1. Presented by : NORAZLIYATI YAHYA2009905123 NURHARANI SELAMAT2009324059 NUR HAFIZA NGADENIN2009720649

2. QUANTITATIVE DATA ANALYSIS 3/6/20162 DATA ANALYSIS DESCRITIVE STATISTICS INFERENTIAL STATISTICS STATISTICS IN PERSPECTIVE

3. QUANTITATIVE DATA Frequency polygons Techniques for summarizing quantitative data Skewed polygons Histogram & Stem-leaf Plots Normal Curve Average Spreads Standard scores & Normal Curve Correlation

4. 4 FREQUENCY POLYGONS Constructing a frequency polygon List all scores in order of size, group scores into interval Label the horizontal axis by placing all the possible scores at equal intervals Label the vertical axis by indicating frequencies at equal interval Find the point where for each score intersect with frequency, place a dot at the point Connect all the dots with a straight line. l

5. SKEWED POLYGONS 5 Positively Skewed PolygonNegatively Skewed Polygon The tail of the distribution trails off to the right, in the direction of the higher score value The longer tail of the distribution goes off to the left

6. HISTOGRAM 6 Bars arranged from left to right on horizontal axis Width of the bar indicate the range of value in each bar Histogram facts Frequencies are shown in vertical axis, point of intersection is always zero Bars in the histogram touch, indicate they illustrate quantitative rather than categorical data

7. STEM-LEAF PLOTS STEMLEAF 29 372 4655 541555 60 7 STEMLEAF 29 327 4556 514555 60 Constructing a Stem-Leaf Plot Mathematics Quiz Score Separate number into a stem and a leaf Group number with the same stem in numerical order Reorder the leaf values in sequence

8. NORMAL CURVE 8 Normal Distribution Majority of the scores are concentrated in the middle of the distribution, scores decrease in frequency the farther away from the middle The smooth curve (distribution curve) shows a generalized distribution of scores that is not limited to one specific set of data The normal curve is symmetrical and bell-curved, commonly used to estimate height and weight, spatial ability and creativity.

9. AVERAGES 9 Measure of Central Tendency Mode The most frequent score in a distribution Median The midpoint - middlemost score or halfway between the two middlemost score Mean Average of all the score in a distribution

10. SPREADS 10 Variability Standard Deviation Facts Represents the spreads of a distribution, describe the variability based on how greater or smaller the standard deviation 34% 68% 95% 13.5% 99.7% 2.15% Mean1 SD2 SD-1 SD-2 SD 50% of all observation fall on each side of the mean 68% of the score fall within one standard deviation of the mean 27% of the observation fall between one or two standard deviation away from the mean 99.7% fall within three standard deviations of the mean

11. STANDARD SCORE & NORMAL CURVE 11 Standard score & Normal Curve z-score How far a raw score is from the mean in standard deviation units Probability Percentage associated with areas under a normal curve, stated in decimal form.3413.1359.0215

12. CORRELATION 12 Correlation Coefficient and Scatterplots Express the degree of relationship between two sets of scores Correlation Coefficient Positive relationship is indicated when high score on one variable accompanied by high score on the other and when low score on one accompanied by low score on the other Scatterplots Used to illustrate different degrees of correlation

13. CATEGORICAL DATA 13 Techniques for summarizing categorical data Frequency Table Bar Graphs and Pie Charts Crossbreak Table

14. CROSSBREAK TABLE 14 Grade Level and Gender of Teachers (Hypothetical Data) MaleFemaleTotal Junior High School Teacher4060100 High School Teacher6040100 Total100 200 MaleFemaleTotal Junior High School Teacher4060100 High School Teacher6040100 Total100 200 Reported a relationship between two categorical variables of interest Junior high school teacher is more likely to be female. A high school teacher is more likely to be male. Exactly one-half of the total group of teachers are female. If gender is unrelated to grade level, the same proportion of junior high school and high school teachers are would be expected female.

15. A researcher administered a study on the average IQ of primary school students at Shah Alam district and finds their average IQ score is 85. Does the average IQ score of students in entire population is also equal to 85 or this sample of students differ from other students in Shah Alam district? If different, how are they different? Are their IQ scores higher or lower? I don’t want to obtain data for entire population but how am I going to estimate how closely the average sample IQ scores with population IQ scores?

