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The Educational Achievement of Indian Children

CHAPTER IV

Results of the Statistical Treatment of the Test Data

INTRODUCTION

The results of the statistical treatment of the test data* obtained by the administration of twelve tests to the eighth grade and twelve tests to the twelfth grade will be discussed under three headings: (1) comparisons of achievement by means of line graphs for the nine geographic areas and for the six types of schools for grades eight and twelve, (2) comparisons of achievement by means of the percentage of overlap between grades eight and twelve where the tests were common to both grade levels, and (3) comparisons of achievement by means of critical ratios for the types of schools for grades eight and twelve. These three types of comparisons were made in order to provide realistic answers to the basic questions stated in Chapter II.

Achievement of Indian Children in Various Geographic Areas

A spot check here and there revealed significant differences in means. This was particularly true of Alaska when compared with other areas and occasionally true for the Oklahoma, Mountain and Pacific areas when compared with other areas on both the eighth and twelfth grade tests. Thus, the reader must make his own judgment regarding the relative achievement of Indian children in the various areas, keeping in mind the discussion in Chapter III with regard to significant differences in achievement.

phone icon Achievement of Indian Children in the Eighth Grade

Figures 1-12 portray graphically the achievement of Indian children in the eighth grade in the nine geographic areas. The short horizontal line on each line graph indicates the mean score and the length of the line indicates the range of scores for the middle two-thirds of the students. An examination of the figures reveals considerable variation in mean achievement in the various geographic areas, but it also reveals a great amount of overlap in achievement. Even though the Indian children in one geographic area have the highest mean achievement on a particular test, there are children in the other areas that exceed the mean of the area with the highest mean achievement.

Figure 1

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Figure 9

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Figure 12

In order to establish ranks based upon the twelve tests as a whole, each of the areas was given a rank on each test. The area with the highest mean was given a rank of 1 on a particular test. The area with the next highest mean was given a rank of 2 on the same test. The other areas were ranked accordingly. Each area was given a rank based on the mean rank for all twelve tests. This system produced the following rank order from best performance on all twelve tests to the poorest performance on all twelve tests: (1) Alaska, (2) Oklahoma, (3) Mountain, (4) Navajo, (5) Dakota, (6) Pacific, (7) Southeast, (8) Pueblo, and (9) Southwest. However, on all the tests, there was considerable overlapping, some children in all areas exceeding the mean of the best group.

The differences in achievement noted in this discussion were no doubt influenced by differences in cultural and educational backgrounds of the children in the various areas. These differences in background were discussed in Chapter II.

Although the data were sketchy, rank order correlations** were run between the ranks on the tests as a whole and the ranks of the areas according to the: (1) percentages of children usually speaking English as a pre-school language, (2) percentages of children usually speaking an Indian dialect as a pre-school language, (3) educational level reached by the mother, (4) percentages of children having all Indian friends, (5) percentages of children having mostly white but some Indian friends, (6) percentages of fullblood Indians, and (7) percentages of halfblood Indians. The correlations were respectively: .42, -.42, .29, -.03, -.03, -.43, and .67. In other words, the greater the degree of contact of the Indian child with the white man's culture, the higher he scores on educational tests. The readers should be reminded that, for the most part, the tests used in the 1950 testing program were originally constructed for use with the American public school population. One must caution the reader that the rank order correlations were based on an N of nine and on very flimsy data. A better designed study with regard to these factors might definitely establish the relationships suggested here.

Figure 13

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phone icon Achievement of Indian Children in the Twelfth Grade

Figures 13-24 portray graphically the achievement of Indian children in the twelfth grade in the nine geographic areas. The same explanation with regard to the line graphs as described for grade eight holds for the twelfth grade.

Using the same ranking system as with grade eight, the rank order of the areas from best performance on all twelve tests to poorest performance on all twelve tests was as follows: (1) Alaska, (2) Mountain, (3) Oklahoma, (4) Pacific, (5) Dakota, (6) Southwest, (7) Southeast, (8) Navajo, and (9) Pueblo.

