ࡱ> 5@ [_bjbj22 (XXtcBBB8"C,NC[2nE(EEEEEEEZZZZZZZ$\R,_[QJEEJJ[EEb[FJFJFJJEEZFJJZFJ0FJvJVUR@SEbE k BJR Tx[0[RxD`0JD`SS&D`?SEFFJNGG*EEE[[$&D0J& Hypothesis Test Official Reading Level vs. Estimated Reading Level One of the challenges for middle grades teachers is to recommend books for their students that they will find interesting and that are at their independent reading levels. One method for determining reading level is the ATOS (Advantage-TASA Open Standard) readability test developed for the Accelerated Reader program. This test is based on comprehension data from 30,000 students reading over 1,000,000 million books. In addition, the ATOS method takes into account words per sentence, characters per word, and average grade level of the words. Unlike some of the other methods used to determine reading level, ATOS uses the entire text of a book and considers book length when establishing the reading level. I have a collection of books that I would like to use in my classroom. Many of my books are in the Accelerated Reader (AR) program, so I can look up their reading levels. Many, however, are not in that program, or are simply not on the AR lists to which I have access. There is another, very simple reading level test some teachers use: Count out ten consecutive sentences in three places in the book, at the beginning, middle and end. Tally the number of words that are 3 syllables or more from each selection, counting repeated words each time they appear. Add the 3 tallies, round to the nearest square, take the square root and adjust the result by adding 3. It takes a short time to make this rough estimate. I would like to use this method in my class, but I am concerned that it may be too rough an estimate. I did a paired t-test to see if the rough estimate is close enough. I compared the two reading level determination methods using a sample of 30 books. I have a list with the AR levels for each of these books. I manually did the 30-sentence tallies on the books, then used this data for the test. Note that the reading level value indicates the grade level at which the student would be expected to read the book with little or no assistance. The paired t-test compared the reading levels at a 95% confidence level, allowing me to compare dependent samples. My null hypothesis was that the difference between the two measures would be zero. I used all three tests to accept or reject the null hypothesis. The confidence indicator test gives a quick answer to the accept or reject question. The t-value test gives a strong indication if the data is skewed and to what direction. The p-value test was used to confirm the other two. As you can see from the MINITAB output below, the null hypothesis must be rejected. By the Confidence Interval method, the number 0 is not within the interval of (1.147, 2.059). By the calculated t-value, 7.19 is in the rejection region, much greater than 1.96. The very low p-value is much less than the -value of 0.025. Paired T-Test and CI: 30-Sentence Reading Level, AR Reading Level N Mean StDev SE Mean 30-Sentence 30 8.567 2.128 0.389 AR Reading L 30 6.963 2.085 0.381 Difference 30 1.603 1.221 0.223 95% CI for mean difference: (1.147, 2.059) T-Test of mean difference = 0 (vs not = 0): T-Value = 7.19 P-Value = 0.000 I did not truly expect to find zero difference in the mean of the two reading level measurement methods. I actually hoped to find that the 30-sentence reading level would be within one grade level of the AR reading level. My study shows that this is not the case. The mean difference is 1.603, showing that the differences are more than half again as great as I had hoped. The following descriptive statistics for the difference values show the range to be from -1.2 to 3.5. Descriptive Statistics: Difference Variable N Mean Median TrMean StDev SE Mean Differen 30 1.603 1.800 1.673 1.221 0.223 Variable Minimum Maximum Q1 Q3 Differen -1.200 3.500 1.050 2.700 Because the t-value is so much larger than the upper limit of the acceptance region, I suspected that the data for the differences is skewed toward the upper end. The following graph shows that this is true. I had hoped to use the 30-sentence method, but as this graph shows, 77% of the reading levels calculated with this method are more than one grade level higher than the value calculated using the ATOS-based AR method. This would result in recommendations to students that were well beyond their capabilities, running the risk of turning them off from reading altogether.  