Bài giảng Sinh thống kê

© 2006 1 Sinh thống kê GS TS Lê Hoàng Ninh © 2006Evidence-based Chiropractic 2 Dịnh nghỉa một số thuật ngữ trong sinh thống kê • Dữ liệu: – Số đo hay quan sát một biến số • Biến số: – Đặc trưng được khảo sát đo đạt – Có thể có nhiều trị số khác nhau từ đối tượng nầy đến đối tượng khác © 2006Evidence-based Chiropractic 3 Định nghĩa từ dùng trong thống kê • Biến số độc lập – Có trước biến số phụ thuộc; căn nguyên/ nguyên nhân của một hệ quả nào đó – Thuốc lá -> ung thư phổi – Thuốc A -> khỏi bệnh • Biến số phụ thuộc: – Số đo hệ quả,/ kết cuộc – Trị số phụ thuộc và biến độc lập © 2006Evidence-based Chiropractic 4 Từ …. • Tham số (Parameters) – Dữ liệu/ số đo trên quần thể (Summary data from a population) • Số thống kê (Statistics) – Dữ liệu/ số đo trên mẫu (Summary data from a sample) © 2006Evidence-based Chiropractic 5 Quần thể • Quần thể là tập hợp các cá thể mà mẫu được lấy ra – e.g., headache patients in a chiropractic office; automobile crash victims in an emergency room • Trong nghiên cứu, không thể đo đạt khảo sát trên toàn bộ quần thể • Do vậy cần phải lấy mẫu ( tổ hợp con của quần thể) © 2006Evidence-based Chiropractic 6 Mẫu ngẫu nhiên • Các đối tượng được lấy ra từ quần thể để sao cho các cá thể có cơ hội như nhau được chọn ra • Mẫu ngẫu nhiên thì đại diện cho quần thể • Mẫu không ngẫu nhiên thì không đại diện – May be biased regarding age, severity of the condition, socioeconomic status etc. © 2006Evidence-based Chiropractic 7 Mẫu ngẫu nhiên • Mẫu ngẫu nhiên hiếm có trong các nghiên cứu chăm sóc bệnh nhân • Thay vào đó, dùng phân phối ngẫu nhiên vào 2 nhóm điều trị và nhóm chứng – Each person has an equal chance of being assigned to either of the groups • Phân phối ngẫu nhiên vào các nhóm = randomization © 2006Evidence-based Chiropractic 8 Thống kê mô tả (DSs) • Cách tóm tắt dữ liệu • Minh họa bộ dữ liệu = shape, central tendency, and variability of a set of data – The shape of data has to do with the frequencies of the values of observations © 2006Evidence-based Chiropractic 9 Thống kê mô tả – Khuynh hướng trung tâm : vị trí chính giữa bộ dữ liệu – Khuynh hướng biến thiên: các trị số phía dưới , phía trên trị số trung tâm • Dispersion • Thống kê mô tả khác biệt với thống kê suy lý – Thống kê mô tả không thể kiểm định giả thuyết © 2006Evidence-based Chiropractic 10 MỘT BỘ DỮ LiỆU Case # Visits 1 7 2 2 3 2 4 3 5 4 6 3 7 5 8 3 9 4 10 6 11 2 12 3 13 7 14 4 • Distribution provides a summary of: – Frequencies of each of the values • 2 – 3 • 3 – 4 • 4 – 3 • 5 – 1 • 6 – 1 • 7 – 2 – Ranges of values • Lowest = 2 • Highest = 7 etc. © 2006Evidence-based Chiropractic 11 Bảng phân phối tần số Frequency Percent Cumulative % • 2 3 21.4 21.4 • 3 4 28.6 50.0 • 4 3 21.4 71.4 • 5 1 7.1 78.5 • 6 1 7.1 85.6 • 7 2 14.3 100.0 © 2006Evidence-based Chiropractic 12 PHÂN PHỐI TẦN SỐ ĐƯỢC BIỂU THỊ BẰNG histogram © 2006Evidence-based Chiropractic 13 Histograms (cont.) • A histogram is a type of bar chart, but there are no spaces between the bars • Histograms are used to visually depict frequency distributions of continuous data • Bar charts are used to depict categorical information – e.g., Male–Female, Mild–Moderate–Severe, etc. © 2006Evidence-based Chiropractic 14 SỐ ĐO KHUYNH HƯỚNG TRUNG TÂM • Số trung bình – The most commonly used DS • Tính số trung bình – Add all values of a series of numbers and then divided by the total number of elements © 2006Evidence-based Chiropractic 15 Công thức tính số trung bình • Trung bình mẫu • Trung bình quần thể  (X bar) refers to the mean of a sample and refers to the mean of a population  EX is a command that adds all of the X values  n is the total number of values in the series of a sample and N is the same for a population X μ N X  n X X   © 2006Evidence-based Chiropractic 16 Số đo trung tâm • Mode – The most frequently occurring value in a series – The modal value is the highest bar in a histogram Mode © 2006Evidence-based Chiropractic 17 Số đo trung