Competence Differences in Literacy,Numeracy,and Problem Solving According to Sex

Abstract

This study aimed to determine individual- and country-level latent classes in literacy, numeracy and problem-solving competencies of individuals participating in the Programme for the International Assessment of Adult Competencies 2015. Specifically, it sought to distinguish these classes in relation to individuals’ sex and to identify the state of prediction of the determined latent classes by each person’s level of education. The study population consisted of 116,301 adults aged 16 to 65 years in 20 countries. Multilevel latent class analysis was conducted to consider the nested data structure and determine the number of latent classes. According to the results of the multilevel latent class analysis, Turkey and Chile were in the low achievement group in all skills, while Japan was in the most successful group. Moreover, the results revealed that sex and education level had a considerable influence on certain competence levels.

Keywords

adult competence education level PIAAC sex multilevel latent class analysis

Introduction

Many notable experimental works that focus on long-term national economic growth refer to human capital. A citizenry’s abilities in mathematics, science, and technology skills are understood as the fundamental aspects of human capital associated with the labor force, and this focus has made it easier for educators and policy makers to illustrate growth rates due to explanations of variations in the quality of the labor force (Hanushek & Kimko, 2000). When measured against an individual’s accomplishment in the labor market and the economy’s capacity to grow, cognitive achievement successfully measures students’ accomplishment in the standardized tests that substitute for the related labor market skills (Calero & Choi, 2017; Hanushek & Woessmann, 2008). Some studies have employed various adult skill measures to evaluate the quality of labor forces by country. Prominent examples include the International Adult Literacy Survey, the Adult Literacy and Life Skills Survey, and the Programme for the International Assessment of Adult Competencies (PIAAC).

Among the assessment studies, PIAAC was developed by the Organisation for Economic Co-operation and Development (OECD) to evaluate the competence of adults aged 16 to 65 years in literacy, numeracy, and problem solving in technology-rich environments (PSTRE; OECD, 2013b), which are deemed crucial information-processing skills for 21st-century economies. Policy makers, analysts, and researchers can benefit from the abundant data PIAAC offers in relation to the evolution of a population’s skills, and the relationships between education system and the labor market, for instance (OECD, 2016a).

This study aimed to determine individual- and country-level latent classes/clusters in literacy, numeracy, and problem-solving skills, based on the sex of individuals who participated in PIAAC 2015. It also sought to identify the state of prediction of the latent classes, which emerged at the individual level by level of education.

The Term “Sex” and Research on Sex Differences

“The word sex will refer to the male and female sex and the component biological parts that determine whether one is male or female . . . ” (Stoller, 1968, pp. vi-vii). As Education, Audiovisual and Culture Executive Agency (EACEA, 2010) stated, an approach originating in the 20th century suggests that innate differences in the biology of girls and boys cause the two sexes to be different in various aspects. Generally, men possess more spatial, numerical, and mechanical skills and are more inclined to conceive the world on the basis of objects, concepts, and theories, whereas women possess more advanced verbal skills and conceive the world on the basis of personal, aesthetic, and ethical terms, as they physically and psychologically mature before men. According to another approach, men’s and women’s social roles are influenced by history, culture, and society. Changes in their perceptions operate parallel to the progress of society (EACEA, 2010). The main premise of this perspective is that sex difference is a cultural fact rooted in a specific culture. This view sees education as a tool to clarify sex differences, to incentivize greater equality between the sexes and to challenge stereotyped assumptions (Arellano, 2013).

Sex difference research remains central to the study of gender issues in education, and is particularly outstanding in cross-cultural studies of achievement (EACEA, 2010). The results of PIAAC 2015 in relation to sex differences in skills across certain assessment domains between countries are remarkable. According to the Survey of Adult Skills (OECD, 2016a), no notable difference exists in literacy proficiency between sexes in almost all countries. However, a statistically meaningful difference, albeit small, has been reported for some of the states/economies examined: men scored 11 points higher in Turkey and 8 points higher in Chile compared with women, whereas women scored 5 and 6 points higher in Greece and Poland, respectively, in literacy proficiency. The greatest gap was found in Jakarta (Indonesia), with men scoring 14 points higher than women (OECD, 2016a). In addition, when the highest level competencies reached are examined according to sex, it is seen that a higher ratio of men is in the higher levels of competency. Generally, 10% of men and 8% of women managed to reach the fourth and the fifth competency levels in literacy. The same gender gap found in literacy is also found in numeracy, however, at an ever more pronounced level, where 12% of men and 7% of women have managed to reach the fourth and the fifth competency levels. Among all the countries examined, men’s average scores are 12 points higher than women in terms of numeracy, with the greatest sex gap being reported for Chile and Turkey (approximately 20 points) and the lowest gap found in Central and Eastern European countries such as Estonia, Lithuania, Poland, Slovenia, and the Slovak Republic. Concerning the literacy evaluation, Jakarta was the only place where the gap between sexes was 14 points greater compared with the results on numeracy (8 points; OECD, 2016a). In relation to PSTRE, although men were likely to possess a small advantage over women, the sex gap was small. Generally, 33% of men and 29% of women achieved Levels 2 or 3. Nonetheless, the ratio of men and women who were unsuccessful at the information and communication technologies core exam or who were unfamiliar with computers was rather steady, albeit somewhat greater among men in some of the states/economies (OECD, 2016a).

Differences in achievement based on sex can also be seen in international studies which collected data from young people and were undertaken in different years. For instance, according to the Programme for International Student Assessment (PISA) 2012, boys’ scores in mathematics in 38 OECD states/economies exceeded that of girls by approximately 11 points. Nevertheless, among 10% of the students with the highest scores in mathematics, boys scored on average 20 points greater than girls (OECD, 2015). Furthermore, the PISA 2012 evaluation of problem solving (a computer-based test) showed that 15-year-old boys had slightly higher scores (7 points higher) than girls (OECD, 2013a). These findings can be associated with the numeracy and PSTRE skills which are dealt with in this study. The results of yet another international study, the Trends in International Mathematics and Science Study (TIMSS) 2015, demonstrated that there was no difference in the achievements of the fourth- and eighth-grade students based on sex, with girls being significantly more successful in mathematics than boys in some countries and vice versa in others (Mullis, Martin, Foy, & Hooper, 2016). Consequently, it can be observed that different findings have been gathered by research studies in international contexts carried out with different age groups. This may originate from the fact that the age groups are different and the research studies have different understandings of literacy. For this reason, sex and the three skills (literacy, numeracy, and PSTRE) are evaluated in this study together.