16. INFERENTIAL STATISTIC oWhat is inferential statistic? It is the Statistical Technique/Method using obtained sample data to infer the corresponding population. It is the Statistical Technique/Method using obtained sample data to infer the corresponding population. oType of inferential statistics SAMPLE SAMPLE = 10.14 POPULATION μ =? 1. Estimation Using a sample mean to estimate a population mean Example: Interval Estimation: Confidence Intervals 2. Hypothesis testing  Comparing 2 means  Comparing 2 proportions  Association between one variable and another variable

17. 1. INTERVAL ESTIMATION RESEARCH OBJECTIVE : To identify the average IQ of primary school students at Shah Alam district. To identify the average IQ of primary school students at Shah Alam district. Population o Population: 1,000 students of Shah Alam primary schools Sample o Sample : 65 primary school students Sample Mean o Sample Mean : 85 Standard Error of Mean o Standard Error of Mean : 2.0 Interval Estimation o Interval Estimation : 95% Confidence Interval = 85 1.96(2) = 85 3.92 = 81.08 or 88.92 Interpretation o Interpretation: Researcher has 95% confidence that the average IQ of primary students at Shah Alam district is between 81.08 or 88.92

18. SAMPLING ERROR What is sampling error? The difference between the population mean and the sample mean Why does sampling error occurs? Different samples drawn from the same population can have different properties How can we quantify sampling error? Using standard error of mean. It is useful because it allows us to represent the amount of sampling error associated with our sampling process—how much error we can expect on average. S S S P

19. 1. HYPOTHESIS TESTING What is hypothesis testing? What is hypothesis testing? o A hypothesis is an assumption about the population parameter. oA parameter is a characteristic of the population; mean or relationship. oThe parameter must be identified before analysis. Steps in conducting hypothesis testing Steps in conducting hypothesis testing 1.State the null hypothesis and research hypothesis. 2.Identify the appropriate test. 3.State the decision rule for rejecting null hypothesis.

20. NULL HYPOTHESIS RESEARCH HYPOTHESIS NO There is NO difference between the population mean of students using method A and the population mean of students using method B NO EFFECT Treatment X has NO EFFECT on outcome Y LESS The grade point average of juniors is LESS than 3.0 EQUAL The average IQ score of primary school students at Shah Alam district EQUAL to 85 GREATER The population mean of students using method A is GREATER than the population mean of students using method B AN EFFECT Treatment X has AN EFFECT on outcome Y AT LEAST The grade point average of juniors is AT LEAST 3.0 GREATER The average IQ score of primary school students at Shah Alam district is GREATER 85

21. NULL HYPOTHESIS EQUAL NULL HYPOTHESIS The average IQ score of primary school students at Shah Alam district EQUAL to 85  This test is called one sample t test.  At the end of the hypothesis testing, we will get a P value.  If the P value is less than 0.05, we reject the Null Hypothesis and conclude as Research Hypothesis.  If the P value is more than or equal to 0.05, we cannot reject the Null Hypothesis.  In above example, if we get P =0.01, we reject the null GREATER hypothesis, then we conclude Research Hypothesis “the average IQ score of primary school students at Shah Alam district is GREATER 85 ”.

22. ONE AND TWO-TAILED TEST

23. Susie has pneumoniaSusie does not have pneumonia Doctors says that symptoms like Susie’s occur only 5 percent of the time in healthy people. To be safe, however, he decides to treat Susie for pneumonia Doctor is correct. Susie does have pneumonia and the treatment cures her. Doctor is wrong. Susie’s treatment was unnecessary and possibly unpleasant and expensive. Type 1 error. Doctor says that symptoms like Susie’s occur 95 percent of the time in healthy people. In his judgement, therefore, her symptoms are a false alarm and do not warrant treatment, and he decides not to treat Susie for pneumonia Doctor is wrong. Susie is not treated and may suffer serious consequences. Type II error. Doctor is correct. Unnecessary treatment is avoided. A HYPOTHETICAL EXAMPLE OF TYPE 1 AND TYPE II ERRORS

24. TYPE OF TESTS Quantitative data  t-test for means  ANOVA  ANCOVA  MANOVA  MANCOVA  t-test for r Categorical data  t-test for difference in proportion PARAMETRIC TEST NON PARAMETRIC TEST Quantitative data  Mann-Whitney U test  Kruskall-Wallis one way analysis of variance  Sign test  Friedman two ways analysis of variance Categorical data Chi-square test

25. Quantitative Data Comparing Groups Quantitative Data Frequency polygons → central tendency

26. Interpretation 1.Information of known groups 2.Effect size, ES: 3.Inferential statistics Mean experimental gain – mean comparison gain Std dev. of gain of comparison group

27. Categorical Data Comparing Groups Categorical Data Crossbreak tables Table 1 Felony Sentences for Fraud by Gender Type of Sentence GenderProbationPrisonTotals Male241135 Female132235 Totals373370

28. Table 1 Felony Sentences for Fraud by Gender (frequencies added) GenderProbationPrisonTotals Male 24 (3.178) 11 (2.398)35 Female 13 (2.565) 22 (3.091)35 Totals373370

29. Interpretation Place data in tables Calculate contingency coefficient c = √ X2X2 X 2 + n

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