The differences in achievement noted were no doubt influenced by differences in cultural and educational backgrounds of the children. These differences were discussed in Chapter II.

Although the data were sketchy, rank order correlations were computed between the ranks on the tests as a whole and the ranks of the areas according to the: (1) percentages of children usually speaking English as a pre-school language, (2) percentages of children usually speaking an Indian dialect as a pre-school language, (3) percentages of children having all Indian friends, (4) percentages of children having mostly white but some Indian friends, (5) percentages of fullblood Indians, and (6) percentages of halfblood Indians. These correlations were respectively: .55, -.37, -.37, .40, -.38, and .78.

phone icon Comparison of Areas by Grade Levels

The rank order correlation between the ranks of the areas on the eighth grade level on the tests as a whole and the ranks of the areas on the twelfth grade level on the tests as a whole was .73. This indicates that the areas were quite consistent in performance on the tests as a whole on the eighth and twelfth grade levels. This tentatively establishes a hierarchy of areas with regard to educational achievement.

THE ACHIEVEMENT OF THE EIGHTH AND TWELFTH GRADES ON THE SAME TESTS

The children in the eighth and twelfth grades took these some tests: Pressey Vocabulary, USIST Arithmetic-Factor Abilities, USIST Free Writing-Length and Errors, USIST Use of Resources, Pressey Capitalization, Pressey Good Usage, Pressey Punctuation, and Pressey Sentence Structure.

Table 16 shows the percentage of students in the various types of schools in the eighth grade who exceeded the mean of the twelfth grade. An important consideration in a comparison involving two grade levels, is whether or not the tests had a ceiling for the upper grade level. An examination of the distributions for these nine tests showed that only one of the tests had a ceiling for the twelfth grade. This test was the Pressey Vocabulary. About 20 per cent of the twelfth graders fell in the top class interval, which is an indication that the same students might have scored higher had the test been longer.

In a sense, the less the percentage of overlap between the two grades, the greater the development from grade eight to twelve. This would be especially true if the scores represented the achievement of the same pupils on the same tests when in grade eight and when in grade twelve. However, the students represented here were eighth graders in 1950 and twelfth graders in 1950. The percentages of overlap as shown in Table 16 are quite considerable indicating that the students in the eighth grade had achieved higher standards than their counterparts in the twelfth grade. This seems to indicate that an upsurge is taking place in Indian education.

An examination of Table 16 indicates that the percentages of overlap were lowest for the non-reservation boarding and Indians in public schools. This would point to the conclusion that more educational growth had taken place in four years on the part of the twelfth graders in these types of schools than in the reservation boarding, day, and mission schools.

Table 16

ACHIEVEMENT OF THE EIGHTH AND TWELFTH GRADE STUDENTS BY TYPES OF SCHOOLS

Tables 17-40 indicate the differences in means, the standard error of the differences, and the critical ratios between the six types of schools. Fifteen critical ratios are presented for each test. The symbols on the left hand side of each table refer to the following types of schools:

RB -Reservation Boarding
D -Day
M -Mission
NRB -Non-reservation Boarding
PI -Indian children in public schools
PW

-White children in public schools

phone icon Achievement of the Eighth Grade Students by Types of Schools

An examination of Tables 17-28 revealed that Indian students in the:

1. Reservation boarding schools achieved no more on the twelve tests than did the children in the day and mission schools.

2. Non-reservation boarding schools achieved significantly more than the children in the reservation boarding schools on five tests: Pressey Punctuation, Reading to Appreciate General Significance, Reading to Understand Precise Directions, Orleans Arithmetic Computation, and Arithmetic-Factor Abilities.

3. Public schools achieved significantly more than the children in the reservation boarding schools on five tests: Pressey Vocabulary, Pressey Punctuation, Reading to Appreciate General Significance, Reading to Understand Precise Directions, and Arithmetic-Factor Abilities. The reverse was true in the case of the Free Writing Test-Length.