Differences in adult skills according to sex may also result from differences in individuals’ levels of education. For instance, Eurostat (2016)’s study points out that regarding the completion of tertiary education (bachelor’s, master’s, or doctoral), the sex gap is turning in favor of women in European countries. According to the results of the study conducted by Eurostat, when the distribution of individuals aged 15 to 64 years with tertiary education was examined in 2016, Switzerland had the highest percentage of males (41.4), while Italy had the lowest (13.4). The highest percentage of education for women was found in Estonia (42.6), which was also the country with the highest sex gap (17.2). The lowest education percentage for women was observed in Turkey (14.5). Although the percentage of educated individuals increased in both sex groups from 2007 to 2016, it remains very low in some countries. In 28 out of 33 countries, women have a higher percentage of education (Eurostat, 2016). This also indicates that the proportion of women receiving education at this level has increased over the years. Other studies have also shown that the rate of female participation in education has exceeded that of men in the majority of European countries. For example, according to Barro and Lee’s (2010) Educational Attainment Data, in 21 out of 24 developed economies, women born in the second half of the 1970 have graduated from university at a higher ratio than men. The review presented above suggests that many factors may be associated with the sex gap, including individuals’ educational level and national norms. However, PIAAC questionnaires include a limited number of variables regarding the effect of sex on skills. For this reason, educational level was selected as an independent variable in this study. Furthermore, most previous studies on sex differences in education only surveyed school-age students for sex differences in reading, mathematics and/or science assessment domains, primarily focusing on international large-scale tests such as PISA and TIMSS (e.g., Marks, 2008; Solheim & Lundetræ, 2016; van Langen, Bosker, & Dekkers, 2006). Only a study (Arora & Pawlowski, 2017) evaluating the results of PIAAC for the comparison of sex differences in the achievement of numeracy exists. In that study, the authors indicated that the gap in terms of sex in mathematics achievement of 15-year-olds who participated in the PISA 2003 was seen to remain the same or advance in PIAAC 2012, when the group members were around 23. The gap between the sexes, in fact, increased in many countries around the world during this time period. Finland and the United States, however, experienced the highest rates of increase.

Although previous research on sex differences in education has compared data from different countries, no comparative study exists that has simultaneously examined changes over three basic assessment domains (literacy, numeracy, and PSTRE) in different countries. In this context, the present study makes four principal contributions to the literature. First, comparison by sex was undertaken by considering all three assessment domains (literacy, numeracy, and PSTRE) in all countries that participated in PIAAC 2015. This offers an opportunity to examine the validity of stereotypes that suggest that females are more successful in literacy, whereas males are more successful in numeracy and problem solving. Second, most studies have performed a comparison between countries at a single level, either individual- or country-based (e.g., Arora & Pawlowski, 2017; Lindemann, 2015; Marks, 2008; Solheim & Lundetræ, 2016). However, in this study, a two-level analysis comprising both individual and country level was undertaken to obtain more reliable results. Third, while previous studies on differences in achievement based on sex are largely confined to students at school age, this study focuses on young and middle-aged adults and their skills in PIAAC, which is assumed to be methodologically robust and relatively original (OECD, 2016c). Fourth, this study proposes that homogenous clusters or classes are created from heterogeneous groups, meaning that individuals with similar traits constitute the latent classes by coming together. This makes it easier to understand the data by examining those with similar characteristics in the same group, and allows for unpredictable relations to emerge (e.g., the majority of individuals with high-level literacy proficiency are male). Furthermore, latent class analysis (LCA) analyses both categorical (e.g., sex) and continuous (e.g., achievement) variables simultaneously unlike other models (e.g., hierarchical linear models). Thus, the current study presents a full picture by approaching sex and the three basic assessment domains together. In this context, the research seeks to answer the following questions:

What are the latent clusters or classes at individual and country level created by sex and the literacy, numeracy, and problem-solving skills of individuals who participated in PIAAC 2015?

To what extent are the latent clusters that emerged at the individual level predicted by level of education?

Method

Population and Sample

The target population for the survey comprised individuals aged 16 to 65 years who resided in one of the countries that participated in PIAAC 2015 at the time of data collection (OECD, 2016b). Of the 33 participant countries, 13 were excluded from the analysis due to a lack of data regarding the dependent or independent variables investigated in this study. For example, some countries did not possess the necessary data because the PSTRE test was conducted online. As a result, analyses were carried out using the data obtained from 20 countries. The sample was selected from the adults aged 16 to 65 years from each country using a multistage sample design for each stage of selection (OECD, 2016a). Furthermore, the total sample of the study comprised 116,301 adults (54,681 males and 61,618 females). Some characteristics of the sample are presented in Table 1.

Table 1.

Some Characteristics of the Adults Participating in PIAAC.

Countries	Mean age, years			Frequencies
Countries	All	Male	Female	Male	Female	Sum
Belgium	41	41	41	2,700	2,763	5,463
Chile	39	38	40	2,198	3,014	5,212
Czech Republic	39	38	39	2,769	3,333	6,102
Denmark	44	44	44	3,615	3,713	7,328
Finland	42	42	42	2,757	2,707	5,464
Greece	41	40	41	2,220	2,705	4,925
Ireland	40	40	40	2,744	3,239	5,983
Israel	37	37	37	2,790	2,748	5,538
Japan	42	42	42	2,517	2,761	5,278
Korea	41	41	41	3,102	3,565	6,667
Lithuania	43	41	44	2,033	3,060	5,093
The Netherlands	42	42	41	2,545	2,624	5,170
Norway	40	40	40	2,655	2,473	5,128
Poland	31	31	32	4,733	4,633	9,366
Russia	36	34	37	1,344	2,547	3,892
Slovak Republic	39	39	40	2,706	3,017	5,723
Slovenia	41	41	42	2,616	2,715	5,331
Sweden	41	41	41	2,253	2,216	4,469
Turkey	38	38	38	2,647	2,630	5,277
The United Kingdom	41	41	41	3,737	5,155	8,892
Mean	40	40	40	2,734.05	3,080.90	5,815.05

Note. PIAAC = Programme for the International Assessment of Adult Competencies.

