Making More Sense of
School Data
分析學校自評數據
Dr. Soh Kay Cheng
蘇啟禎博士
Consultant (QA)
EMB, Hong Kong SAR
jensoh@singnet.com.sg
Soh KC(2006) Making sense of school data
1
Why do we need data (statistics)?
為何要用數據(統計數字)﹖
 Is a special
language
 Ensures objectivity
 Avoids
misunderstanding
 Facilitates
communication
它是特殊的語言
它確保客觀
它避免誤解
它促進溝通
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2
Data for School Self-evaluation
學校自評的數據
 Describing status




 描述現狀
例如 KPM 4教師的學歷與經驗
e.g., KPM4 Teacher qualification &
experience
 描述見解
Describing views
例如 KPM 2教師對領導的評價
e.g., KPM 2 Staff’s views on
leadership
 描述表現
Describing performance
例如KPM 22學生出席率
e.g,, KPM22 Student attendance
 描述趨勢
Describing trends
例如KPM 9過去三年學生閱讀習
e.g., KPM9 Students’ reading
habits of past 3 years
 比較技術
Techniques for comparisons
例如 KPM 4教師學歷與本港參考
數據比較
e.g., Compare KPM4 Teacher
qualification with Hong Kong’s
Reference Data
Soh KC(2006) Making sense of school data
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Describing needs reference data
描述需要參考數據
 孤立的數據（如%）
 A statistic (e.g., %) standing
沒有多大意義甚至毫
alone has little or no meaning.
無意義。數據要有意
One or more points are
義﹐必須另有數據作
needed for meaningful
為參考。
interpretation of the given
 參考數據可能是隱含
statistic.
的﹐假設數據使用者
 Reference points may be
已有共識.
implicit, assuming the users
have common understanding.  隱含的數據必須明朗
化﹐明確指出參考數
 Implicit reference points need
據的性質。
be made explicit.
Soh KC(2006) Making sense of school data
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Good for a laugh
A professor of statistics meets a colleague
on his way to the lecture. The colleague
heartily greets him, “Good morning,
professor!” and then respectfully asks,
“How is your wife?”
And the professor absent-mindedly says,
“….?”
Soh KC(2006) Making sense of school data
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Describing status
描述現狀
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How popular are these ECAs?
這些課外活動受歡迎嗎
課外活動學會/小組的數目
學會 / 小組
組數
課外活動學會/小組的數目
學會/ 小組
組數
人數
每組平均人數
學術
1
學術
1
50
50
體育
9
體育
9
270
30
藝術
5
藝術
5
50
10
興趣
9
興趣
9
90
10
社會服務
12
社會服務
12
240
20
 The number of groups may not reflect the popularity of each activity.
 The nature of the activities may have an impact on their popularity.
 In addition to the number of units, it is good to report also the group
sizes to reflect their populatiry.
 每種活動的組別數目不一定反映活動受歡迎的程度。
 活動是否受歡迎﹐和活動的性質有關。
 除報告組數外﹐同時也報告各組人數﹐更能反映活動受歡迎的程度。
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Box-and-whisker plot as reference
盒鬚圖作為參照
 EMB issued Reports on Key
Performance Measures
Reference Data 2003/2004
for both primary and
secondary schools.
 The median is the mid-point
of a distribution. 50% of the
schools are at or above
(below) the median.
 Top 25% are at or above the
75th percentile. Likewise,
bottom 25% are below the
25th percentile. The middle
50% are between the 25th
and 75% percentiles.
 教統局印發2003/2004年度
中小學校表現評量參考數據
報告。
 中位數將學校分為上下兩個
群組﹐各有50%。
 最高的25% 在75百分位數或
以上。最低的25%在25百分
位數之下。中間的50%在兩
者之間。
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Use of box-and-whisker plot
盒鬚圖的運用
百份率
Percentage (%)
The percentage of subject-trained
Chinese and Mathematics teachers
of school are both 85%. How would
you report on these?
For Chinese, the school is at the
median of reference data
For Mathematics, the school is
among the top quarter.
本校已接受專科訓練的中文和數學教師
的百分率均為 85%。這情況怎麼報告？
已接受專科訓練的三個核心科目教師的百分比
% of Subject-trained Teachers
100
90
*
85%
*
80
70
60
中文教師方面，本校位列於參考數據的
中位數。
50
數學教師方面，本校位列於最高的四分
之一之內。
40
中文科教師
Subject-trained Chi Teachers
Soh KC(2006) Making sense of school data
數學科教師
Subject-trained Maths Teachers
9
Description is not evaluation
描述不等於評估
KPM3 教師專業發展
教師參與持續專業發展的平均時數
82.2
校長參與持續專業發展的時數
207.0
教學人員（包括教師與校長）在持續專業發展方面的平均預算支出
$127.3
教學人員（包括教師與校長）在持續專業發展方面的平均實際支出
$96.7
 Is it good that the teachers spent 82.2 hours and HK$127.3 on
professional development? What about the principal?
