(3) Univ Coimbra, Fac of Psychology and Educational Sciences; Centre for Research in Neuropsychology and Cognitive and Behavioural Intervention (CINEICC), Portugal

Introduction

The concept of g or general intelligence was created by Charles Spearman, who established g as a measure of performance in a variety of tests (Carter, 2005). Spearman's theory is based on two factors: the g factor (general intelligence) and the s factor (specific intellectual abilities). Spearman, however, implies that a real intelligence test will be highly g loaded (Murphy & Davidshofer, 2004; Simões, 2000). Several studies contend that Raven's Standard Progressive Matrices (RSPM) is one of the purest and best measures of the g factor (Raven et al., 2000; Jensen, 1980; 1998; Orme, 1966). The g factor is based on two components: eductive ability and reproductive ability. The first corresponds to the capacity to forge new knowledge, discern meaning in confusion, perceive, and identify relationships. The RSPM was conceived to measure this eductive ability (Raven et al., 2000 ). Additionally, Cattell (1963) suggests two related but conceptually distinct aspects: fluid intelligence and crystallized intelligence. Fluid intelligence is defined as the ability to see relationships, dealing mainly with reasoning capability (Cairo Martínez et al., 2000;Cattell, 1963; Murphy & Davidshofer, 2004). Fluid intelligence is most loaded in tests with virtually no educational or cultural content, such as RSPM (Jensen, 1998). Therefore, this test allows assessing abstract thinking capabilities, solving new problems, reasoning, and analogies (Cairo Martínez et al., 2000 ). On another classification, Jensen (1987) raised the hypothesis of two types of entirely different cognitive processes, which he called Level I and Level II. Level II's ability involves transformation or manipulation of the input to arrive at the output through abilities like reasoning, problem-solving, inference, generalization, and conceptual categorization. Level II is much the same as Spearman's g, common to all complex cognitive abilities’ tests. Similarly, Level II is near what Cattel referred to as fluid intelligence (Jensen, 1987). Jensen (1998), Kaplan and Saccuzzo ( 2012) consider that RSPM is a fluid reasoning measure. In all the theories, reasoning seems to be the common element (Simões, 2000).

The best-known form of the Raven's Progressive Matrices (RPM) (published in 1938) is RSPM, devised in England by J. C. Raven, a psychologist, and L. S. Penrose, a geneticist. It was created to measure as completely as possible in a single test the eduction processes that Spearman regarded as the essence of intelligence (Jensen, 1980). The RSPM is the most widely used test on five continents (Irvine & Berry, 1988), being suitable from age six to adulthood since it covers a greater cognitive ability variation (Jensen, 1980; Raven, 1941). Orme ( 1966), Jensen (1980), Karnes et al. (1982) consider that the RSPM measure a very fundamental aspect of cognitive performance not influenced by cultural influences. RSPM consists almost entirely of perceiving key features and relationships and discovering the abstract rules that govern the differences among the elements in the matrix. The RSPM test consists of a set of entirely non-verbal tasks specially designed to reduce item dependence on acquired knowledge, cultural and scholastic content while calling for reasoning ability (Jensen, 1980).

The RSPM consists of sixty diagrammatic puzzles divided into five sets (A, B, C, D, and E) (Lovett et al., 2007; Raven et al., 2000). The items are organized in/sets of gradual difficulty: each set begins with easy items, and these are followed by items that become progressively more challenging (Jensen, 1980; Raven, 1941; Raven et al., 2000). Each item has one missing cell in a matrix (always in the lower right corner), and the subject is required to select the best completion solution among a number of choices (Jensen, 1980; Lovett et al., 2007; Raven, 1941 ; Raven et al., 2000). The solution depends on the complexity of the items (abstract material through figures or geometric designs) and the number of elements involved in reasoning ability. The variety of forms, relationships, and transformations are practically unlimited (Jensen, 1980). The five sets provide the opportunity to understand the method of thought required to solve the problems and five progressive assessments of a person's intellectual ability capacity ( Raven et al., 2000). To ensure interest and the absence of fatigue, each problem is presented and elaborated with precision and as far as possible, pleasing to look at, ensuring that the person does not become discouraged and lose interest in the subject. The test instructions are so simple, and the tasks requirements so obvious to most of the participants that the instructions may even be given by pantomime (Jensen, 1980; Raven et al., 2000).

The RSPM can be individually or to a group (Jensen, 1980). The RSPM manual stipulates that, if time is limited, then the test should be used as a measure ofintellectual efficiency and not the g factor ( Raven et al., 2000). The timed version is not a pure measure of fluid ability given the fact that it is influenced by a speed factor that discriminates against people who work more slowly and carefully (Raven et al., 2000).