As can be seen in Table 1, the ratio for participating in the assessment in terms of sex are close to each other. Since the mean age according to countries are in the range of 31 to 44 years, it can be expressed that the sample is generally composed of middle-aged adults.

Tools for Data Collection

The data collection of the Survey of Adult Skills was undertaken from April 2014 to the end of March 2015 (OECD, 2016a). The study was implemented by trained interviewers either at the respondent’s house or at a place agreed on by both the interviewer and respondent. Data are collected via questionnaire and achievement tests from participants. The questionnaire is composed of 258 variables that were calculated at least 258 times, most frequently more than 400 times. As each and every country has unique needs, there were different number of items for countries (Yamamoto, Khorramdel, & von Davier, 2013) and it required 30 to 45 minutes to complete depending on the respondent (OECD, 2016a). It measures demographic traits, educational familiarity, employment market practices, and activities regarding the abilities that are measured. In this study, information on individuals’ sex and educational level were obtained from questionnaire data. In 324 booklets, 166 items made up the cognitive measurement and they are divided as such: 76 literacy items, 76 numeracy items, 14 problem-solving items. Each booklet is completed in 50 to 60 minutes. Two formats namely short open-ended answers on papers and open responses such as marking the correct word on computer are used in applying the cognitive items. The answers given by the respondents were sorted into the following four groups: right, wrong, excluded, and not demonstrated (Yamamoto et al., 2013). Data regarding PIAAC 2015 were obtained from the OECD’s international PIAAC website (http://vs-web-fs-1.oecd.org/piaac/puf-data/SPSS/).

In the Survey of Adult Skills, literacy is defined as “understanding, evaluating, using and engaging with written texts to participate in society, to achieve one’s goals, and to develop one’s knowledge and potential” (OECD, 2012c, p. 20), and numeracy is defined as “the ability to access, use, interpret and communicate mathematical information and ideas, in order to engage in and manage the mathematical demands of a range of situations in adult life” (OECD, 2012c, p. 34). For PSTRE, required competency is defined as “using digital technology, communication tools and networks to acquire and evaluate information, communicate with others and perform practical tasks” (OECD, 2012c, p. 47). The outcomes of the assessment are stated with a scale of 500 points in which the higher scores refer to higher proficiency. In order to better comment on the scores, the scale is separated into six proficiency levels regarding literacy and numeracy (ranging from the lowest below Level 1 to the highest at Level 5) and four levels for PSTRE (from the lowest below Level 1 to the highest at Level 3; OECD, 2016a). For the educational level variable, PIAAC used the classification ranges from International Standard Classification of Education (ISCED), including 1 to 6 from the lowest to the highest level of education. The classification of education levels presented comprises the following (OECD, 2013b): 1 = No formal qualification or below ISCED 1 and ISCED 1, illiterate and primary education, 2 = ISCED 2, lower secondary education, 3 = ISCED 3 (A, B, C), secondary education, 4 = ISCED 4 (A, B, C), postsecondary education, 5 = ISCED 5 (A and B) bachelor degree and master degree, first stage of tertiary education, and 6 = ISCED 6, second stage of tertiary education.

Data Analysis

In order to better understand the results from PIAAC, the addressed variables (i.e., literacy, numeracy, and PSTRE skills and sex at individual level and the same skills at the country level) should be grouped according to their similar characteristics due to the fact that PIAAC data have heterogeneous characteristics. This grouping is conducted with LCA. A latent (unobserved or hidden) variable represents a concept that cannot be measured directly. Observed variables are needed in order for these variables to be measured. The concept named latent class represents the categories of the latent variable. In the LCA, it was assumed that all of the observable variables caused an unobservable latent variable, and that latent classes (groups or subtypes of cases) are formed based on the patterns of the variables (Vermunt & Magidson, 2004). In short, homogeneous clusters or classes are created from heterogeneous groups. Furthermore, unlike parametric analyses, LCA analyses both categorical (e.g., sex) and continuous (e.g., achievement) variables at the same time. In this context, latent classes were created in this study at the individual and country levels, and considered the literacy, numeracy, and PSTRE skills and sex of the individuals. Afterward, which latent group each individual is in, meaning which latent class the individual is a member of is examined. For this reason, multilevel latent class analysis (MLCA) was used since it can analyze both the individual and country level as well as the common effect of country and individual variables.

Plausible values (PVs) have been used in revealing literacy, numeracy, and PSTRE skills of individuals. PVs—which are multiple imputations—drawn from a posteriori distribution by combining the item response theory scaling of the cognitive items with a latent regression model using information from a population model (Yamamoto et al., 2013). As Yamamoto et al. (2013) used PV to scale PIAAC data, in this study, the weighted mean of each of the 10 PVs of each country, and afterward the average of these 10 means was computed. Then, as the first step, MLCA was conducted with attention to the hierarchical data structure (individuals are nested in countries), and determined the number of latent classes in individuals’ literacy, numeracy, and PSTRE skills in relation to their sex at the individual and country levels. As a result of MLCA, clusters are obtained at the individual level and Group Classes (GClasses) are obtained at the country level.

After analyzing the possible models at the individual and country levels in the MLCA, the simplest model with the minimum number of latent classes and predictive parameters is preferred as a means of determining the most suitable model (Vermunt, 2003; Vermunt & Magidson, 2004). In this study, to obtain the optimal number of clusters, the log-likelihood and the Bayesian information criterion (BIC) were used. These are statistical measurements that show how compatible a model is with data. It is utilized to determine which model is the data more compatible with when predictions are made according to more than one model. For the selection of the model, the results of the simulation study by Lukočienė, Varriale, and Vermunt (2010) were considered and the BIC value was used as a criterion. At the second stage, a three-step analysis was undertaken to determine the predictive ability of the education-level variable at the individual level for the emerging multilevel latent classes. The relationship between educational level of adults and clusters emerged at the individual level and is examined with a three-step process within this scope in this study. Latent Gold 5.1 package program, which allows for MLCA with its latest version, was used for the data analysis as it user friendly (Vermunt & Magidson, 2013).