 Reference points needed could be Hong Kong norm, school’s past
records, or pre-determined targets.
 教師花費82.2小時和港幣127.3元於專業發展，理想嗎？校長方面呢？
 其他可用的參考資料，如香港常模、本校往年數據、或預定目標。
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Good to have another laugh
A young man boasts about his wife and
says, “My wife has a perfect figure of 100,
it’s 38-24-38.”
His middle-age friend, not wanting to lose
face, says calmly, “My wife has a perfect
figure adding up to 100, too. It is ….”
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Describing views
描述見解
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Scale and dispersion
尺度與變異
KPM02 教職員對學校領導層的觀感


校長的領導能力與態度
4.01
副校長的領導能力與態度
4.07
中層領導人員的領導能力與態度
4.01
Five-point scale was used. This
fact is implicit and needs be
made explicit. Should it be a 10point scale, the interpretation
would be rather different.
The two means of 4.01 give the
impression that the Principal
and the Middle Management
were equally favorably
evaluated. What if the SD for
Principal is 0.06 and that for the
Middle Management 1.12?

報告採用五度量表。尺度應
該說明。假如所用的是十度
量表，則各階層領導所得的
評估便非常不同。

兩個平均數4.01似乎顯示校
長與中管理層得到同樣的好
評。假如校長的標準差(SD)
是0.06，而中管理層的是1.12，
應作何解釋？
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Poverty is relative
A rich American wanted to show his son how rich they were.
He took the little boy to a seaside village in the South.
When everything was over, the father asked, “Son, what
have you learned from this trip?”
The boy said, “Oh, yes! We keep one dog and they have
four. Sitting at our patio, the view ends at the gate 50
yards away, but at their, there is no end to the horizon.
We built walls to protect ourselves, they have friends to
protect them….Thank you father, for showing me how….”
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Describing performance
描述表現
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Absolute and relative standards
絕對標準與相對標準
學生從學校圖書館借用資料頻數(中一至中三）
1 每周一次或以上
24.2%
2 每兩周一次
22.1%
3 每月一次
36.5%
4 每月少於一次
15.8%
5 從不
1.4%
•
•
Relative standard:
36.5% is the mode.
相對標準
•
•
Absolute standard:
46.3% borrowed at least
once in two weeks.
絕對標準
預期目標：每兩週借
用資料至少一次的學
生有50%或以上。
實際上﹐每兩週借用
資料至少一次的學生
有46.3%﹐接近預期
目標50%。 。
借用層次有五個。其中最高的是“每月一次”。
因此﹐學生借用資料頻數的眾數(36.5%)為“每
月一次”。
Soh KC(2006) Making sense of school data
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The dangerous average
Mr. Dumb Bell jumped into the sea from a
jetty and got a big hump on his forehead,
because the sign board says:
First 30 meters,
average depth 5 meters!
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Describing trends
描述趨勢
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Evaluation varies with reference data
評價隨參考數據而變
校內學科測驗成績
學科 2003 2004 2005
中文 41.2 55.0 52.3
英文 22.8 44.7 35.3
數學 13.1 33.9 39.3
 Relatively speaking, there was an
improvement in 2004 over 2003 in all
three subjects, but, there is a
retrogression from 2004 to 2005 in
the two languages.
 Assumption: Papers of the three
years are equivalent.
 Need HK norms for the three years
for proper interpretation.
60
50
40
30
20
10
0
2003
2004
中文
英文
2005
數學
 相對而言，2004的成績比2003的好，
有進步。但是，從2004 到2005, 兩
語文科有退步的現象。
 假設：三年的考卷難度相同。
 正確的解釋需要三年的香港常模作
為參考資料。
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Effect Size
效果强度
學校數據
參考數據
比參考數據
課程策劃與組織
3.65
3.54
+0.11*
課程管理
3.70
3.57
+0.21*
教學策略和技巧
3.65
3.45
+0.20*
*比參考數據 +/-0.1或以上
 Comparison with Reference Data
is a good effort. However, +/-0.1  將本校的情況和參考數據比較，
是好的做法。 但是﹐以+/-0.1
is arbitrary.
為臨界值﹐似乎武斷。
 If SDs are available, then effect
sizes can be calculated for more  如有標準差﹐可轉化為效果強
meaningful interpretation.
