Statistical analysis of the lithic furniture of the Ifri Ouberrid site in Ain Elleuh in the Moroccan Central Middle Atlas

The archeological potential of the central Medium Atlas is characterized by its richness and its diversity. The lithic furniture discovered in the site of Ifri Ouberrid is very significant and its exploration requires a powerful statistical tool allowing to simultaneously process all the quantities of objects collected in the various abductions. The Principal Component Analysis – A.C.P. is the most favorable and necessary method to fully understand and refine the work of archeologists.


I. INTRODUCTION
The cave of Ifri Ouberrid is located in the municipality of Aïn Elleuh, about 15km as the crow flies at the south of the city of Azrou. It's formed of two caves which pierce a cliff in oolithique limestone. The main cave measures 6m of breadth at the entrance on a height of 2,30m and about 10 meters deep. Excavations carried out in the main cave have allowed to reveal anthropogenic deposits that extend to a depth of about 1,80 m. Their analysis has identified 7 stratigraphic units that contain two important human's occupations: the first would go back to the early Neolithic and would be dated 6846 ± 56 cal. BP and the second would be of epipaleolithic age and would be located around 8222-8416 cal. BP. These two levels of occupation have delivered important quantities of lithic industry with a clear dominance of debitage products and nuclei attesting to intense debitage on the site itself.

II.
METHOD AND ANALYSIS The total number of lithic furniture collected in the Ifri Ouberrid site is 4051 pieces. All the archaeological levels have delivered, although in a visibly unequal way, objects in rather significant quantities. The  8  2  136  22  25  111  346  9  64  9  3  112  36  34  167  366  8  72  3  4  71  35  33  63  160  1  36  3  5  101  42  61  43  210  5  46  2  6  82  31  31  84  241  5  47  4  7  38  31  27  14  139  3  25  2  8  14  5  10  2  51  1  83  9  14  4  0  4  26  0  48  10  0  0  0  2  7  0  9  Total 690 222  249  716 2129 45 40  51 We know how to analyze each of these six variables separately, either by drawing a graph or by calculating numerical summaries. We also know that we can look at the links between two variables (for example shards and lamellas), either by making a graph of the cloud of dots type, or by calculating their linear correlation coefficient, or by carrying out the regression of one on the other. However, how to study six variables simultaneously, if only by making a graph ? The difficulty comes from the fact that the individuals (the removals) are no longer represented in a plane, space of dimension 2, but in a space of dimension 6 (each removal being characterized by the 6 objects detected). The objective of the Principal Component Analysis (A.C.P) is to return to a reduced dimension space by distorting the reality as little as possible. It is therefore necessary to obtain the most relevant summary of the initial data. We present below some results of the A.C.P. performed with SPSS software on this data. This will help to realize the possibilities of the method. The results have been limited to two decimals, although software programs generally provide much more, but they are rarely useful.

III. PRELIMINARY RESULTS
The software first provides the average, standard deviation, minimum and maximum of each variable. It is therefore, for the moment, univariate studies.

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The cloud of points in dimension 6 is not the same and its global dispersion has changed a lot. The first two factors alone account for almost the entire dispersion of the cloud, which allows to neglect the other 4. As a result, the 2-dimensional charts summarize almost exactly the actual configuration of the data in dimension 6: the goal (relevant summary of the small-scale data) is therefore achieved. But these two columns also make it possible to give a meaning to the factors and thus to the axes of the graphs.

Fig. 1: Representation of the variables
Thus, we see that the first factor is correlated positively, and quite strongly, with each of the 6 initial variables: the higher the removal, the greater the quantity of lithic furniture is significant on axis 1; conversely, the deeper it is, the lower the quantity; the axis 1 represents, in some ways, the overall result for all 6 types of objects considered compared to the abductions made. As regards axis 2, it opposes, on the one hand, shards, blades and lamellas (positive correlations), on the other hand, nucleus, debris and splinters and tools (negative correlations). It is therefore an axis of opposition between these two types of objects. This interpretation can be specified with graphs and tables relating to abductions. We present them below. Note that the presentation quality of each type of object is relevant. Debris and splinters are represented at 99,10%. It should be noted that each removal represents 1 element out of 10, hence a weight or a weighting of 1/10 = 0,10, which is provided by the first column of the table.

V. RESULTS ON THE ABDUCTIONS
The following 2 columns provide the coordinates of the removals, on the first two axes (the factors) and thus allowed to draw up the abductions graph. The latter makes it possible to specify the meaning of the axes, therefore of the factors.

Fig. 2: Representation of the abductions
We confirm that as well as the first axis represents the overall result of the removals: if we take their score on axis 1, we obtain the same ranking as if we take their overall average. Moreover, the highest removal on the graph, the one with the highest coordinate on axis 2, is the removal 5 which the results are the most contrasting in favor of debris and splinters and shards. This is exactly the opposite for removal 1 where 583 debris and splinters were obtained, 226 nucleus and 122 shards, but small quantities of tools, blades and lamellas. It should be noted that the removal 10 has a score close to 0 on the axis 2 because the quantity of objects obtained is very homogeneous for each type of object.

VI. CONCLUSION
The contributions of the variance removals according to the axes 1 and 2 (remember that we use the variance here to measure the dispersion) are given by the general contributions, ie the dispersion in dimension 6 (it is what is called the inertia of the cloud of abductions, the notion of inertia generalizes that of variance in any dimension, the variance always being relative to a single variable). These contributions are provided in percentages and make it possible to locate the most important removals at each axis (or the cloud in dimension 6). They are generally used to refine the interpretation of the results of the analysis. The first removal represents nearly 94% of the variance: it is preponderant in the definition of the axis 1, in contrast, the contribution of the removal 10 is almost null. Finally, concerning the quality of the representation, the removal 1 is represented at 100%: its representation is then very good.