Despite the popularity of RSPM, one limitation is the time required to administer the full set of items (Bilker et al., 2012 ; Chiesi et al., 2012). The main concern regarding its length is the possibility of excluding some items, which might limit the differentiation of different levels of performance. The failure to distinguish between the various levels of performance and the diminution of administration time results in an incapability to maintain the original scale's properties, especially its discriminative power (Chiesi et al., 2012). For example, a correct answer for some of the RSPM items requires the simultaneous mental manipulation of three or four different fundaments, which takes some time. The easier and much less time-consuming manipulation of only one or two of these fundaments will lead to a reliable selection of one of the distractors, which is generally seen in cognitively less able participants. Participants who have enough time to solve each matrix come to conclusions that it is not based on pure guesswork (even when wrong). Furthermore, the additional time is of little use (Jensen, 1980).

The RSPM can be applied in school contexts, workplaces, and even at home, as well as in the laboratory (Raven et al., 2000). Due to its non-verbal format, the RSPM is used with a broad range of populations for whom language processing is minimized, for example, foreign language groups, the deaf, and also with economically disadvantaged groups ( Jensen, 1980;Karnes et al., 1982; Raven et al., 2000). The RSPM has also been used in several cross-cultural studies (Jensen, 1980;Karnes et al., 1982; Kush, 1996; Powers & Barkan, 1986).

We chose the RSPM because it is the most widely used test compared to the Special Form and Advanced Form of the MPR (Raven & Raven, 2003).

This study's primary goal was to identify the psychometric properties of the RSPM in a sample of the Portuguese population since the psychometric data of RSPM is lacking. As specific goals, we intended to explore (1) the effect of variables such as age, sex, and education in the performance of RSPM, (2) to determine the internal consistency, and the test-retest reliability, (3) the convergent validity, correlating RSPM to other instruments used in the test battery.

Methods

Participants

A sample of 525 volunteers was recruited using a convenience sampling method. Recruitment took place in the community, and 1.1% (n = 6) refused to participate. People did not receive any financial compensation for participating but were given the option to receive the results and their interpretation (64 participants requested these results, 12.3%).

Predetermined criteria that precluded consideration for the study included (a) being of Portuguese nationality or living in Portugal for more than five years, (b) having received more than 50% of their education in Portugal.

The participants were stratified according to age: 12 to 17 years; 18 to 30 years; 31 to 40 years; 41 to 50 years; 51 to 60 years; 61 to 70 years; 71 to 80 years and 81 to 90 years.

Participants in our sample were also stratified according to their educational level, divided into four categories: without education, basic education (we have grouped the three basic education levels), secondary education, and higher education ^{^[1]} . We have no information on thirty-five of the participants.

Portuguese regions were grouped according to our territorial units (North, Central Region, South, and Autonomous Regions). In the South region, we included Alentejo and Algarve and merged with Autonomous Regions for statistical analysis. We have no information on 162 of the participants.

The residence place was evaluated by questioning whether the participants lived in an urban, transition area, or a rural environment (Statistics Portugal, 2014). We have no information on forty-two of the participants.

Procedure and Measures

All participants signed a consent form which included a description of the experiment, rights to confidentiality, and their right to end participation according to the Helsinki Declaration. All the participants were evaluated individually by five graduate students trained in administering the tests with an approximate duration of one hour. Most of the participants were administered the Clock Drawing Test (Shulman et al., 1986), Rey 15-Item Memory Test (Boone et al., 2002), Zung Self-Rating Anxiety Scale (Serra et al., 1982), Edinburgh Handedness Inventory (Espírito-Santo et al., 2017), Frontal Assessment Battery (Dubois et al., 2000), Stroop test (Garcia et al., 2016; Stroop, 1935), RSPM (Raven et al., 2000), and the Rey Complex Figure Test (Rey, 2002). In the RSPM, all subjects were instructed by the guidelines established by the authors of the test (Raven et al., 2000).

RSPM (Raven et al., 2000), a non-verbal test, consists of 60 tasks presented in black and white and divided into five series numbered alphabetically. Each set consists of twelve items. Participants were asked to select the missing part from six or eight options given below each matrix. A participant's score is the number of correct answers, ranging from 0 to 60 (Al-Shahomee, 2012;Bilker et al., 2012;Raven & Raven, 2003; Savage-McGlynn, 2012). Each participant completed the RSPM hetero-administrative form. The RSPM was administered untimed (Raven et al., 2000). Administration time varied from 9 min to 120 min, and the average administration time was 32.32 (SD = 15.11).

