1 / 60

Data Analysis

Chapter 8. Data Analysis. Chapter 6 Data Analysis. In this chapter, we focus on 3 parts:. 1. Descriptive Analysis 2. Two-way Analysis of Variance 3. Forecasting. Chapter 6 Data Analysis. 1. Descriptive Analysis. 1.1 Index Numbers 1.2 Exponential Smoothing. Chapter 6 Data Analysis.

lucas-bonner
Télécharger la présentation

Data Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 Data Analysis

  2. Chapter 6Data Analysis In this chapter, we focus on 3 parts: • 1. Descriptive Analysis • 2. Two-way Analysis of Variance • 3. Forecasting

  3. Chapter 6Data Analysis 1. Descriptive Analysis • 1.1 Index Numbers • 1.2 Exponential Smoothing

  4. Chapter 6Data Analysis 1.1 Index Numbers • Index Number – a number that measures the change in a variable over time relative to the value of the variable during a specific base period • Simple Index Number – index based on the relative changes (over time) in the price or quantity of a single commodity

  5. Chapter 6Data Analysis 1.1 Index Numbers Laspeyres and Paasche Indexes compared • The Laspeyres Index weights by the purchase quantities of the baseline period • The Paasche Index weights by the purchase quantities of the period the index value represents. • Laspeyres Index is most appropriate when baseline purchase quantities are reasonable approximations of purchases in subsequent periods. • Paasche Index is most appropriate when you want to compare current to baseline prices at current purchase levels

  6. Chapter 6Data Analysis 1.1 Index Numbers • Calculating a Laspeyres Index • Collect price info for the k price series (the “basket”) to be used, denoted as P1t, P2t…Pkt • Select a base period t0 • Collect purchase quantity info for base period, denoted as Q1t0, Q2t0…..Qkt0 • Calculate weighted totals for each time period using the formula • Calculate the index using the formula

  7. Chapter 6Data Analysis 1.1 Index Numbers • Calculating a Paasche Index • Collect price info for the k price series to be used, denoted as P1t, P2t…Pkt • Select a base period t0 • Collect purchase quantity info for every period, denoted as Q1t, Q2t…..Qkt • Calculate the index for time t using the formula

  8. Chapter 6Data Analysis 1.2 Exponential Smoothing • Exponential smoothing is a type of weighted average that applies a weight w to past and current values of the time series. (Yiactual value) • Exponential smoothing constant (w) lies between 0 and 1, and smoothed series Et is calculated as: • How much influence • does the past have when w = 0 and when w = 1?

  9. Chapter 6Data Analysis 1.2 Exponential Smoothing • Selection of smoothing constant w is made by researcher. • Small values of w give less weight to current value, yield a smoother series • Large values of w give more weight to current value, yield a more variable series

  10. Chapter 6Data Analysis 2 Two-way Analysis of Variance • Two-way ANOVA is a type of study design with one numerical outcome variable and two categorical explanatory variables. • Example – In a completely randomised design we may wish to compare outcome by age, gender or disease severity. Subjects are grouped by one such factor and then randomly assigned one treatment. • Technical term for such a group is block and the study design is also called randomised block design

  11. Chapter 6Data Analysis 2 Two-way Analysis of Variance • 2.1 Randomised Block Design • 2.2 Analysis in Two-way ANOVA – 1 • 2.3 Analysis of Two-way ANOVA by the regression method

  12. Chapter 6Data Analysis 2.1 Randomised Block Design • Blocks are formed on the basis of expected homogeneity of response in each block (or group). • The purpose is to reduce variation in response within each block (or group) due to biological differences between individual subjects on account of age, sex or severity of disease.

  13. Chapter 6Data Analysis 2.1 Randomised Block Design • Randomised block design is a more robust design than the simple randomised design. • The investigator can take into account simultaneously the effects of two factors on an outcome of interest. • Additionally, the investigator can test for interaction, if any, between the two factors.

  14. Chapter 6Data Analysis 2.1 Randomised Block Design Steps in Planning a Randomised Block Design • Subjects are randomly selected to constitute a random sample. • Subjects likely to have similar response (homogeneity) are put together to form a block. • To each member in a block intervention is assigned such that each subject receives one treatment. • Comparisons of treatment outcomes are made within each block

  15. Chapter 6Data Analysis 2.2 Analysis in Two-way ANOVA - 1 The variance (total sum of squares) is first partitioned intoWITHIN and BETWEEN sum of squares. Sum of Squares BETWEENis next partitioned by intervention, blocking and interaction SSTOTAL SS BETWEEN SS WITHIN SS INTERVENTION SS BLOCKING SS INTERACTION

  16. Chapter 6Data Analysis 2.2 Analysis in Two-way ANOVA - 1 method. And an interaction between gender and teaching method is being sought. Analysis of Two-way ANOVA is demonstrated in the slides that follow. The study is about a n experiment involving a teaching method in which professional actors were brought in to play the role of patients in a medical school. The test scores of male and female students who were taught either by the conventional method of lectures, seminars and tutorials and the role-play method were recorded. The hypotheses being tested are: Role-play method is superior to conventional way of teaching. Female students in general have better test scores than male students. Role-play method makes a better impact on students of a particular gender. Thus, there are two factors – gender and teaching method. And an interaction between teaching method and gender is being sought.