4. Mission schools achieved significantly more than the children in the day schools on only one test, namely, Pressey Vocabulary.

5. Non-reservation boarding schools achieved significantly more than the children in the day schools on six tests: Pressey Vocabulary, Pressey Capitalization, Pressey Punctuation, Reading to Appreciate General Significance, Reading to Understand Precise Directions, Arithmetic-Factor Abilities, and Use of Resources.

6 Public schools achieved significantly more than the children in the day schools on four tests: Pressey Vocabulary, Pressey Capitalization, Pressey Punctuation, and Use of Resources.

Table 17 & 18

Table 19 & 20

Table 21 &22

Table 23 & 24

Table 25 & 26

Table 27 & 28

7. Non-reservation boarding schools achieved significantly more than the children in the mission schools on two tests: Pressey Capitalization and Reading to Understand Precise Directions.

8. Public schools achieved no more on the twelve tests than did the children in the mission and non-reservation boarding schools.

An examination of Tables 17-28 revealed that the white children in the public schools achieved significantly more than the Indian children in the:

1. Reservation boarding schools on eleven tests.

2. Day schools on ten tests.

3. Mission schools on six tests.

4. Non-reservation boarding schools on seven tests.

5. Public schools on nine tests.

Thus, in competition with the white schools, the rankings of the Indian schools in terms of significant critical ratios in order from best to poorest were: Non-reservation boarding, mission, reservation boarding, public Indian, and day.

Using the same ranking system as described for grade eight with geographic areas, the rank order of the types of schools from the best performance on all twelve tests to poorest performance on all twelve tests was as follows: (1) Public Indian, (2) non-reservation boarding, (3) mission, (4) reservation boarding, and (5) day. Although the N was only five, rank order correlations were run between the ranks given above and the ranks according to: (1) percentages of children usually speaking English as a pre-school language, (2) percentages of children usually speaking an Indian dialect as a pre-school language, (3) educational level reached by the mother, (4) percentages of children having all Indian friends, (5) percentages of children having mostly white but some Indian friends, (6) percentages of fullblood Indians, and (7) percentages of halfblood Indians. The correlations were respectively: .60, -.70, .67, -.53, .60, -.90, and -.10.

phone icon Achievement of the Twelfth Grade Students by Types of Schools

An examination of Tables 29-40 revealed that Indian children in the:

1. Reservation boarding schools achieved no more on the twelve tests than did the children in the day schools.

2. Mission schools achieved significantly more than the children in the reservation boarding schools on three tests: Arithmetic-Factor Abilities, Free Writing-Length, and Free Writing-Errors.

3. Non-reservation boarding schools achieved significantly more than the children in the reservation boarding schools on all twelve tests.

4. Public schools achieved significantly more than the children in the reservation boarding schools on six tests: Pressey Vocabulary, Pressey Good Usage, Reading to Predict Outcomes of Given Events, Arithmetic-Factor Abilities, Use of Resources, and Free Writing-Errors.

5. Mission schools achieved significantly more than the children in the day schools on only one test: Pressey Vocabulary.

6. Non-reservation boarding schools achieved significantly more than the children in the day schools on nine tests: Pressey Vocabulary, Pressey Capitalization, Pressey Good Usage, Pressey Punctuation, Pressey Sentence Structure, Reading to Predict the Outcomes of Given Events, Reading to Note Details, Arithmetic-Factor Abilities, and Health and Safety.

7. Public schools achieved significantly more than the children in the day schools on seven tests: Pressey Vocabulary, Pressey Capitalization, Pressey Good Usage, Pressey Sentence Structure, Reading to Predict the Outcomes of Given Events, Arithmetic-Factor Abilities, and Use of Resources.

8. Non-reservation boarding schools achieved significantly more than the children in the mission schools on two tests: Pressey Punctuation and Reading to Note Details.

Table 29

Table 30 & 31

Table 32 & 33

Table 34 & 35

Table 36 & 37

Table 38 & 39

Table 40

9. Public schools achieved significantly more than the children in the mission schools on two tests: Pressey Punctuation and Free Writing-Length.

