numbers: the observed and expected number of small bones in chambers 5, 8, and all others. Spoiler alert: based on what you've written, the p-value will be indistinguisible from 0.
The "thankfully" line made me chuckle. Thank you for the levity.

#### ButtMike

##### New Member
@ButtMike: are you sure you entered the dataset in the proper way? I have used SPSS in the past, and I recall that it is quite "tricky" to properly arrange data to get cross-tabulation. It requires the so-called "long form". I do not have SPSS right now, but I recall you should first define your data format in a separate facility, and then run the analysis. Your data should have three columns: two for the categories, one for the frequencies. Why don't you try the PAST program I was referring to earlier, which is quite popular among scientists (archaeologists included) and with a spreadsheet-like interface.

Hope this helps
Gm
I am not entering the dataset correctly. I was able to download the PAST program and tried entering the dataset. I do not see where to define my data. I have made three columns: Column A is the observed totals of each type of bone(listed in the nine rows) in the three areas of the cave (hand/foot in Operation V; hand foot in Operation VIII; hand/foot in Operation V Lot 1; epiphyses in Operation V; epiphyses in Operation VIII; etc.); Column B is the expected totals of each type of bone those same areas; and Column C is the frequency of each bone type in the entire collection. When I run the test after clicking the "Sample vs. expected" box it gives an error message stating I need to select two columns. It is not accepting the two columns I highlighted (A and B). This is why I feel I have not entered the dataset correctly.
I very much appreciate your willingness to help me tackle this challenge. I have not been posting my data here on talkstats to avoid authorship conflicts. Please forgive my reliance on your advice but I have nowhere else to turn. I have visited our university's Economic Statistics department who have been unable to assist as they sit confused. There is a communication barrier that I have not been able to overcome. I have also visited our Statistics tutors at the university library and they have asked for me to bring my PC into the lab because I no longer have a working login after my graduation. Haha Yikes! I will download PAST into my laptop and visit the tutoring lab once more.