Rey 15-Item Memory Test (15-IMT)

The 15-IMT (Boone et al., 2002) evaluates suspect effort of participants. The 15-IMT involves the memorization of 15 different items, making it appear the task harder than it is. The test consists of two tasks: recall task and recognition task. This formula provides the score: recall correct + (recognition correct – false positive). Given the result of the application of this formula, consider a cut of 20 points. We used the test to detect the simulation and the insufficient effort of the participants (Griffin et al., 1997;Reznek, 2005;Simões et al., 2010; Slick et al., 2004). The Cronbach's alpha of this instrument was .80, and 174 people responded to this tool because of the moment the 15-IMT was included in the neuropsychological battery.

Zung Self-Rating Anxiety Scale (SAS Zung)

The SAS Zung (Serra et al., 1982) is a self-administered scale to measure anxiety state; namely, the anxiety felt at the time of the evaluation. This scale consists of twenty items on a Likert scale where items responses are ranked from 1 to 4, except the items 5, 9, 13, 17, 19, which are scored in reverse (4, 3, 2, 1). The total score ranges from 20 to 80, with higher scores corresponding to more frequent symptoms. Results above 40 indicate that the individual has a high likelihood of suffering from clinically significant anxiety. We used this test to discriminate between participants who experienced anxiety at the time of the evaluation of those who did not (Serra et al., 1982). The Cronbach's alpha of this instrument was .78. One hundred seventy-four people answered to SAS Zung, also because of its timing on the neuropsychological battery.

Rey Complex Figure Test (RCFT)

The RCFT (Rey, 2002) consists of three tasks that occur at different times: the copy task, the immediate recall (3 minutes), and delayed recall (20 minutes). In the copy task, the participant must reproduce the figure on a piece of paper. After three minutes, the participant is asked to reproduce the figure from memory without prior warning. Twenty minutes later, the participant is requested to reproduce the figure from memory again. Each copy is scored for the accurate reproduction and placement of 18 elements and may have a maximum score of 36 points (Rey, 2002). This test evaluates implicit memory and visuospatial ability, and we have selected this test because Thurstone (Murphy & Davidshofer, 2004) had considered these skills as primary mental abilities. The Cronbach's alpha of this instrument was .85 (n = 199).

Statistical Analysis

We used the Statistical Package for the Social Sciences (IBM SPSS Statistics for Macintosh, Version 27.0) to perform data analysis.

The analysis was carried out in the following manner. First, a descriptive statistical analysis was used to determine the mean, standard deviation, frequencies, percentages of RSPM scores. To explore the proportion of cases that fall into each category of each demographic variable categorized and compare this ratio with hypothetical values, we used a chi-square test for goodness of fit (Pallant, 2016).

Then it was verified that the normality of score distribution of RSPM using the Shapiro-Wilk test and the measures of kurtosis and skewness.

We used Student's t-test/ANOVA of one and two factors and the Pearson correlations to explore the effects of sociodemographic characteristics (age, sex, education, regions, and place of residence) on the performance of RSPM. For the independent samples t-test, a power of .95, and an alpha of .05, the sample would need 210 participants. As for the ANOVA of one factor, a .95 power, and a .05 alpha, the sample would have between 252 and 360 attendees. As for the two-factor ANOVA, .95 and power a .05 alpha, the sample would need to have 400 participants (Faul et al., 2007a, 2007b). For the analysis of variance (ANOVA), we determined the homogeneity of variances according to Levene's test. In the case of existing homogeneity (p > .05), we used the Hochberg posthoc test. Otherwise, the Games-Howell posthoc test would be used both with the Bonferroni correction ( p / number of pairwise comparisons).

For the analysis of the psychometric properties, we determined the internal consistency through Cronbach's alpha. For the analysis of temporal stability test-retest, we used Pearson's correlations and paired samples t-test. For the analysis of internal consistency for an alpha of .01, a power of .95, and an expected Cronbach's alpha of .89 (Moran, 1986), the sample size needed would be 13 participants (Bonett, 2002; Chang, 2014). The test's reliabilities for the different groups were determined by recoding the items to 0 (incorrect) and 1 (correct).

For convergent validity, we computed correlational analysis with some of the tests used in the neuropsychological battery. As for the correlational analysis, a power of .95 and an alpha of .05, the sample would have to consist of 314 participants (Faul et al., 2007a, 2007b). We also computed correlational analysis relating the RSPM scores with age, years of study, and total time took by the participants.

Results

From the initial pool (525 participants), three people (two Brazilian and one Angolan nationals) were excluded since our study's goal was to confine it to the Portuguese population.

Seventeen participants that scored below 19 on 15-IMT test had significantly lower scores on RSPM [participants with suspect effort:M ± SD = 28.35 ± 11.41; non-suspect effort: M ± SD = 43.00 ± 9.56; t₍₁₇₂₎= 5.89; p < .001; CI95% [8.98; 20.32], than those of the participants without suspect effort. The effect size was very large (Cohen's d = 1.50; CI95% [0.97; 2.02]).