10. Public schools achieved significantly more than the children in the non-reservation boarding schools on one test: Pressey Vocabulary. The reverse was true with Free Writing-Length.

An examination of Tables 29-40 reveals that the white children in the public schools achieved significantly more than the Indian children in the:

1. Reservation boarding schools on eleven tests.

2. Day schools on ten tests.

3. Mission schools on five tests.

4. Non-reservation schools on six tests.

5. Public schools on three tests.

Thus, in competition with the white schools, the rankings of the Indian schools in terms of significant critical ratios in order from best to poorest were: public Indian, mission, non-reservation boarding, reservation boarding, and day.

Using the same system of ranking as described previously, the rank order of the types of schools from best performance on all twelve tests was as follows: (1) public Indian, (2) non-reservation boarding, (3) mission, (4) reservation boarding, and (5) day. Although the N was small or five, rank order correlations were computed between the ranks given above and the ranks according to: (1) percentages of children usually speaking English as a pre-school language, (2) percentages of children usually speaking an Indian dialect as a pre-school language, (3) percentages of children having all Indian friends, (4) percentages of children having mostly white but some Indian friends, (5) percentages of fullblood Indians, and (6) percentages of halfblood Indians. The correlations were respectively: .90, -1.00, -.90, 1.00, -.50, and-.20.

phone icon Comparison of Types of Schools by Grade Levels

The rank order correlations between the ranks of the types of schools on the eighth grade level on the tests as a whole and the ranks of the types of schools on the twelfth grade level on the tests as a whole, was 1.00. This indicates that the types of schools were quite consistent in performance on the tests as a whole on the eighth and twelfth grade levels. This tentatively establishes a hierarchy of types of schools with regard to educational achievement.

SUMMARY

The rank order correlations for grade eight and twelve for the various types of schools were considerably higher than those obtained with geographic areas. Although it must be remembered that these correlations with regard to types of schools were based on an N of five, they do make a strong case for the statement: the greater the degree of contact of the Indian child with the white man's culture, the higher he scores on educational tests.

The correlations between the achievement rankings in the eighth and twelfth grades according to geographic area and to types of schools would seem to indicate that the same cultural and educational factors were in operation at both levels. This tentatively establishes a hierarchy of geographic areas and types of schools with regard to educational achievement.

If differences in cultural and educational background will produce differences in educational achievement among Indians, then wider differences in cultural and educational background as they exist between Indian children and white children should produce even greater differences in educational achievement in favor of white children. This proved to be true in some instances in this study. Thus, it seems logical to say, that, as the cultural and educational backgrounds of Indian children become more like those of white children, the more closely will the educational achievement of Indian children match that of white children.

* Raw or untreated scores.

** The significance of a rank correlation coefficient may be tested by means of Olds's Tables.** When N is 9 as in the case of the correlations computed for the nine areas, correlations of .60 and ?.60 would have sums of squares of rank differences of 48 and 192 respectively. The probability of not exceeding 48 by chance alone or of getting less than 192 by chance alone, is .0470. It may be concluded at this level, that a correlation exists between the two rankings.
In light of the above discussion, the probability that the sum of squares of rank differences, when N is 9, will not be exceeded by chance alone (in the case of a positive correlation) is: (1) about .05 when r is .60, (2) about .10 when r is .48, and (3) about .20 when r is .33. The same probabilities hold for negative correlations of the same size.
The probability that the sum of squares of rank differences, when N is 5, will not be exceeded by chance alone (in the case of a positive correlation) is: (1) about .O5 when r is .85, (2) about .10 when r is .70, and (3) about .20 when r is .55. The same probabilities hold for negative correlations of the same size.
**E. G. Olds. "Distributions of Sums of Squares of Rank Differences for Small Numbers of Individuals." Annals of Mathematical Statistics, 9 (March 1938) 133-149.

 

 

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Last modified August 17, 2006