# **3.1. Participants**

The target population of this study is comprised of third grade students from public primary schools in the region of Junin. There are 1,684 public primary schools in Junin, with a total of 32,700 third grade students enrolled (see Annex 7.4.a). The Junin study used a multistage cluster sampling approach.<sup>22</sup> The first stage applied a probability-proportional-to-size sampling method to select the clusters, which in this case were the schools.<sup>23</sup> To ensure there would be enough students from each type of school to run separate analyses and comparisons by groups, all public primary schools of Junin were divided into three subgroups by type of school, according to the categories established by the Ministry of Education: full grade schools, multigrade with more than one teacher (hereafter “multigrade”) and multigrade with only one teacher (hereafter “singleteacher”).<sup>24</sup> Schools were selected randomly from each group. The next stages consisted of randomly selecting elements within the original cluster: first, one section of each relevant grade in each school, and then a sample of students in each selected section (see Annex 7.3 for details). The oral test was administered to the random sample of students in each grade (5 students per class in 2<sup>nd</sup> and 6<sup>th</sup> grades, and 10 in 3<sup>rd</sup> grade). The written test was administered to all students from the selected third-grade classroom present at the time.

In this paper, we use a sample of all 475 third-grade students who took both the oral and written tests for the comparative analysis between the two tests.<sup>25</sup> The schools in the sample vary in size and location to account for the diversity of the population. The smaller school has 12 students and the largest has 1713, ranging from 1 to 52 teachers. All nine UGELs (the Local Education Management Offices mapped to the provinces) were represented and the distribution across provinces in the sample is similar to that of the population (see Table 20 in Annex 7.4.b).

**Table 4. Number of third grade students by type of school**

|||**Popul**<br>|**ation**<br>|**Sam**<br>|**ple**<br>|
|---|---|---|---|---|---|
|||**Freq.**|**Pct.**|**Freq.**|**Pct.**|
|**Total**||**32,700**|**100.00**|**475**|**100.00**|
||Single-teacher|3,157|9.65%|104|21.89|
|**Type of school**|Multigrade|12,582|38.48%|164|34.53|
||Fullgrade|16,961|51.87%|207|43.58|
|**School location**|Rural|16,595|50.75|307|64.63|
||Urban|16,105|49.25|168|35.37|

About 52 percent of students in the sample attend rural schools, and 60 percent go to full grade schools. The sample does not follow the distribution across types of schools found in the population. This bias, introduced with the sampling strategy, is corrected in the analyses by adjusting the sample according to the real probability of selection in the population with an

> 22 Cluster sampling is a sampling technique used when "natural" groupings are evident in a statistical population. In this technique, the total population is divided into these groups (or clusters) and a sample of the groups is selected. The clusters should be mutually exclusive and collectively exhaustive. In single-stage cluster sampling, all the elements from each of the selected clusters are used. In multi-stage cluster sampling, a random sampling technique is applied to the elements from each of the selected clusters. In this case, the authors opted for the latter, as using all sample elements in all the selected clusters was too costly and not necessary for the purpose of the study.

> 23 In this method, the probability of selecting a cluster in any given population varies conversely with the size of the cluster. That is, the probability of a school being selected in the sample is higher for schools with larger student populations and lower for those with fewer students.

> 24 About 10 percent of third grade students in Junin attend single-teacher schools, 38 percent attend multigrade schools and 52 percent attend full grade schools.

> 25 The psychometric analysis of the written test was done with a broader sample including all 1,001 students who took the written test (whether they took also the oral test or not).

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