Forty participants with Zung scores below 40 performed poorly on RSPM [anxious: M ± SD = 38.00 ± 12.21; non-anxious participants: M ± SD = 42.63 ± 9.95; t _(55.358) = 2.19; p < .05; CI95% [0.46; 8.80], but the effect size was small (Cohen's d = 0.44; CI95% [0.08; 0.79]).

Of these 522 participants (Table 1), 250 were men (47.9%) and 272 women (52.1%). Ages ranged between 12 and 95 years (M = 46.35; SD = 20.92).

The educational level ranged between illiteracy (3.1%) and 28 years of schooling (M = 10.23; SD = 5.30). According to the territorial units, 333 subjects (81.4%) lived in the Central region (Aveiro, Castelo Branco, Coimbra, Guarda, Leiria, part of Santarém, and Viseu) 41 (10.0%) in the North, 16 (3.9%) in Lisbon Metropolitan Area (Lisboa, Sintra), 15 (3.7%) in Alentejo and four (1.0%) in the autonomous regions of Azores and Madeira.

Regarding the place of residence, 257 subjects (51.7%) lived in an urban area, while 194 (39.0%) and 46 (9.3%) lived in a rural area and a transition area, respectively.

Through the chi-square test for goodness of fit is possible to verify that the sample was not balanced by sociodemographic variables.

Table 1 Sociodemographic Characteristics
		n	%	Census 2011
Age
(M ± SD = 46.35 ± 20.92)	10-19	59	11.3	10.7
	20-29	70	13.4	11.7
	30-39	85	16.3	15.1
	40-49	83	15.9	14.6
	50-59	80	15.3	13.3
	60-69	67	12.8	11.2
	≥ 70	78	14.9	13.8
Sex
	Men	250	47.9	47.8
	Women	272	52.1	52.2
Education level
(M ± SD = 10.23 ± 5.30)	Without education	15	3.1	8.3
	Basic education	256	52.6	54.7
	Secondary education	109	22.4	19.9
	Higher education	107	22.0	17.1
Regions
	North	41	10.0	35.1
	Center	349	85.3	21.9
	South and A.R.	19	4.6	16.3
Area of residence
	Urban	257	51.7	—
	Transition area	46	9.3	—
	Rural	194	39.0	—
Note . N = 522. South and A.R. = South and Autonomous Regions (Azores and Madeira).

Descriptives

The average RSPM score was 41.18 (SD = 12.03). Shapiro-Wilk test indicated a non-normal distribution (p < .001). The RSPM scores distribution was negative and slightly skewed (Si = -0.78) and slightly leptokurtic ( Ku = -0.13). However, kurtosis values (lower than 7, proper value) and the skewness (over -2), according to Kim (2013), is indicative of normality for samples exceeding 300 participants, allowing the use of parametric tests to investigate and evaluate the presence of statistically significant differences in data.

Influence of Sociodemographic Variables

Table 2 presents the differences in the scores of RSPM between groups defined by sociodemographic variables, using Student's t-test for independent samples or analysis of variance (ANOVA).

The total scores on RSPM differed significantly according to seven age groups [F_{(6, 468)} = 41.91; p < .001], with a large effect (h² = 0.33) (Table 2). The correlational analysis confirms the trend of a decrease in RSPM score relative to age, showing, according to the criteria of Cohen (1988), a high negative correlation (r = -.53; p < .001).

Regarding sex (Table 2), men had statistically significant higher scores than women [t_(516.080) = 3.92; p < .001]. Nevertheless, the effect size was small (Cohen's d = 0.34).

The total scores on RSPM differed significantly according to educational levels [F_{(3, 195)} = 85.75; p < .001], with a large effect (h² = 0.27) (Table 2). The correlational analysis confirmed the trend of an increased score of RSPM through years of study, showing, according to the criteria of Cohen (1988), a high positive correlation (r = .57; p < .001).

The total scores on RSPM (Table 2) differed significantly between regions [ F_{(2, 74)} = 10.12; p < .001], with a small effect (h² = 0.03).

The total scores on RSPM differed significantly between the area of residence [F_{(2, 140)} = 9.37; p < .001], with a small effect (h² = 0.04) (Table 2).

Games-Howell posthoc tests (Table 3), with Bonferroni correction, revealed that the five age groups between 10 and 49 years had significantly higher scores than those groups above 60 years. Also, those in the 50 – 69 age groups differed from those aged above 70 years.

Games-Howell posthoc test (Table 4), with Bonferroni correction, revealed that participants' scores without education differed significantly from participants with all other education levels. Similarly, the scores of participants with secondary and higher education differed significantly from participants who had basic education.

Games-Howell posthoc test (Table 5), with Bonferroni correction, revealed that scores of participants who resided in the Center region were significantly higher than those in the North.