  17. Chapter 6Data Analysis 2.2 Analysis in Two-way ANOVA - 2 • Each Sum of Squares (SS) is divided by its degree of freedom (df) to get the Mean Sum of Squares (MS). • The F statistic is computed for each of the three ratios as MS INTERVENTION ÷ MS WITHIN MS BLOCK ÷ MS WITHIN MS INTERVENTION ÷ MS WITHIN

  18. Chapter 6Data Analysis 2.2 Analysis of Two-way ANOVA - 3 Analysis of Variance for score Source DF SS MS F P sex 1 2839 2839 22.75 0.000 Tchmthd 1 1782 1782 14.28 0.001 Error 29 3619 125 Total 31 8240

  19. Chapter 6Data Analysis 2.2 Analysis of Two-way ANOVA - 4 Individual 95% CI Sex Mean --------+---------+---------+---------+--- 0 58.5 (------*------) 1 39.6 (-------*------) --------+---------+---------+---------+--- 40.0 48.0 56.0 64.0 Individual 95% CI Tchmthd Mean ---------+---------+---------+---------+-- 0 56.5 (-------*-------) 1 41.6 (-------*--------) ---------+---------+---------+---------+-- 42.0 49.0 56.0 63.0

  20. Chapter 6Data Analysis 2.2 Analysis of Tw0-way ANOVA - 5 Analysis of Variance for SCORE Source DF SS MS F P SEX 1 2839 2839 22.64 0.000 TCHMTHD 1 1782 1782 14.21 0.001 INTERACTN 1 108 108 0.86 0.361 Error 28 3511 125 Total 31 8240 Interaction is not significant P = 0.361

  21. Chapter 6Data Analysis 2.2 Analysis of Two-way ANOVA - 6 Individual 95% CI SEX Mean --------+---------+---------+---------+--- 0 58.5 (------*------) 1 39.6 (-------*------) --------+---------+---------+---------+--- 40.0 48.0 56.0 64.0 Individual 95% CI TCHMTHD Mean ---------+---------+---------+---------+-- 0 56.5 (-------*-------) 1 41.6 (-------*--------) ---------+---------+---------+---------+-- 42.0 49.0 56.0 63.0

  22. Chapter 6Data Analysis 2.3 Analysis of Two-way ANOVA by the regression method (reference coding) The regression equation is SCORE = 65.9 - 18.8 SEX - 14.9 TCHMTHD Predictor Coef SE Coef T P Constant 65.913 3.420 19.27 0.000 SEX -18.838 3.950 -4.77 0.000 TCHMTHD -14.925 3.950 -3.78 0.001 S = 11.17 R-Sq = 56.1% R-Sq(adj) = 53.1% Analysis of Variance Source DF SS MS F P Regression 2 4620.9 2310.4 18.51 0.000 Residual Error 29 3619.0 124.8 Total 31 8239.8

  23. Chapter 6Data Analysis 2.3 Analysis of Two-way ANOVA by the regression method (effect coding) The regression equation is SCORE = 49.0 - 9.42 EFCT-Sex - 7.46 EFCT-Tchmthd - 1.84 Interaction Predictor Coef SE Coef T P Constant 49.031 1.980 24.77 0.000 EFCT-Sex -9.419 1.980 -4.76 0.000 EFCT-Tch -7.463 1.980 -3.77 0.001 Interact -1.838 1.980 -0.93 0.361 S = 11.20 R-Sq = 57.4% R-Sq(adj) = 52.8%

  24. Chapter 6Data Analysis Reference Coding and Effect Coding - 1 • In both methods, for k explanatory variables k-1 dummy variables are created. • In reference coding the value 1 is assigned to the group of interest and 0 to all others (e.g. Female =1; Male =0). • In effect coding the value −1 is assigned to control group; +1 to the group of interest (e.g. new treatment), and 0 to all others (e.g. Female =1; Male (control group) = −1; Role Play = +1; conventional teaching (control) = −1).

  25. Chapter 6Data Analysis Reference Coding and Effect Coding - 2 • In reference coding the β coefficients of the regression equation provide estimates of the differences in means from the control (reference) group for various treatment groups. • In effect coding the β coefficients provide the differences from the overall mean response for each treatment group.

  26. Chapter 6Data Analysis 3.1 The concept of market forecast 3.2 The theoretical bases of forecast 3.3 The classification of forecast methods 3.4 Qualitative Forecast Methods 3.5 Quantitative Forecast Methods 3 Marketing Forecasting

  27. Chapter 6Data Analysis 3.1 The concept of market forecast • Based on market surveys and by applying scientific methods, to estimate the development situation of objects-forecasted in a certain period in future in order to help managers to improve decisions-making qualify. The process is generally called as market forecast. • In this chapter, objects-forecasted mainly are need quantities of products, sometime may also be product prices, competitive situations, environmental factors, and so on.