Results

Latent Student and Country Classes

As the first step, MLCA at the individual and country levels was conducted based on data set requirements (individual comprise nested countries). The results of the analysis in the Table 2 are presented as “cluster” at individual level, and as “class” at country level. Since country- and individual-level analyses are carried out in the model simultaneously, different models are tried to identify the model which fits data the best both at individual and country level. Table 2 presents the log-likelihood values, BIC, and the numbers of parameters.

Table 2.

The Fit Measures of the Results of Analysis on Literacy, Numeracy, and PSTRE.

Models, individual and country level	LL	BIC (LL)	Npar
Literacy
8Cluster-11GClass	−659171.8708	1319636.433	111
8Cluster-10GClass	−659055.3843	1319310.2932	103
9Cluster-10GClass	−659673.5364	1320697.994	116
Numeracy
6Cluster-7GClass	−670058.409	1340803.924	59
6Cluster-6GClass	−670012.6045	1340642.44	53
7Cluster-6GClass	−669967.4154	1340656.875	62
PSTRE
7Cluster-8GClass	−455489.2099	911835.3209	76
7Cluster-7GClass	455468.8442	911715.6646	69
8Cluster-7GClass	−455580.7187	912052.1636	79

Note. PSTRE = problem solving in technology-rich environments; LL = log-likelihood; BIC = Bayesian information criterion; Npar = numbers of parameters; the fit models are in boldface.

In considering the results from MLCA, the BIC estimate gradually decreased from the 1Cluster-1GClass model to the 8Cluster-10GClass model for literacy. However, the increase in the BIC for the 9Cluster-10GClass model suggests that 8Cluster-10GClass was the favored model for literacy. The results also show that the BIC was smallest for the 6Cluster-6GClass model for numeracy and for the 7Cluster-7GClass model for the PSTRE. When the results are broadly evaluated, it can be seen that the classes that emerged at the individual level are between 6 and 8 clusters, whereas the classes that emerged at the country level are between 6 and 10 GClass. It can be observed that the highest number of classes are in the groups composed of literacy and sex variables at the country level. This indicates that the addressed variables are more heterogeneous than the other variables. The class probabilities of the models (class size) and the mean value at each class of dependent variables which represents the average scores of the dependent variables (e.g., literacy) of the individuals in that class (country level) based on these models are displayed in Table 3.

Table 3.

The Class Probabilities of the 10-6 and 7GClass Models and the Mean Values at Each Class of Dependent Variables.

GClasses	1	2	3	4	5	6	7	8	9	10
Literacy
Size	0.06	0.04	0.02	0.11	0.08	0.05	0.11	0.11	0.07	0.35
Mean	225.88	251.48	266.19	271.66	271.93	272.77	276.09	279.60	284.56	297.23
Male	0.48	0.49	0.40	0.42	0.47	0.50	0.45	0.35	0.50	0.48
Female	0.52	0.51	0.60	0.58	0.53	0.50	0.55	0.65	0.50	0.52
Countries	Chile Turkey	Greece Israel Slovenia	Lithuania	The United Kingdom	Korea Slovak Republic	Ireland Denmark Belgium Poland	Czech Republic	Russia	Finland The Netherlands Norway Sweden	Japan
Numeracy
Size	0.07	0.14	0.12	0.11	0.14	0.42
Mean	216.04	258.61	262.54	274.49	276.44	288.24
Male	0.47	0.44	0.46	0.34	0.46	0.48
Female	0.53	0.56	0.54	0.66	0.54	0.52
Countries	ChileTurkey	IrelandThe United KingdomIsraelSlovenia	LithuaniaGreecePolandKorea	Russia	BelgiumCzech RepublicDenmarkSlovak Republic	JapanFinlandThe NetherlandsNorwaySweden
PSTRE
Size	0.05	0.10	0.03	0.20	0.05	0.21	0.36
Mean	254.95	257.22	269.03	279.14	280.49	284.67	294.37
Male	0.43	0.57	0.50	0.40	0.50	0.48	0.52
Female	0.57	0.43	0.50	0.60	0.50	0.52	0.48
Countries	ChileGreeceLithuania	Turkey	IsraelSlovenia	IrelandThe United KingdomRussia	PolandBelgiumDenmark	KoreaSlovak RepublicCzech RepublicThe NetherlandsNorway	JapanFinlandSweden

Note. PSTRE = problem solving in technology-rich environments; class sizes are in boldface.

As regards literacy, nine small clusters (Clusters 1 to 9) and one large cluster (Cluster 10) existed at the country level. As the largest cluster, 35% of the students were assigned to Cluster 10, which consisted of those who had high scores in literacy. The literacy scores of the students increased from Cluster 1 to Cluster 10. In this context, the Cluster 1 is named as the low achievement group, while the Cluster 10 is named as medium–high achievement group. At the country level, for numeracy existed one large (Cluster 6) and five small clusters (Clusters 1 to 5). Cluster 1 was the smallest cluster consisting of countries with the lowest scores in numeracy. The numeracy scores of countries increased from Cluster 1 (low achievement) to Cluster 6 (medium–high achievement). At the country level for PSTRE, there existed one large (Cluster 7), two medium (Clusters 4 and 6), and four small clusters (Clusters 1, 2, 3, and 5) with the PSTRE scores of the countries increasing from Cluster 1 (low achievement) to Cluster 7 (medium achievement). The first six clusters represented first-level competencies and the scores of the individuals increased steadily. Table 4 presents the class probabilities of the 8-6 and 7Cluster models and the mean value at each class (individual level) of dependent variables based on these models.

Table 4.

The Class Probabilities of the 8-6 and 7Cluster Models and Mean at Each Cluster of Dependent Variables.