The Games-Howell posthoc test (Table 6) with Bonferroni correction revealed that scores of participants who resided in an urban or rural area were significantly higher than those residing in a transition zone.

Table 2 Differences in Scores of Raven's Standard Progressive Matrices in the Sociodemographic Variables
		n	M ± SD	CI 95% IL – UL	Min – Max
Age
F _{(6, 468)} = 41.91; p < .001; η² = 0.33	10 – 19	59	45.83 ± 7.28	43.93 – 47.73	24 – 59
	20 – 29	70	46.90 ± 7.84	45.03 – 48.77	25 – 60
	30 – 39	85	46.20 ± 9.32	44.19 – 48.21	18 – 60
	40 – 49	83	44.39 ± 9.92	42.22 – 46.55	18 – 60
	50 – 59	80	42.48 ± 10.84	40.06 – 44.89	12 – 59
	60 – 69	67	35.87 ± 11.97	32.95 – 38.78	9 – 58
	> 70	78	26.90 ± 11.09	24.40 – 29.40	2 – 51
Sex
t _(516.080) = 3.92; p < .001; d = 0.34	Men	250	43.29 ± 10.77	41.95 – 44.63	9 – 60
t _(516.080) = 3.92; p < .001; d = 0.34	Women	272	39.25 ± 12.80	37.72 – 40.77	2 – 60
Education level
F _{(3, 195)} = 85.75; p < .001; η² = 0.27	Without education	15	20.93 ± 7.21	16.94 – 24.92	14 – 36
	Basic education	256	36.96 ± 12.01	35.48 – 38.43	2 – 59
	Secondary education	109	46.69 ± 8.05	45.16 – 48.22	24 – 60
	Higher education	107	47.91 ± 8.07	46.36 – 49.45	12 – 60
Regions
F _{(2, 74)} = 10.12; p < .001; η² = 0.03	North	41	34.83 ± 11.24	31.28 – 38.38	15 – 59
	Center	349	41.79 ± 12.11	40.52 – 43.07	12 – 60
	South and A.R.	19	41.42 ± 6.55	38.26 – 44.58	30 – 55
Area of residence
F _{(2, 140)} = 9.37; p < .001; η² = 0.04	Urban	257	42.65 ± 11.36	41.25 – 44.04	12 – 60
	Transition area	46	33.93 ± 13.83	29.83 – 38.04	13 – 60
	Rural	194	41.03 ± 11.56	39.39 – 42.67	9 – 59
Note . N = 522. d = Cohen's d; η ² = eta-squared (sum of squares between groups / sum of the squares); South and A.R. = South and Autonomous Regions.

Table 3 Posthoc Comparisons of Scores of Raven's Standard Progressive Matrices in Age Groups
Pairwise comparisons^a		Mean difference	p	d	Interpretation d
10 – 19 (M ± SD = 45.83 ± 7.28)	60 – 69	9.97	< .001	0.99	large effect
10 – 19 (M ± SD = 45.83 ± 7.28)	> 70	18.93	< .001	1.58	very large effect
20 – 29 (M ± SD = 46.90 ± 7.84)	60 – 69	11.03	< .001	0.92	large effect
20 – 29 (M ± SD = 46.90 ± 7.84)	> 70	20.00	< .001	1.67	very large effect
30 – 39 (M ± SD = 46.20 ± 9.32)	60 – 69	10.33	< .001	0.86	large effect
30 – 39 (M ± SD = 46.20 ± 9.32)	> 70	19.30	< .001	1.61	very large effect
40 – 49 (M ± SD = 44.39 ± 9.92)	60 – 69	8.52	< .001	0.71	medium effect
40 – 49 (M ± SD = 44.39 ± 9.92)	> 70	17.49	< .001	1.46	very large effect
50 – 59 (M ± SD = 42.48 ± 10.84)	> 70	15.58	< .001	1.30	very large effect
60 – 69 (M ± SD = 35.87 ± 11.97)	> 70	8.97	< .001	0.75	medium effect
Note . N = 522. F_{(6, 468)} = 41.91; p < .001. d = Cohen’s d. ^a Only statistically significant differences are presented.

Table 4 Posthoc Comparisons of Scores of Raven's Standard Progressive Matrices in Educational Levels
Pairwise comparisons^a		Mean difference	p	d	Interpretation d
Basic education (M ± SD = 36.96 ± 12.01)	Without education	16.02	< .001	1.34	very large effect
Secondary education (M ± SD = 46.69 ± 8.05)	Without education	25.76	< .001	2.15	very large effect
Secondary education (M ± SD = 46.69 ± 8.05)	Basic education	9.73	< .001	0.81	large effect
Higher education (M ± SD = 47.91 ± 8.07)	Without education	26.97	< .001	2.25	very large effect
Higher education (M ± SD = 47.91 ± 8.07)	Basic education	10.95	< .001	0.91	large effect
Note . N = 522. F_{(3, 195)} = 85.75; p < .001. d = Cohen’s d. ^a Only statistically significant differences are presented.