  28. Chapter 6Data Analysis 3.2 The theoretical bases of forecast • (1)The continuity principle: ●It is also called as inertia principle. Because of existing inertia, any system doesn't change its basic characteristics in the short run. Attention: all time series analysis methods are based on this principle.

  29. Chapter 6Data Analysis 3.2 The theoretical bases of forecast • (2)The analogy principle: ●time analogy:to make aninference in future from the past and the present. When two things and more things have characteristic similarity (structure, mode, property, and develop tendency), we can forecast the developing things and the ready-to-develop things by studying the developed or advanced things. Attention: analogy is suitable to the homogeneous things, also to inhomogeneous things.

  30. Chapter 6Data Analysis 3.2 The theoretical bases of forecast • (2)The analogy principle: ●(continual to front page) sampling analogy: to make aninference about the whole from the part. When the whole and the part have characteristic similarity, we can forecast the whole by studying the part. Attention: the similarity is the key point either between the things with difference in advance time, or between the whole and the part.

  31. Chapter 6Data Analysis 3.2 The theoretical bases of forecast • (3)The relevancy principle: ●the theory considers that there is relativity among things, especially between two relevance things or causal things. All statistical regression analysis methods are based on this principle.

  32. Chapter 6Data Analysis 3.3 The classification of forecast methods Although there are many theoretical forecast methods, in general forecast can be classified as two types: • qualitative forecast • quantitative forecast.

  33. Chapter 6Data Analysis 3.3.1 Qualitative forecast • Qualitative forecast emphasizes the development tendencies (maybe essential characteristics), and is suitable to cases which there are a fewer and lack of data, such as science and technology forecast, development forecast of infant industries, long-term forecast, and forecasting things with uncertainty, etc.

  34. Chapter 6Data Analysis 3.3.2 Quantitative forecast • Quantitative forecast emphasizes the quantitative relationships of developing things. Essentially it is a kind of methods based on quantitative trend extrapolation, and is suitable to cases which there are many data.

  35. Chapter 6Data Analysis 3.3.3 The comparison of two methods • Qualitative forecast might contribute to the analysis of the basic trends, development inflection point, and the essence of things. Quantitative forecast can draw us numeral development concepts, and bring us conveniences of applying forecast results. None of two methods should be our preference, otherwise we probably abuse forecast methods.

  36. Chapter 6Data Analysis 3.4 Qualitative Forecast Methods • Delphi method • Social investigation or consumer survey • Colligating seller’s opinions • having an informal discussion of a team • Integration of expert’s forecasts • The method of subjective probabilities above methods all belong to non-models.

  37. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Exponential Smoothing: ●mathematical model: ●signs and meanings: to explain every sign and its meaning ●αvalue: αis greater, means that the more late sample observations, the more its influence on forecast results. Vice versa. Recommendation: α= 2/(n+1)

  38. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Exponential Smoothing: ●mathematical model----horizontal trend: ● mathematical model----lineal trend:

  39. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Exponential Smoothing: ●mathematical model---- quadratic curve trend:

  40. Chapter 6Data Analysis horizontal lineal quadratic curve 3.5 Quantitative Forecast Methods • Exponential Smoothing: ●how to choose mathematical models: according to the trend of sample observations on coordinate diagram.

  41. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Exponential Smoothing: ●how to determine initial values of smoothing parameters: in general, the first observation value instead of them. ●superiorities of exponential smoothing: the storage data only is a fewer and it is suitable to forecast in short run. ●application cases: reference to another teaching materials.

  42. Chapter 6Data Analysis Sales,Y 0 Time,t 3.5 Quantitative Forecast Methods • The growth curve: ●mathematical model: • Logistic curve: • Gompertz curve

  43. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • The growth curve: ●mathematical processing of initial observations: • For Logistic curve: 2. For Gompertz curve: The processed data of observations can be used for calculation of parameters k, a and b. The calculation formulas are as following:

  44. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Calculation of k, a, and b: Attention: the processed data of observations must be blacked into 3 groups, thus we can obtain 3 sum values When the number of initial data is not integer multiple of 3, we must add or cut down data of initials.

  45. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: ●An independent variable and a dependent variable are chosen on the model, and the varied relation of y and x is linear. This model is widely applied in quantitative forecasts. ●the standard model: y=a+bx to non-standard equation, it is must transferred as standard model.

  46. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: ●determination of the coefficient a and b: by means of method of minimum squares, let the variance minimization, and the calculation of is as following: and let derivatives of Q to a and b are equal to 0, then

  47. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: We can get a and b:

  48. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: ●then the forecast model is: It is necessary to check if the model the built model is of high quality, the checking methods are: 1. standards error analysis:

  49. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: in general, the following is required: 2. correlation coefficient and test of significance. The calculation of correlation coefficient is:

  50. Chapter 6Data Analysis 3.5 Quantitative Forecast Methods • Linear regression: ●discussion of correlation coefficient R: 〓when R=0, means y doesn't have the correlation with x, the case is called 0- correlation, so the built model can’t be applied to forecast. 〓when R=1, means y has the direct correlation with x. 〓in general, R is required to meet R>0.7. when R<0.3, means the built model can not be applied. When 0.3<R<0.7, means the model is not good and worthless.

More Related