Clusters	1	2	3	4	5	6	7	8
Literacy
Size	0.01	0.07	0.05	0.16	0.19	0.24	0.07	0.21
Mean	114.28	211.68	232.92	259.39	261.45	294.97	299.68	321.36
Competence	Below 1	1	2	2	2	3	3	4
Male	0.52	0.29	0.97	0.45	0.34	0.26	0.99	0.53
Female	0.48	0.71	0.03	0.55	0.66	0.74	0.01	0.47
Numeracy
Size	0.03	0.17	0.22	0.20	0.25	0.13
Mean	154.13	226.63	263.26	272.07	302.03	324.34
Competence	Below 1	2	2	2	3	4
Male	0.35	0.41	0.00	0.98	0.27	0.85
Female	0.65	0.49	1.00	0.02	0.73	0.15
PSTRE
Size	0.06	0.11	0.02	0.37	0.31	0.06	0.07
Mean	219.38	257.72	260.21	265.84	307.92	313.16	330.13
Competence	Below 1	1	1	1	2	2	2
Male	0.38	0.82	0.77	0.32	0.54	0.02	0.96
Female	0.62	0.18	0.23	0.68	0.46	0.98	0.04

Note. PSTRE = problem solving in technology-rich environments; class sizes are in boldface.

As shown in Table 4, for literacy there were two medium (Clusters 6 and 8) and six small clusters (Clusters 1 to 5 and 7). As the smallest cluster, Cluster 1 consisted of individuals who had low scores in literacy. The literacy scores of individuals increased from Cluster 1 (below the first level) to Cluster 8 (the fourth level). There were more women in Clusters 2, 5 and 6 and more men in Clusters 3 and 7. Concerning the individual level for numeracy, there were four medium (Clusters 2 to 5) and two small clusters (Clusters 1 and 6). As the largest cluster, 25% of the students were assigned to Cluster 5. As the smallest cluster, Cluster 1 comprised students with low scores in numeracy. When the distribution of sex in the clusters was evaluated, it was noted that Cluster 3 was almost completely composed of women. Furthermore, there was a higher number of women in Clusters 1 and 5 and a higher number of men in Clusters 4 and 6. The proportion of women and men was similar in Cluster 2. The numeracy scores of the students increased from Cluster 1 (below the first level) to Cluster 6 (high achievement). At the individual level for PSTRE, there were two large (Clusters 4 and 5) and five small clusters (Clusters 1, 2, 3, and 6). As the largest cluster, Cluster 4 contained 37% of the students and the lowest clusters were found to be Clusters 1 and 6. The PSTRE scores of the students increased from Cluster 1 (below Level 1) to Cluster 7 (Level 2). No other cluster existed with a problem-solving average that was sufficient for the third level of competence. When the distribution of sexes in the clusters was evaluated, it was observed that women represented a higher percentage of Clusters 1, 4, and 6; whereas men were more numerous in Clusters 2, 3, and 7. Cluster 5 contained an almost equal number of women and men.

Relations Between Individual-Level Clusters and Individuals’ Educational Levels

Following the determination of the clusters, a process carried out according to the most suitable models, a three-step analysis was conducted on the data. Table 5 presents the probabilities and parameters of the three-step model for all of the education levels at the three competence assessment domains. As demonstrated by the results of the Wald test (Table 5), education level predicted the latent class membership which means that the individual is involved in the relevant subgroup (latent class) in a significant way in all of the competence assessment domains.

Table 5.

The Probabilities at Each Latent Cluster and Parameters of the Three-Step Model for all of the Competence Assessment Domains According to Education Level.

Wald	Clusters	Competence level of clusters	Class size	Education level
Wald	Clusters	Competence level of clusters	Class size	1	2	3	4	5	6
Literacy
16977.6335*	1	Below 1	0.01	0.04	0.01	0.00	0.00	0.00	0.01
	2	1	0.11	0.64	0.23	0.07	0.00	0.04	0.01
	3	2	0.09	0.16	0.15	0.10	0.04	0.05	0.00
	4	2	0.17	0.00	0.35	0.25	0.04	0.05	0.00
	5	2	0.23	0.15	0.06	0.26	0.56	0.20	0.51
	6	3	0.19	0.00	0.11	0.15	0.22	0.35	0.00
	7	3	0.08	0.00	0.06	0.11	0.08	0.08	0.01
	8	4	0.12	0.02	0.02	0.06	0.06	0.24	0.45
Numeracy
11372.4666*	1	Below 1	0.05	0.34	0.09	0.02	0.01	0.00	0.02
	2	2	0.23	0.60	0.36	0.24	0.14	0.11	0.14
	3	2	0.21	0.00	0.22	0.25	0.40	0.17	0.11
	4	2	0.21	0.04	0.27	0.30	0.30	0.11	0.03
	5	3	0.20	0.01	0.05	0.12	0.07	0.42	0.41
	6	4	0.10	0.01	0.02	0.07	0.08	0.19	0.29
PSTRE
138733.2907*	1	Below 1	0.08	0.14	0.13	0.10	0.20	0.03	0.00
	2	1	0.11	0.22	0.21	0.17	0.00	0.03	0.00
	3	1	0.03	0.17	0.01	0.02	0.00	0.04	0.00
	4	1	0.40	0.47	0.30	0.42	0.55	0.37	0.48
	5	2	0.30	0.00	0.34	0.26	0.22	0.36	0.33
	6	2	0.04	0.00	0.00	0.01	0.00	0.09	0.12
	7	2	0.05	0.00	0.00	0.03	0.02	0.08	0.07

Note. PSTRE = problem solving in technology-rich environments. Proportions ≥0.30 are in boldface.

p < .05.

As shown in Table 5, in the case of literacy a 64% probability was stated that the individuals in Cluster 2 (first competence level) would respond to education level as “1 (below ISCED 1, ISCED 1 and ISCED 2, i.e., illiterate, primary, and lower secondary education).” Moreover, Cluster 1 contained an almost equal number of women and men with the lowest literacy achievement, and Cluster 2 displayed a low level of literacy achievement and was composed of a high number of women. This situation can be interpreted as women with a low level of education have low-literacy skills. In the classes where males represent the majority (Clusters 3 and 7), it can be observed that there is no significant possibility of males’ having low-literacy skills according to the level of education. In contrast, in the classes where females are the majority (Clusters 2, 5, and 6), the state of being at a high level of competence increases as the level of education increases.