Table 6 Posthoc Comparisons of Scores of the Raven's Standard Progressive Matrices in Place of Residence
Pairwise comparisons^a		Mean difference	p	d	Interpretation d
Urban (M ± SD = 42.65 ± 11.36)	Transition area	8.71	< .001	0.73	medium effect
Rural (M ± SD = 41.03 ± 11.56)	Transition area	7.10	< .01	0.59	medium effect
Note . N = 522. F₍ _{2, 140}₎ = 9.37; p < .001. d = Cohen’s d. ^a Only statistically significant differences are presented.

A two-way analysis of variance (age groups x sex) showed a non-significant effect on RSPM scores [F_{(6, 508)} = 1.63; p > .05]. The scores by age groups and sex are presented in Table 7.

A two-way analysis of variance (education level x age groups) showed a significant effect on RSPM scores [F_{(9, 468)} = 2.45; p < .05]. The scores by education level and age groups are presented in Table 8.

Table 7 Descriptives of Scores of the Raven's Standard Progressive Matrices by Age Groups x Sex
Age groups	Men		Women
Age groups	n	M ± SD	n	M ± SD
10 – 19	17	43.29 ± 8.75	42	46.86 ± 6.44
20 – 29	53	46.64 ± 8.39	17	47.71 ± 5.92
30 – 39	52	47.83 ± 8.98	33	43.64 ± 9.39
40 – 49	39	44.15 ± 10.44	44	44.59 ± 9.56
50 – 59	39	43.97 ± 9.26	41	41.05 ± 12,10
60 – 69	28	36.04 ± 11.73	39	35.74 ± 12.29
> 70	22	30.95 ± 10.31	56	25.30 ± 11.06
Note . N = 522.

Table 8 Descriptives of the Raven's Standard Progressive Matrices Scores by Education Level x Age
Education Level		Age Groups
Education Level		10 – 19	20 – 29	30 – 39	40 – 49	50 – 59	60 – 69	> 70
Without education
	n	—	—	—	—	—	—	15
	M	—	—	—	—	—	—	20.93
	(SD)	(—)	(—)	(—)	(—)	(—)	(—)	(7.21)
Basic education
	n	23	7	18	37	60	52	59
	M	47.39	39.57	42.28	39.38	40.15	33.40	29.32
	(SD)	(7.17)	(11.57)	(9.46)	(11.18)	(11.29)	(11.06)	(11.03)
Secondary education
	n	26	16	33	15	10	9	—
	M	44.08	47.56	46.58	47.93	49.10	48.33	—
	(SD)	(7.91)	(7.92)	(9.22)	(8.31)	(4.63)	(6.34)	(—)
Higher education
	n	—	26	34	31	10	6	—
	M	—	48.46	47.91	48.65	49.80	38.50	—
	(SD)	(—)	(7.25)	(8.99)	(5.56)	(5.53)	(15.06)	(—)
Note . N = 522.

A two-way analysis of variance (education level x sex) revealed a non-significant effect on RSPM scores [F_{(3, 479)} = 1.09; p > .05]. Table 9 presents the scores by education level and sex.

Table 9 Descriptives of the Raven's Standard Progressive Matrices Scores by Education Level x Sex
Education Level	Men		Women
Education Level	n	M ± SD	n	M ± SD
Without education	3	19.33 ± 9.24	12	21.33 ± 7.05
Basic education	114	39.32 ± 10.46	142	35.06 ± 12.84
Secondary education	60	47.65 ± 8.16	49	45.51 ± 7.85
Higher education	65	48.08 ± 8.07	42	47.64 ± 8.16
Note . N = 522.

A two-way analysis of variance (age groups x regions) revealed a non-significant effect on RSPM scores [F_{(10, 390)} = 1.78; p > .05] (Table 10).

Table 10 Descriptives of the Raven's Standard Progressive Matrices Scores by Age Groups x Regions
Age Groups	North		Center		South and A.R.
Age Groups	n	M ± SD	n	M ± SD	n	M ± SD
10 – 19	8	41.00 ± 6.33	41	47.46 ± 7.19	6	40.33 ± 5.16
20 – 29	7	41.29 ± 10.11	51	47.65 ± 7.89	2	48.00 ± 9.90
30 – 39	5	41.20 ± 14.64	51	46.35 ± 9.08	5	43.60 ± 7.23
40 – 49	8	29.63 ± 11.50	51	46.69 ± 7.81	2	41.00 ± 1.41
50 – 59	6	29.83 ± 10.25	55	43.71 ± 10.65	—	— ± —
60 – 69	4	24.25 ± 6.70	39	38.15 ± 11.06	4	37.25 ± 6.90
> 70	3	30.67 ± 5.03	61	25.79 ± 10.16	—	— ± —
Note . N = 522. South and A.R. = South and Autonomous Regions.