度(Effect size),更有意義。
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Conversion to effect size
效果強度的轉化
School
Mean
Reference Data
Mean (SD)
Effect Size
課程策劃與組織
3.65
3.54 (0.25)
0.44
課程管理
3.70
3.57 (0.18)
0.72
教學策略和技巧
3.65
3.45 (1.15)
0.20
註﹕參考數據是虛擬的。
 With reference to the normal distribution, ES can be used to
evaluate differences in percentages.
ES = (Mean – Norm) / SD
 如參照常態分佈﹐百分率可轉化為效果強度﹐以便檢定百分率差異的
意義。
效果強度 = （平均數 – 常模）/ 標準差
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Effect size ‘standards’
效果強度的‘標準’
Difference in %
Effect size
Description
Below 0.2
Negligible effect
微效果
Between 8 and 18 %
Between
0.20 and 0.49
Small effect
小效果
Between 19 and 28%
Between
0.50 and 0.79
Between
0.80 and 0.99
1.00 and
above
Moderate effect
中等效果
Below 8%
Between 29 and 34%
35% or more
Soh KC(2006) Making sense of school data
Large effect
大效果
Very large effect
極大效果
22
Summary 綱要
Use data to ensure objectivity and
1.
common frame of mind.
2.
2. Use data to describe status, views,
performance, and trends.
3.
3. Use reference data for meaningful
4.
interpretation.
5.
4. Use %’s for comparison.
6.
5. Use reference data for evaluation。
6. Data for reference may be the norms,
7.
past records, or targets.
7. Two means of the same magnitude
may have different meaning. Watch out 8.
for difference in variability.
8. Use absolute or relative standard to
9.
describe performance
9. Use curves to indicate trends and
10.
watch out for tacit assumptions.
10. Use effect size ‘standards’ for objective
evaluation of effects.
1.
用數據溝通，力求客觀共識。
用數據描述現狀﹑見解﹑表
現﹑與趨勢。
用參考數據作有意義的詮釋。
用百分比作比較。
用參考數據來評估。
參考的數據可能是常模﹑記
錄﹑或目標。
兩個相同的平均數可能有不同
意義。注意變數的大小。
用絕對標準或相對標準描述表
現。
用曲線圖表達趨勢﹐並注意隱
含的假設。
用效果強度的「標準」進行客
觀的評估。
Soh KC(2006) Making sense of school data
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Statistics are estimates
I asked a statistician for
her telephone number and
she gave me an estimate.
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Comparison Techniques
比較技術
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Purpose
School reports always present summary
data such as the mean, the SD, etc.
Statistical calculators on the Internet can
be used to make some of the needed
comparisons.
This part of the seminar introduces such
calculators to enable schools to make
finer interpretation.
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Comparison with expected performance
與預期表現比較
N
65
Mean
3.71
The result of a survey on KPM2
Teachers’ view on the principal’s
leadership. If the expected mean
is 3.50, was the principal more
favorably evaluated than is
expected?
This calls for a one-sample t-test
and the critical value of p is set at
0.05.
SD
0.35
KPM2 教師對校長領導能力的評
估，調查結果如表所示。
如果預期平均數為3.50，校長所
得平均數是否較預期的為高？
這需要用單組t-測加以鑒定，並以
0.05為p的臨界值。
Soh KC(2006) Making sense of school data
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The result shows that the obtained
mean (3.71) is statistically greater
than the expected mean (3.50).
The principal was evaluated higher
than the expected.
統計分析結果顯示，實得的平均數
（3.71）的確高於預期的平均數
（3.50）。校長所得評估的確比預
期的高。
http://glass.ed.asu.edu/stats/analysis/ttest.html
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Comparison of two groups
兩群組比較
Teachers
N
65
Mean
3.52
SD
0.30
Parents
125
3.75
0.65
The table shows the ratings on
KPM11 School culture given by
teachers and parents. Did the
parents evaluate the school
more favorably than did the
teachers?
上表顯示教師與家長對KPM11
學校文化的評估。兩者對學校的
確有不同評價嗎？
這必須用獨立t-測加以鑒定，並
以0.05為p的臨界值。
This calls for an independent ttest and the critical p is set at
0.05
Soh KC(2006) Making sense of school data
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http://glass.ed.asu.edu/stats/analysis/t2test.html
The result shows that the difference
(0.23) between the two means is
unlikely a chance occurrence. Parents
did evaluated the school more
favourably than did the teachers.
統計結果顯示，兩平均數之差
(0.23) 並非機遇現象。家長對學
校的評價的確高於教師的評價。
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Comparison of many groups
多群組比較
Teachers (N=65)
Students (N=120)
Parents (N=105)
The ratings on KPM 11 School
culture as given by teachers,
students, and parents are shown
above. Did the three groups
differ in their rating?
This calls for one-way ANOVA
(analysis of variance) followed
by pair-wise comparisons.