tâm • Trung vịn – The value that divides a series of values in half when they are all listed in order – When there are an odd number of values • The median is the middle value – When there are an even number of values • Count from each end of the series toward the middle and then average the 2 middle values © 2006Evidence-based Chiropractic 18 Số đo trung tâm • Each of the three methods of measuring central tendency has certain advantages and disadvantages • Which method should be used? – It depends on the type of data that is being analyzed – e.g., categorical, continuous, and the level of measurement that is involved © 2006Evidence-based Chiropractic 19 Cấp độ số đo • There are 4 levels of measurement – Nominal, ordinal, interval, and ratio 1. Nominal – Data are coded by a number, name, or letter that is assigned to a category or group – Examples • Gender (e.g., male, female) • Treatment preference (e.g., manipulation, mobilization, massage) © 2006Evidence-based Chiropractic 20 Cấp độ số đo 2. Ordinal – Is similar to nominal because the measurements involve categories – However, the categories are ordered by rank – Examples • Pain level (e.g., mild, moderate, severe) • Military rank (e.g., lieutenant, captain, major, colonel, general) © 2006Evidence-based Chiropractic 21 Cấp độ số đo • Ordinal values only describe order, not quantity – Thus, severe pain is not the same as 2 times mild pain • The only mathematical operations allowed for nominal and ordinal data are counting of categories – e.g., 25 males and 30 females © 2006Evidence-based Chiropractic 22 Cấp độ số đo 3. Khoảng – Measurements are ordered (like ordinal data) – Have equal intervals – Does not have a true zero – Examples • The Fahrenheit scale, where 0° does not correspond to an absence of heat (no true zero) • In contrast to Kelvin, which does have a true zero © 2006Evidence-based Chiropractic 23 Cấp độ số đo 4. Ratio – Measurements have equal intervals – There is a true zero – Ratio is the most advanced level of measurement, which can handle most types of mathematical operations © 2006Evidence-based Chiropractic 24 Levels of measurement (cont.) • Ratio examples – Range of motion • No movement corresponds to zero degrees • The interval between 10 and 20 degrees is the same as between 40 and 50 degrees – Lifting capacity • A person who is unable to lift scores zero • A person who lifts 30 kg can lift twice as much as one who lifts 15 kg © 2006Evidence-based Chiropractic 25 Levels of measurement (cont.) • NOIR is a mnemonic to help remember the names and order of the levels of measurement – Nominal Ordinal Interval Ratio © 2006Evidence-based Chiropractic 26 Cấp độ số đo Measurement scale Permissible mathematic operations Best measure of central tendency Nominal Counting Mode Ordinal Greater or less than operations Median Interval Addition and subtraction Symmetrical – Mean Skewed – Median Ratio Addition, subtraction, multiplication and division Symmetrical – Mean Skewed – Median © 2006Evidence-based Chiropractic 27 Hình dạng bộ dữ liệu • Histograms of frequency distributions have shape • Distributions are often symmetrical with most scores falling in the middle and fewer toward the extremes • Most biological data are symmetrically distributed and form a normal curve ( bell- shaped curve) © 2006Evidence-based Chiropractic 28 Hình dạng bộ dữ liệu Line depicting the shape of the data © 2006Evidence-based Chiropractic 29 Phân phối bình thường • The area under a normal curve has a normal distribution ( Gaussian distribution) • Properties of a normal distribution – It is symmetric about its mean – The highest point is at its mean © 2006Evidence-based Chiropractic 30 The normal distribution (cont.) Mean A normal distribution is symmetric about its mean As one moves away from the mean in either direction the height of the curve decreases, approaching, but never reaching zero The highest point of the overlying normal curve is at the mean © 