Finally, another two-way analysis of variance (age groups x place of residence) showed a non-significant effect on RSPM scores [F _{(12, 476)} = 1.06; p > .05]. The scores by age groups and regions are presented in Table 11.

Table 11 Descriptives of the Raven's Standard Progressive Matrices Scores by Age Groups x Place of Residence
Age groups	Urban		Transition area		Rural
Age groups	n	M ± SD	n	M ± SD	n	M ± SD
10 – 19	29	44.07 ± 7.98	2	48.50 ± 7.78	28	47.46 ± 6.25
20 – 29	52	47.33 ± 8.35	3	42.33 ± 6.11	14	46.21 ± 6.40
30 – 39	47	44.64 ± 9.82	3	38.33 ± 17.79	32	48.31 ± 6.89
40 – 49	49	43.80 ± 11.13	5	46.80 ± 17.31	25	43.80 ± 5.03
50 – 59	38	42.05 ± 12.21	3	34.67 ± 17.01	32	44.56 ± 7.80
60 – 69	22	36.82 ± 12.44	7	33.71 ± 10.75	33	35.45 ± 11.95
> 70	20	28.45 ± 10.96	23	28.17 ± 11.83	30	24.90 ± 10.21
Note . N = 522.

Psychometric properties

Reliability

In the present study, a Cronbach's alpha of .94 was obtained for the total sample, indicating a high internal consistency among the RSPM items (Murphy & Davidshofer, 2004).

Correlations

In Table 12, we can see correlations between Raven's Standard Progressive Matrices, Rey Complex Figure Test-Copy, Rey Complex Figure Test-Immediate Recall, and Rey Complex Figure Test-Delayed Recall were all high to moderate (R² between 22.1% and 77.4%). The correlation with Zung Self-Rating Anxiety Scale was low and negative (R ² = 7.3%). Additionally, the correlational analysis showed no correlation between RSPM scores and the total time taken by the participants (r = .09; R² = 8.1%; p > .05).

Table 12 Correlations between Raven's Standard Progressive Matrices and the other Study Measures
Measures	1	2	3	4	5
1. RSPM	—	.55^***	.49^***	.47^***	-.27^***
2. RCFT Copy		—	.50^***	.48^***	-.27^***
3. RCFT Immediate Recall			—	.88^***	-.22^***
4. RCFT Delayed Recall				—	-.24^***
5. SAS Zung					—
Note . N = 522. RSPM = Rey Complex Figure Test – Copy; RCFT = Rey Complex Figure Test; SAS Zung = Zung Self-Rating Anxiety Scale. *** p < .001.

Test-retest reliability

To evaluate the temporal stability of RSPM, due to logistic reasons only a sub-sample of 12 participants was re-tested after the initial test administration (2.3%). The retest followed the same procedures as the initial testing. The test-retest interval averaged 4.67 months (SD = 1.37). Through the Student’s t test for paired samples we found that there were no differences between the two moments [t ₍₁₁₎ = 1.84; p > .05; d = 0.53 (medium effect)], and the Pearson's correlation coefficient was .82 (p < .001), corresponding to a strong positive correlation between the two moments. The same was done for each sex, founding that there were no differences between the two moments, both for men [t₍₃₎ = 0.72; p > .05; d = 0.15 (negligible effect)] and for women [t₍₇₎ = 1.65; p > .05; d = 0.32 (small effect)] (Table 13).

Table 13 Stability of Raven's Standard Progressive Matrices Scores Regarding the Global Sample and Sex Subgroups
		n	M	SD	r
Total Group	Test	12	41.67	11.68	.82^***
Total Group	Test-retest	12	45.25	10.45	.82^***
Men	Test	4	46.75	13.60	.94
Men	Test-retest	4	48.75	9.88	.94
Women	Test	8	39.13	10.63	.76^*
Women	Test-retest	8	43.50	10.93	.76^*
Note . N = 522. *** p < .001; * p < .05.

Discussion

Our goal was to study the psychometric properties of Raven's Standard Progressive Matrices in a sample of the Portuguese population.

