More Related Content
Similar to Planning-Data-Analysis-Using-Statistics_20241016_063349_0000.pptx (20)
Recently uploaded (20)
Planning-Data-Analysis-Using-Statistics_20241016_063349_0000.pptx
- 2. Data Analysis Strategies Exploratory Data Analysis -this type of data is used when it is not clear what to expect from the data, this strategy uses numerical and visual presentations like graphs. Descriptive Data Analysis -this data analysis used to described, show or summarize data in a meaningful way leading to a simple interpretation. The common descriptive statistic data are, frequency, percentage, measure of central tendency and measures of dispersion. Inferential Data Analysis -this data analysis test the hypotheses about the set data to reach conclusion, this data includes the test of significance of difference such as; T-test, analysis of variance (ANOVA) and test of relationship such as; product moment coefficient or correlation or Pearson r, Spearman tho, linear regression and Chi-square test.
- 3. Quantitative Analysis The following are the levels of measurement scales: ➤NOMINAL SCALE ➤ORDINAL SCALE ➤INTERVAL SCALE ➤RATIO SCALE
- 4. •Nominal scale -a nominal scale of measurement is used to label variables. It is sometimes called categorical data • Ordinal scale -ordinal scale of measurement assigns order on items on the characteristics being measured. The order in role(e.g first, second, third); order of agreement(e.g agree, disagree) or economic status(e.g low, average high)
- 5. •Interval scale -a scale that has equal units of measurement, thereby making it possible to interpret the order of the scale scores and distance between them. However, interval scales do not have true zero. In addition it can be addition or subtraction but it cannot be multiplied. • Ratio scale - it is considered as the highest level of measurement, it has the characteristics of the interval scale thus it has zero point. All descriptive and inferential statistics may be applied.
- 6. A. Descriptive Data Analysis 1. MEASURES OF CENTRAL TENDENCY -The common measures of central tendency, sometimes called measures of location or center, includes mean, median and mode.
- 7. number of observations sum of observations (x ̄ )= x ∑ n Mea n -often called the arithmetic average of a set data. Frequently used for interval or ratio data, the symbol (x bar) denote the arithmetic mean. The formula is: Mean (x ̄ ) =
- 8. Mean for Ungrouped Data 1. Find the mean of the measurement 18, 26, 27, 29 30. Formula: x ̄ = x ∑ n =18+26+27+29+3 0 5 = 130 5 = 26
- 9. number of observations frequency of each class x ̄ = fx ∑ n W Mean for Grouped Data Mean (x ̄ )= The formula is: X class midpoint The weighted mean Formula and example for weighted mean: Where: f= frequency x= numerical value or item in a set of data n= numbers of observations in the data
- 11. Media n - Is the midpoint of the distribution, it represents the date where 50% of the values fall down and the 50% fall above it •Median for Ungrouped Data -the median may be calculated from ungrouped data by doing the following steps. 1. Arrange the items (scores, responses, observations) from lowest to highest 2.Count to the middle value. For an odd number of values arranged from lowest highest, the median corresponds to value. If the array contains an even number of observations, the median is the average of the two values.
- 12. Exam ple: Consider these even numbers of numerical values: 12,15,18,22,30,32 The two middle values 18 and 22. if the average of the two middle numbers is taken, that is 18+22=40 and divided by 2. the median is 20. answer: the median is 20
- 13. Median for Grouped Data If the data are grouped into classes, the median will fall into one of the classes as t (^ n / 2 )^ nt value. The process involves several steps and has for its general form following: Median = L + i (n / 2 -F) where: L = lower limit of the class containing the median (median class) i = interval size n = total number of items or observations F = frequency in the class preceding the median class f = frequency of the median class f
- 14. Exam ple:
- 15. Exam ple:
- 16. Exam ple:
- 17. Mode The mode is the most frequently occurring value in a set of observations, in cases where there is more than one observation which is the highest but with equal frequency, the distribution is bimodal ( with 2 highest observations) or multimodal with more than two highest observations. In cases, where every item has an equal number of observations, there is no mode. The mode is appropriate for nominal data.
- 18. Exam ple: The number of hours spent by 10 students in an internet café was as follows: 2,2,2,3,3,4,4,4,5,5 Solution: Both 2 and 4 have a frequency of 3. The data is therefore bimodal. Answer: mode = 2 and 4
- 19. Measures of Dispersion The extent of the spread, or the dispersion of the data is described by a group of measures called measures of dispersion, also called measures of variability. The measures to be considered are the range, average or mean deviation, standard deviation and the variance.
- 20. Ran ge Range is the difference between the largest and the smallest values in a set of data. Ex: Consider the following scores obtained by ten (10)students participating in a mathematics contest: 6,10,12,15,18,18,20,23,25,28 Thus, this range is 22. the scores ranges from 6-28.
- 21. Average (Mean) Deviation This measure of spread is defined as the absolute or deviation between the values in a set of data and the mean, divided by the total number of values in the set of data. In mathematics, the term "absolute" represented by the sign "||"simply means taking the value of a number without regard to positive or negative sign.
- 23. Standard Deviation The standard deviation (SD) is measure from the spread of variation of data about the mean. SD is computed by calculating the average distance that the average value is from the mean.
- 24. Formu la: Let us consider the same data used in the illustration for using the range. The values are 6,10,12,15,18,18,20,23,2528 Examp le:
- 27. Interpretation of Standard Deviation The standard deviation allows you to reach conclusions about scores in the distribution the following conclusions can be reached if that distribution of scores is normal: 1. Approximately 68% of the scores in the sample falls within one standard deviation of the mean. 2. Approximately 95% of the scores in the sample falls within two standards deviation of the mean. 3. Approximately 99% of the scores in the sample falls with threes standard deviations of the mean.
- 28. Interpretation of Standard Deviation 4. In the example, with x of 17.5 a standard deviation of 6.95, we can say that, 68% of the scores will fall in the range =(17.5-6.95) to (17.5+6.95) =10.5-24.45 5. Likewise, 95% of the scores will fall in the range =17.5-(2) (6.95) to 17.5+ (2) (6.95) =(17.5-13.9) to (17.5+13.9) =3.6 to 31.4
- 29. Inferential Data Analysis refers to statistical measures and techniques that allow us to use samples make generalizations about the population from which the samples are drawn.
- 30. TEST OF SIGNIFICANCE OF DIFFERENCE (T- TEST) Between Means- for independent samples
- 31. ORRELATED/DEPENDENT SAMPLE (When the same set of respondents or paired sets of respondents are involved)
- 32. BETWEEN PROPORTIONS OR PERCENTAGE ➤For correlated /dependen t samples ➤For independent samples or
- 33. ANALYSIS OF VARIANCE (ANOVA) ANOVA is used when significance of difference of means of two or more groups are to be determined at one time. ONE-WAY ANALYSIS OF VARIANCE A typical ANOVA table:
- 34. Salam