As seen in the results, low-level ISCED (i.e., illiterate, primary, and lower secondary education) were generally in Cluster 2 for literacy and the numeracy. Furthermore, higher levels of education, that is tertiary education, were most likely to be in Cluster 5 for numeracy. Given that women were in the majority in Cluster 5, it can be interpreted that women with a high level of education often achieved higher in numeracy. For PSTRE, individuals with the highest and lowest levels of education were most likely to be in Clusters 4 and 5. In this context, it can be stated that an individual’s level of education does not affect his or her PSTRE achievement.

Discussion, Conclusion, and Suggestions

The main objective of the present study was to determine country- and individual-level latent classes in literacy, numeracy, and PSTRE competencies based on the sex of individuals who participated in PIAAC 2015, and to identify the predictive state of the determined latent classes by individuals’ educational levels. When all of the classes that emerged at the country level were evaluated, the results showed that Chile and Turkey were in the lowest or low achievement groups concerning all skills. Both are developing countries and possess similar characteristics, such as average year of education being lower than the OECD average of 17.5 years (17.1 in Chile and 16.9 in Turkey; OECD, 2016a). In addition, the achievements of students in both countries could be primarily explained by the economic, social and cultural factors (OECD, 2012b). The high effect of economic, social, and cultural factors on education can be interpreted as a result of the lack of equality of opportunity in education provided in both countries. In the same evaluation, it was seen that the Czech Republic, Finland, the Netherlands, Norway, Sweden, and Japan were at the third level of competence in both literacy and numeracy. These highly successful countries are also economically strong. Furthermore, the reasons behind these countries’ having high-level skills (e.g., providing equality of opportunity in education, the quality of the teacher training offered, school curriculum, duration of compulsory education, cultural values given by the teacher, and students’ feeling happy at school) can also be examined in future research.

In all three skill areas, Japan is the only East Asian country in the most successful group. In Japan, particular importance is placed on education and this policy has nourished the country’s economy and helped maintain economic growth due to the production of high technology. Consequently, since World War II it has had high-quality human capital; meaning that the Japanese enabled the creation of personal, social, and economic welfare. Furthermore, the value Japanese society places on education is epitomized by its first-rate teaching force and the presence of high-technology materials in schools, as well as the high level of support provided in the home by families (OECD, 2012d). All of these factors contribute to Japan’s success in all three skill assessment domains and competencies. In this context, the educational policies that the Japanese follow can be examined in detail, since they may guide other countries.

The results from the MLCA revealed that sex had an influence on some clusters at the individual level for all competencies. For example, in literacy, the ratio of males in the second and third competence levels was higher than that of females, and highest at the third level. Thus, it can be inferred that men have higher literacy scores in the highest ability level of literacy. It is observed that this finding is inconsistent with the studies in the literature field which have been conducted with 15-year-old individuals in the recent past. For example, a study using PISA 2000 data determined that sex differences in the distribution of boys and girls in school systems in almost all of the participant countries facilitated girls’ advantage in reading achievement (Marks, 2008). On the other hand, the finding that suggests that men are at higher levels in the high-competency-level group is consistent with studies conducted with individuals aged 15 years in the more recent years. For instance, when the findings of PISA from 2009 to 2015 were compared, it was suggested that the difference between the sexes in favor of girls was decreasing and that boys’ reading achievement was increasing. From 2009 to 2015, the sex gap favoring girls was reduced by 12 points in reading, and the performance of boys, particularly those with high achievements, further improved, whereas the performance of girls (especially those with the lowest achievement) worsened (OECD, 2016c). When the results are evaluated together with the literature, it can be interpreted that the stereotypes that suggest that females are more successful in literacy are not valid. Furthermore, because the PIAAC design differs from PISA (Solheim & Lundetræ, 2016) in some aspects (text type [continuous, fictional], item type, and differences in motivation for testing), there may be differences in literacy according to sex. In fact, men might be considered to be at an advantage compared with women because of the design of PIAAC (e.g., the small number of open-ended questions), and this can make it possible for men to be in a higher competency level in literacy.

Concerning numeracy competence, the great majority of the individuals who reached the fourth level of competence were male. Although most of the individuals at the third competence level were female, when the third and fourth competence levels were evaluated together, it was seen that the proportion of men was higher than that of women. Thus, men also achieved higher levels of success in numeracy. These results are generally consistent with the established literature in the field. For example, boys received better scores than girls in mathematics in PISA 2012 (OECD, 2015). The results of TIMSS 2015, another international study, demonstrated that the differences in student achievement at the fourth- and eighth-grade levels according to sex varied from one country to another (Mullis et al., 2016). These findings indicate that not only is there a general tendency for men to have a higher level of achievement than women but there are also further differences in numeracy achievement between sexes according to countries.

The PSTRE competence of the individuals who participated in PIAAC 2015 was found to be very low. Since there were clusters of a high percentage of women and men at the second level of competence, the differences in achievement according to sex did not draw attention to competence level. Problem solving is a 21st-century skill crucial for all individuals. A review of the literature shows that the achievement of problem-solving skills in computer-based assessments is usually low, consistent with the findings of this study (OECD, 2014). This may result from individuals’ low levels of computer literacy and the fact that problem solving is a high-level skill. However, in this study, there was no difference in the problem-solving skills of participants by sex, whereas in the literature, men were found to be more successful than girls in problem solving, as in the case of numeracy (Gallagher et al., 2000; Perkins & Shiel, 2014). In a study conducted with PISA 2012 data, while the differences in problem-solving achievement according to sex were insignificant in certain countries, in others boys were generally reported to be more successful than girls. Among the 44 countries that participated in PISA 2012, boys received better mean scores than girls in problem solving in 35 countries, while girls received considerably better scores than boys in four countries (Perkins & Shiel, 2014). However, in half of the participants’ countries (n = 22) there was no significant difference between sexes, which supports the findings of the current study. Considering the fact that the PSTRE competencies of the individuals who participated in PIAAC from Japan, Finland, and Sweden are in the best class, without discriminating based on sex, this study advocates future consideration of the educational policies of countries wishing to improve their PSTRE competencies.