The total score of RSPM is 41.18, like others with similar samples (Al-Shahomee, 2012). According to findings in other normative studies, the performance of men is higher than women (Abdel-Khalek, 1988; Lynn & Irwin, 2004). Nevertheless, the effect size of the difference is small (also similar to Abdel-Khalek, 1988), which leads us to think that higher scores in men are not a universal phenomenon. Some authors state that men have an advantage regarding higher scores in general intelligence ( Abdel-Khalek, 1988; Lynn & Irwin, 2004). Others claim that there are no significant differences between men and women (Colom & García-López, 2002; Court, 1983; Dutton et al., 2018 ; Jensen, 1998). According to the study of Carpenter et al. (1990), men get higher scores than women in certain types of items, namely, those that require a solution of addition/subtraction or a distribution of two rules. In other types of items, there are no sex differences in performance. Thus, the difference in our study on the variable sex can relate to this question: different items on RSPM can measure different processes, and sexes differ on them (Mackintosh & Bennett, 2005). By contrast, Rushton et al. (2004) study shows that men have the same scores as women.

According to our study, there are higher scores in urban areas as in Al-Shahomee (2012). Adding to this, participants from the central region had higher scores. This region corresponds to Portugal's highest per capita incomes (PORDATA, 2015), and as is shown in the results and revision of the study of Almeida et al. (2011) and Brouwers et al. (2009), intelligence levels are correlated with per capita incomes.

Regarding levels of education, there are statistically significant differences between the different educational levels, as in Al-Shahomee (2012) and Brouwers et al. (2009). It was also possible to establish that a subject with a secondary or higher educational level gains a higher score than those who have only the basic education or have had no education. These data suggest that this test is not as insensitive to the acquired knowledge, scholastic or cultural content as Jensen pretended (1980). This result also suggests that intelligence assessment should not be based solely on nonverbal tests (Kaya et al., 2016).

In this study, a Cronbach's alpha was obtained for the total sample of .94, a value that must be considered quite satisfactory and is supported by Burke's study (2010). Other studies report that most of the coefficients exceed .90, with a modal value of .91 (review of Raven et al., 2000). Test-retest values from the original work of RSPM (between .83 and .93) reinforces the values found in our study (Raven et al., 2000). The Cronbach's alpha and test-retest are satisfactory, taking into account other studies (Abdel-Khalek, 1988; Moran, 1986). The correlation between scores on the two moments reinforces the good precision instrument temporal stability.

The correlational analysis of our study, which confirms the downward trend of the RSPM scores with age, was similar to the study of Burke (2010).

Limitations and Conclusions

Our study also has some limitations that should be considered when interpreting the findings. First, the main limitation concerns temporal stability due to the small number of participants (n = 12). For the paired samples t-test, a power of 0.95 and an alpha of .05, the sample would need 54 participants (Faul et al., 2007a, 2007b).

An additional limitation regards education level. The educational level was operationalized as the number of years of regular formal schooling completed with success. This approach is vulnerable to the numerous changes in the school system that has occurred throughout the last decades in Portugal. For instance, the curricula of regular school have suffered significant modifications. Since 2005, a large portion of the Portuguese adult population with low education has enrolled in the "New Opportunities" initiative to enhance their qualifications and to acquire primary (9th grade) or secondary (12th grade) level education certificates. However, the actual equivalence between regular school and "New Opportunities" education programs is still unknown. So, for the purpose of this study, only regular schooling was credited to the participants' educational background. Considering these continuing changes in education, future studies should assess the reliability of the normative algorithms and update the norms if necessary.

During the tests, the participants were not taking medication and had no symptoms of a disease that might potentially affect the performance of the tests. However, it is possible that there were participants suffering from undiagnosed conditions or mild cognitive deficit. In the future, more medical information should be gathered regarding the possible effect of disease/medication on test results.

Furthermore, more research is needed to develop studies of this nature, given the relative lack of published studies. Our aim in writing this article was to help overcome the lack of instruments adapted to the Portuguese population, and we hope our contribution will encourage further studies with the RSPM. The data from this study suggest that this is a tool with the potential to be used in the Portuguese population.

Conflict of interest | Conflito de interesses : None| Nenhum.
Funding sources |Fontes de financiamento: None| Nenhuma.
Contributes: IG : Literature review; Collection, data input and handling; Manuscript drafting. HES: Project coordination and design. Contribution to the writing of the manuscript; Data processing and discussion; Revision of the final draft of the manuscript. CP: Contribution to the writing of the manuscript; Collection, data input and handling; Revision of the final draft of the manuscript.

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^{^[1]} In the Portuguese education system the 1st cycle of basic education is from 1st to 4th grade; the 2nd cycle of basic education is from 5th to 6th grade; 3rd basic education is from 7th to 9th grade; secondary education is from 10th to 12th grade, and the higher education corresponds to the university or college.

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ARTIGO ORIGINAL

Psychometric properties of the Raven's Standard Progressive Matrices in a Portuguese sample

Propriedades Psicométricas da Forma Geral das Matrizes Progressivas de Raven numa amostra portuguesa

Abstract

Resumo