EMBED MinitabGraph.Document \s  By changing the formula for the 30-sentence method so that in the final step the adjustment value is 1 instead of 3, the following is obtained: Paired T-Test and CI: 30-Sentence Reading Level +1, AR Reading Level N Mean StDev SE Mean 30-Sentence 30 6.633 2.173 0.397 AR Reading L 30 6.963 2.085 0.381 Difference 30 -0.330 1.213 0.222 95% CI for mean difference: (-0.783, 0.123) T-Test of mean difference = 0 (vs not = 0): T-Value = -1.49 P-Value = 0.147 When adding only 1 as the last step, the 30-sentence method result does fall within the acceptance range. By the Confidence Interval method, the number 0 is within the interval of (-0.783, 0.123). By the calculated t-value, -1.47 is in the acceptance region, between -1.96 and 1.96. The p-value of 0.147 is greater than the -value of 0.025. Furthermore, the dot-plot below shows a much more acceptable range for the difference. Now 73% of the books are within one grade level of the AR method.  EMBED MinitabGraph.Document \s  To summarize what I found in my study, the published version of the 30-sentence test does not accurately estimate a books reading level. By altering the method, I was able to bring the estimates much closer to the reading levels determined through the ATOS-based AR method. This study could be improved by comparing the 30-sentence method to other methods, such as the Flesch-Kincaid method, then averaging the group of difference values. This would compare the simple 30-sentence method against several more scientific methods, perhaps resulting in a more precise adjustment value. Data Used in the Study Book TitleAR Reading Level30-Sentence Reading LevelDifference30-Sentence Reading Level +1Difference +119848.9101.18-0.9Briar Rose6.292.870.8By the Shores of Silver Lake6.26-0.24-2.2I Am the Cheese8.590.590.5James and the Giant Peach7.1102.980.9Let the Circle Be Unbroken6.870.25-1.8Moby Dick10.3121.710-0.3My Brother Sam Is Dead6.25-1.23-3.2GHIqy% & I Z o   h i j p 5@Gw T~¾ѺѲѤդh,h;hPh@h-h h`\ hU^9\hU^9hU^9\hhDyh(hN hv-hv-hU^9h`hv-hrhrhr5CJaJhv-5CJaJh@5CJaJ8HI  i j H  NP:34_ h7$8$H$^hgd,gdU^9 & FgdU^9gdgd(gd4^^Z_(*LNPR#%ldUY(ʶ흌~zzsogjhUh hv-hh\hCJOJQJ^JaJ h5CJOJQJ\^JaJhh, h,h;CJOJQJ^JaJ&h,h;5CJOJQJ\^JaJ h@5CJOJQJ\^JaJ hU^9h` hU^9hPhvYh@ h;h;h;hP#_MN,-6 7$8$H$^gdvY`gdvY`gd 7$8$H$gdgdvY h7$8$H$^hgd,()+-hG #$lm. 0 !!!!!!!!I"""##T#w###7$8$:$;$<$˽๲܈܄܄}okhHhMCJOJQJ^JaJ hU^9h`h!t hv-h`j`hvYUjSC hvYUVjhvYUh-h@ hvYhvYh\hvYCJOJQJ^JaJ hvY5CJOJQJ\^JaJh`hvYhjhUjeSC hCJUVaJ(6hFG!!!!!##8$9$:$;$S$T$_$p$$$If`gdvYgd`^gdvYgdvY 7$8$H$gdvY 7$8$H$^gdvY<$R$S$T$$$$$$$$%%%E%F%q%r%%%%%%%\.\/\I\J\l\m\\\\\\\]]4]5]\]]]~]]]]]]]]^^^^>^?^_^`^^^^^^^^^^^^^D_M_뻵h!t h!tCJ hU^9hMUhHCJOJQJ^JaJhHCJaJ hH5CJOJQJ\^JaJhHhHhM5hHhH5F$$$$$If$$$$Ifkd $$IflֈL\ lX D%80%644 lap<$$$$$$ $$Ifa$$$$$Ifkd $$IflֈL\ lX D%''8''''0%644 lap<$$$$$$ $$Ifa$$$%$Ifkd $$IflֈL\ lX D%''8''''0%644 lap<%%%%%$% $$Ifa$$%%%5%$Ifkd $$IflֈL\ lX D%''8''''0%644 lap<5%9%;%?%A%E% $$Ifa$E%F%`%$Ifkd$$IflֈL\ lX D%''8''''0%644 lap<`%d%g%k%m%q% $$Ifa$q%r%%$Ifkd$$IflֈL\ lX D%''8''''0%644 lap<%%%%%% $$Ifa$%%%$Ifkd$$IflֈL\ lX D%''8''''0%644 lap<%%%%%% $$Ifa$%%%$Ifkd$$IflֈL\ lX D%''8''''0%644 lap<%%%%%% $$Ifa$%%\$Ifkd$$IflֈL\ lX D%''8''''0%644 lap<Roll of Thunder, Hear My Cry7.191.97-0.1Stowaway6.170.95-1.1The Color Purple6.981.16-0.9The Great Gatsby7.3102.780.7The Hitchhiker's Guide to the Galaxy8.3112.790.7The Last of the Mohicans10.3132.7110.7The Midwife's Apprentice69371The Runaway Jury810280The Scarlet Letter11.7131.311-0.7Vanity Fair12.412-0.410-2.4Caddie Woodlawn5.671.45-0.6Toning the Sweep5.671.45-0.6Matilda Bone5.793.371.3The Egypt Game5.593.571.5Chasing Redbird57250Out of the Dust5.371.75-0.3Of Mice and Men4.572.550.5The Road to Memphis87-15-3Wringer4.561.54-0.5Shiloh5.171.95-0.1Number the Stars57250Our Only May Amelia4.872.250.2 Jean M. 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