The results from the three-step analysis suggested that education level was influential in certain competence levels, that is, a low or high level of education created differences based on sex. However, deviating from the findings in the literature, it is determined that the level of education does not have an influence on the classes that emerge according to the literacy success of men and classes that emerge according to the PSTRE competencies of men and women. Some previous research has recognized that differences exist in favor of men in relation to the educational levels of men and women (Marks, 2008; McDaniel, 2010; OECD, 2014). For example, data from the OECD (2012a) shows that in Austria, Ireland, Switzerland, and Turkey, men are still more likely to enter the higher levels of tertiary education. In Turkey and Japan, this male advantage also holds for lower levels of tertiary education. Other studies have revealed that women have reached men in terms of educational level in several Western countries (Buchmann, DiPrete, & McDaniel, 2008; OECD, 2012a; Pekkarinen, 2012; Snyder & Dillow, 2011; van Hek, Kraaykamp, & Wolbers, 2016). Moreover, some advancements toward women in education have been shown to be getting more popular in almost all Western countries, even though these improvements are at different degrees of speed and comprehensiveness.

In spite of notable improvements in recent years, Arab countries are still marked by high sex discrimination in education (The United Nations Educational, Scientific and Cultural Organization, 2010). The main explanation for this is the position of women in the culture, in which patriarchy predominates (Smits & Huisman, 2012). Other factors that deepen these inequalities in education include lower expectations of girls by families and schools, such as those regarding levels of education and girls’ future profession (Marks, 2008).

The results of PIAAC are an important resource offering insights into the effectiveness of educational decisions. This is because this assessment comprises basic skills on literacy, numeracy, and PSTRE performance of individuals aged 16 to 65 years. Based on these results, useful recommendations can be made for educators and policy makers in 20 countries, as well as in other countries with similar educational systems. Educators and policy makers should account for the fact that academic success is greatly influenced by students’ sex and educational level. Given that these influences vary from country to country, individuals with higher levels of education are more likely to take part in clusters with higher levels of competence, especially in literacy and numeracy. Consequently, raising the education level to bachelor degree status and higher might reduce the competence differences among adults. In addition, by taking the country-based variations among skills according to sex into account, countries can and should reduce these differences. Furthermore, the results of PIAAC indicate that receiving education, practice, and proficiency in literacy and numeracy represent varied approaches toward the human capital of individuals (OECD, 2016a). Thus, the results of the current research are also important for human capital. The present study has shed light on the factors that can predict the literacy, numeracy, and PSTRE competencies of individuals aged 16 to 65 years in 20 countries by applying MLCA, thus significantly contributing to the establishment of knowledge and filling a gap in the existing literature.

As in every research study, this work has certain limitations that should be considered. First, although the sample was large and international, the individuals in the sample did not fully represent all individuals within the same age range, and several countries had to be excluded from the analysis. Second, the absence of other possible relevant variables may have resulted in omitted-variable bias. Third, although the present study provides valuable information regarding literacy, numeracy, and PSTRE competencies, the relationships between the variables cannot be assumed to be causal. Future studies should therefore address the issues of generalizability and causality. Another focus for future research could be an investigation of the role of cultural differences in individuals’ competencies, based on data from PIAAC and other assessments.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Seher Yalcin

Author Biography

Seher Yalcin is a PhD research assistant at the Department of Measurement and Evaluation, in Ankara University, Turkey. She is interested in large scale assessments, latent class models, psychological factors related to students’ achievement, multilevel statistical methods, and cross-cultural studies.

References

Arellano

D. M. C.

(2013). Gender differences in reading comprehension achievement in English as a foreign language in compulsory secondary education. Tejuelo, 17, 67-84.

Arora

Pawlowski

(2017). Examining gender differences in the mathematical literacy of 15-year-olds and the numeracy skills of the age cohorts as adults. Retrieved from https://static1.squarespace.com/static/51bb74b8e4b0139570ddf020/t/588a18c13a04118a0c68116e/1485445313820/Arora_Pawlowski_PIAAC_2017.pdf

Barro

R. J.

Lee

J. W.

(2010). A new data set of educational attainment in the world, 1950-2010 (NBER Working Paper No. 15902). Retrieved from https://www.nber.org/papers/w15902.pdf

Buchmann

DiPrete

T. A.

McDaniel

(2008). Gender inequalities in education. Annual Review of Sociology, 34, 319-337.

Calero

Choi

(2017). The distribution of skills among the European adult population and unemployment: A comparative approach. European Journal of Education, 52, 348-364. doi:10.1111/ejed.12222

Education, Audiovisual and Culture Executive Agency. (2010). Gender differences in educational outcomes: Study on the measures taken and the current situation in Europe. Brussels, Belgium: Eurydice.

Eurostat. (2016). Database: Population by educational attainment level, sex and age (%): Main indicators. Retrieved from http://ec.europa.eu/eurostat/data/database

Gallagher

A. M.

De Lisi

Holst

P. C.

McGillicuddy-DeLisi

A. V.

Morley

Cahalan

(2000). Gender differences in advanced mathematical problem solving. Journal of Experimental Child Psychology, 75, 165-190.

Hanushek

Kimko

(2000). Schooling, labor-force quality, and the growth of nations. American Economic Review, 90, 1184-1208.

10.

Hanushek

E. A.

Woessmann

. (2008). The role of cognitive skills in economic development. Journal of Economic Literature, 46, 607-668.

11.

Lindemann

D. J.

(2015). Gender and numeracy skill use: Cross-national revelations from PIAAC. Retrieved from https://static1.squarespace.com/static/51bb74b8e4b0139570ddf020/t/54da75e1e4b02b7088614c36/1423603169721/Lindemann_PIAAC.pdf

12.