2006Evidence-based Chiropractic 31 The normal distribution (cont.) Mean = Median = Mode © 2006Evidence-based Chiropractic 32 Phân phối lệch (Skewed distributions) • The data are not distributed symmetrically in skewed distributions – Consequently, the mean, median, and mode are not equal and are in different positions – Scores are clustered at one end of the distribution – A small number of extreme values are located in the limits of the opposite end © 2006Evidence-based Chiropractic 33 Phân phối lệch • Skew is always toward the direction of the longer tail – Positive if skewed to the right – Negative if to the left The mean is shifted the most © 2006Evidence-based Chiropractic 34 Phân phối lệch Skewed distributions • Because the mean is shifted so much, it is not the best estimate of the average score for skewed distributions • The median is a better estimate of the center of skewed distributions – It will be the central point of any distribution – 50% of the values are above and 50% below the median © 2006Evidence-based Chiropractic 35 Những tính chất đường cong bình thường • About 68.3% of the area under a normal curve is within one standard deviation (SD) of the mean • About 95.5% is within two SDs • About 99.7% is within three SDs © 2006Evidence-based Chiropractic 36 More properties of normal curves (cont.) © 2006Evidence-based Chiropractic 37 Độ lệch chuẩn (SD) • SD is a measure of the variability of a set of data • The mean represents the average of a group of scores, with some of the scores being above the mean and some below – This range of scores is referred to as variability or spread • Variance (S2) is another measure of spread © 2006Evidence-based Chiropractic 38 SD (cont.) • In effect, SD is the average amount of spread in a distribution of scores • The next slide is a group of 10 patients whose mean age is 40 years – Some are older than 40 and some younger © 2006Evidence-based Chiropractic 39 SD (cont.) Ages are spread out along an X axis The amount ages are spread out is known as dispersion or spread © 2006Evidence-based Chiropractic 40 Distances ages deviate above and below the mean Adding deviations always equals zero Etc. © 2006Evidence-based Chiropractic 41 Calculating S2 • To find the average, one would normally total the scores above and below the mean, add them together, and then divide by the number of values • However, the total always equals zero – Values must first be squared, which cancels the negative signs © 2006Evidence-based Chiropractic 42 Calculating S2 cont. Symbol for SD of a sample  for a population S2 is not in the same units (age), but SD is © 2006Evidence-based Chiropractic 43 Wide spread results in higher SDs narrow spread in lower SDs © 2006Evidence-based Chiropractic 44 Spread is important when comparing 2 or more group means It is more difficult to see a clear distinction between groups in the upper example because the spread is wider, even though the means are the same © 2006Evidence-based Chiropractic 45 z-scores • The number of SDs that a specific score is above or below the mean in a distribution • Raw scores can be converted to z-scores by subtracting the mean from the raw score then dividing the difference by the SD    X z © 2006Evidence-based Chiropractic 46 z-scores (cont.) • Standardization – The process of converting raw to z-scores – The resulting distribution of z-scores will always have a mean of zero, a SD of one, and an area under the curve equal to one • The proportion of scores that are higher or lower than a specific z-score can be determined by referring to a z-table © 2006Evidence-based Chiropractic 47 z-scores (cont.) Refer to a z-table to find proportion under the curve © 2006Evidence-based Chiropractic 48 z-scores (cont.) Partial z-table (to z = 1.5) showing proportions of the area under a normal curve for different values of z. Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94410.9 32 Corresponds to the area under the curve in black