Mean
3.51
3.65
3.83
SD
0.35
0.45
0.52
針對 KPM 11 學校文化，教師、
學生、與家長作以上的評估。三
組的評價的確有差異嗎？
這需要用單向變異分析（oneway analysis of variance）鑒
定，並再用配對t-測。
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http://statpages.org/anova1sm.html
The analysis shows that p<0.05; there is
at least one significant difference among
the three means.
分析結果顯示p<0.05，表示至少有
一對的平均數有非機遇的差異。
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32
http://glass.ed.asu.edu/stats/analysis/t2test.html
As there are three pair-wise tests,
Bonferroni adjustment is applied to
avoid accumulation of error. For
three tests, the p-value should be
0.05/3 or 0.0166. To check on
these p-values, see the next slide.
有三對平均數作配對比較，必須作
Bonferroni調整，以避免誤差的累
積，而p-值應該是0.05/3 or
0.0166. 要確定這三個p-值，請看
下頁。
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http://department.obg.cuhk.edu.hk/researchsupport/T_Test.asp
(65 + 120 - 2)
For all three t-values (21.76, 43.82,
and 27.84), the corresponding p is
0.0001. The differences among the
three means are statistically
significance; the differences are
very unlikely chance occurrences.
三個 t-數(21.76, 43.82, and 27.84)
配對比較的相應p-值是0.0001. 它們
之間的差異並非機遇現象；其間的確
有差異。
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Comparison with reference data (1)
與參考數據比較（一）
Professionally trained
Not trained
Hong Kong
96% (62)
4% (3)
School
90% (59)
10% (7)
For KPM 4, the school has 90%
of its 65 teachers professionally
trained. Is this percentage
significantly lower than the
Hong Kong Reference Data?
This calls for a chi-square test
of goodness of fit. The
percentages need be converted
into frequencies for analysis.
學校的65位教師，有90%
受過專業訓練。這和香港參
考資料比較，有差異嗎？
這需要用卡方測驗來鑒定。
並需先將百分數轉為頻數。
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http://www.georgetown.edu/faculty/ballc/webtools/web_chi.html
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Soh KC(2006) Making sense of school data
37
The chi-square test results show
p>0.05; the school’s distribution fits
the Hong Kong distribution.
卡方測驗結果，p>0.05;顯示學校的
分配情況和香港參考數據相配。
Since the chi-square is not significant, the school is not different from
the Hong Kong reference data.
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Comparison with reference data (2)
與參考數據比較（二）
Master
Bachelor
Non-degree
Hong Kong
23% (15)
66% (43)
11% (7)
School
27% (18)
58% (38)
15% (9)
For KPM 4, the school reported the
percentages of teachers with
different qualification as shown
above. Does the school’s
distribution differ significantly from
the Reference Data?
學校教師學歷分佈如表所示。與參
考數據相同嗎？
用卡方測驗鑒定。
This calls for a chi-square test.
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39
Since the chi-square is not
significant (p>0.05), the school’s
distribution is not different from
the Reference Data.
卡方檢查結果，p>0.05 ; 學校的分
佈情況和參考數據的沒有不同。
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Summary 綱要
One-sample t-test for comparing a
observed mean to an expected
mean.
Two-sample t-test for comparing the
means of two independent groups.
One-way ANOVA for comparing more
than two independent means.
Significance of t-value for checking
the probability of an obtained tvalue.
Chi-square test for ascertaining
association between membership
and performance.
單組t-測：比較實際平均數與
預期平均數。
兩組t-測：比較兩組的平均數.
單向變異分析：比較多過兩組
的差異。
t-值的臨界值：檢查所得t-值
是否機遇現象。
卡方測驗：檢定兩個分佈情況
之間的差異。
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Hyperlinks to calculators
One-sample t-test
http://glass.ed.asu.edu/stats/analysis/ttest.html
Two-sample t-test
http://glass.ed.asu.edu/stats/analysis/t2test.html
One-way ANOVA
http://statpages.org/anova1sm.html
Significance of t-value
http://department.obg.cuhk.edu.hk/researchsupport/T_Test.asp
Chi-square test
http://www.georgetown.edu/faculty/ballc/webtools/web_chi.html
Soh KC(2006) Making sense of school data
42
He who laughs last, laughs best
最後一笑
Q: As a principal, how do you develop your
teachers professionally?
A: As a responsible leader, I make sure that
everyone of them is busy and works hard.
Q: What are they working hard on?
A: That does not really matter, as long as they are
working non-stop.
Q: Could you give me an example?
A: For instance, ….
Soh KC(2006) Making sense of school data
43
Thank you
謝謝
Soh KC(2006) Making sense of school data
44