Lukočienė

Varriale

Vermunt

J. K.

(2010). The simultaneous decision(s) about the number of lower- and higher-level classes in multilevel latent class analysis. Sociological Methodology, 40, 247-283. doi:10.1111/j.1467-9531.2010.01231.x

13.

Marks

G. N.

(2008). Accounting for the gender gaps in student performance in reading and mathematics: Evidence from 31 countries. Oxford Review of Education, 34, 89-109.

14.

McDaniel

(2010). Cross-national gender gaps in educational expectations: The influence of national-level gender ideology and educational systems. Comparative Education Review, 54, 27-50.

15.

Mullis

I. V. S.

Martin

M. O.

Foy

Hooper

(2016). TIMSS 2015 international results in mathematics. Retrieved from http://timssandpirls.bc.edu/timss2015/international-results/timss-2015/mathematics/student-achievement/

16.

Organisation for Economic Co-operation and Development. (2012a). Education at a glance 2012: OECD indicators. Retrieved from https://www.oecd-ilibrary.org/docserver/eag-2012-en.pdf?expires=1547715653&id=id&accname=guest&checksum=9DB35314DC367CCE2F327A4C5EF94D2B

17.

Organisation for Economic Co-operation and Development. (2012b). Equity and quality in education: Supporting disadvantaged students and schools. Retrieved from https://www.oecd.org/education/school/50293148.pdf

18.

Organisation for Economic Co-operation and Development. (2012c). Literacy, numeracy and problem solving in technology-rich environments: Framework for the OECD Survey of Adult Skills. Retrieved from https://www.oecd.org/skills/piaac/PIAAC%20Framework%202012–%20Revised%2028oct2013_ebook.pdf

19.

Organisation for Economic Co-operation and Development. (2012d). Strong performers and successful reformers in education: Lessons from PISA for Japan. Retrieved from http://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/49802616.pdf

20.

Organisation for Economic Co-operation and Development. (2013a). PISA 2012 results: Excellence through equity: Giving every student the chance to succeed (Vol. II). Retrieved from http://www.oecd.org/pisa/keyfindings/pisa-2012-results-volume-ii.htm

21.

Organisation for Economic Co-operation and Development. (2013b). Technical report of the Survey of Adult Skills (PIAAC). Retrieved from https://www.oecd.org/skills/piaac/_Technical%20Report_17OCT13.pdf

22.

Organisation for Economic Co-operation and Development. (2014). PISA 2012 results: Creative problem solving: Students’ skills in tackling real-life problems (Vol. V). Retrieved from https://www.oecd.org/pisa/keyfindings/PISA-2012-results-volume-V.pdf

23.

Organisation for Economic Co-operation and Development. (2015). The ABC of gender equality in education aptitude, behaviour, confidence. Retrieved from https://www.oecd.org/pisa/keyfindings/pisa-2012-results-gender-eng.pdf

24.

Organisation for Economic Co-operation and Development. (2016a). OECD skills studies: Skills matter: Further results from the Survey of Adult Skills. Retrieved from https://www.oecd.org/skills/piaac/Skills_Matter_Further_Results_from_the_Survey_of_Adult_Skills.pdf

25.

Organisation for Economic Co-operation and Development. (2016b). OECD skills studies: The Survey of Adult Skills: Reader’s companion. Paris, France: Author.

26.

Organisation for Economic Co-operation and Development. (2016c). PISA 2015: Results in focus. Retrieved from https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf

27.

Pekkarinen

(2012). Gender differences in education (IZA Discussion Paper No. 6390). Retrieved from http://ftp.iza.org/dp6390.pdf

28.

Perkins

Shiel

(2014). Problem solving in PISA: The results of 15-year-olds on the computer-based assessment of problem solving in PISA 2012. Retrieved from http://www.erc.ie/documents/p12psreport.pdf

29.

Smits

Huisman

(2012). Determinants of educational participation and gender differences in education in six Arab countries (NiCE Working Paper No. 12-102). Retrieved from www.ru.nl/publish/pages/516298/nice_12102.pdf

30.

Snyder

T. D.

Dillow

S. A.

(2011). Digest of educational statistics 2010. Washington, DC: National Center of Educational Statistics.

31.

Solheim

O. J.

Lundetræ

(2016). Can test construction account for varying gender differences in international reading achievement tests of children, adolescents and young adults? A study based on Nordic results in PIRLS, PISA and PIAAC. Assessment in Education: Principles, Policy & Practice, 25, 107-126. doi:10.1080/0969594X.2016.1239612

32.

Stoller

R. J.

(1968). Sex and gender: The development of masculinity and femininity (Vol. 1). New York, NY: Science House.

33.

The United Nations Educational, Scientific and Cultural Organization. (2010). EFA Global Monitoring Report 2010: Reaching the marginalized. Retrieved from https://unesdoc.unesco.org/ark:/48223/pf0000186606

34.

van Hek

Kraaykamp

Wolbers

M. H. J

. (2016). Comparing the gender gap in educational attainment: The impact of emancipatory contexts in 33 cohorts across 33 countries. Educational Research and Evaluation, 22, 260-282. doi:10.1080/13803611.2016.1256222

35.

van Langen

Bosker

Dekkers

. (2006). Exploring cross-national differences in gender gaps in education. Educational Research and Evaluation, 12, 155-177.

36.

Vermunt

J. K.

(2003). Multilevel latent class models. Sociological Methodology, 33, 213-239. doi:10.1111/j.0081-1750.2003.t01-1-00131.x

37.

Vermunt

J. K.

Magidson

(2004). Local independence. In Lewis Beck

A. B. M. S.

(Ed.), Encyclopedia of social sciences research methods (pp. 732-733). Thousand Oaks, CA: Sage.

38.

Vermunt

J. K.

Magidson

(2013). Latent GOLD 5.0 upgrade manual. Belmont, MA: Statistical Innovations.

39.

Yamamoto

Khorramdel

von Davier

(2013). Scaling PIAAC cognitive data. In Technical Report of the Survey of Adult Skills (PIAAC) (Chap. 17). Retrieved from https://www.oecd.org/skills/piaac/_Technical%20Report_17OCT13.pdf