Statistics in research
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The document discusses various statistical concepts and methods. It defines statistics as a set of methods for organizing, summarizing, and interpreting information. It also discusses key statistical terms like variables, parameters, sampling error, distributions, and different types of statistical analyses and procedures including descriptive statistics, statistical inference, and various graphical and tabular methods for presenting quantitative and qualitative data.
![For Broadcasting
Mixing your
Video
Measurement Scale LOGO
Another tool of [quantitative] research.
Definition: A rule for the assignment of
numbers to attributes or characteristics of
individuals, or things
Types of measurement has implications for
the type of statistical procedure employed.
Some statistical procedures assume a
certain level of measurement.
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Statistics in research
- 1. For Mixing your STATISTICS IN RESEARCH Broadcasting LOGO Video Dr. Daxaben N. Mehta Principal Smt. S.C.U.Shah Home Science and C.U.Shah Arts & Commerce Mahila College Wadhwancity – Dist: Surendranagar Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 2. For Broadcasting Mixing your Video Why Statistics ? LOGO To understand God's thoughts we must study statistics, for these are the measure of His purpose. — Florence Nightingale Statistical thinking will one day be as necessary a qualification for efficient citizenship as the ability to read and write. — H.G. Wells Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 3. For Mixing your What in Statistics Broadcasting LOGO Video Role of Statistic Asking the Terminology Research Question Hypotheses Collecting Data Testing THEORY Analyzing Data Types of Representing Data Statistics Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 4. For Mixing your Role of Statistics Broadcasting LOGO Video in research • Validity Will this study help answer the research question? • Analysis What analysis, & how should this be interpreted and reported? • Efficiency Is the experiment the correct size, making best use of resources? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 5. For Broadcasting Mixing your Video Statistics LOGO A set of methods, procedures and rules for organizing, summarizing, and interpreting information. There is a distinction between statistics and parameters Here, it would be better to speak of statistical methods. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 6. For Mixing your Parameters and Statistics Broadcasting LOGO Video Parameters and Statistics Parameter: the value of a variable in a population. Statistic: the value of a variable in a sample. Statistics are often used to estimate or draw inferences about parameters. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 7. Statistical inference For Broadcasting Mixing your LOGO Video Statistical inference is the process of estimating population parameters from sample statistics. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 8. For Statistical inference may be used to Broadcasting Mixing your LOGO Video ascertain whether differences exist between groups... 90 80 70 60 Height in inches 50 40 30 20 10 Males Females Are males taller than females? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 9. For Broadcasting Mixing your Video Variable LOGO Variable: any characteristic that can vary across individuals, groups, or objects. For example: Weight Occupation Grade-point average Level of test anxiety Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 10. For Mixing your Variables Broadcasting LOGO Video 1. The dependent variable is always the property you are trying to explain; it is always the object of the research. 2. The independent variable usually occurs earlier in time than the dependent variables. 3. The independent variable is often seen as influencing, directly or indirectly, the dependent variable. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 11. For Broadcasting Mixing your Video Values LOGO Values: the numerical value of a particular realization of a variable. For instance if the variable is weight Than a child weighs15kg then the value of the variable for child is 15. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 12. For Broadcasting Mixing your Video Sampling Error LOGO Sampling error is the difference between a sample statistic and its corresponding population parameter. The values of sample statistics vary from sample to sample, even when all samples are drawn from the same population. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 13. For Broadcasting Mixing your Video Distributions LOGO Organized arrangements of sets of data by order of magnitude or Sequential listings of data points from lowest to highest. Frequency distributions.- A sequential listing of data points combined with the number of times (or frequency with which) each point occurs. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 14. For Broadcasting Mixing your Video Statistical procedures LOGO Statistical procedures are the tools of research. There are several types (or methods) of research studies and the type of statistical procedure used will often vary from one type of research to another. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 15. For Mixing your Statistical procedures Broadcasting LOGO Video The correlational method of research. Examines relationships among two or more variables. The experimental method is used when the researchers wants to establish a cause and effect relationship A quasi-experiment is similar to a (true) experiment except that here the independent variable is not manipulated by the researcher Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 16. For Broadcasting Mixing your Video Measurement Scale LOGO Another tool of [quantitative] research. Definition: A rule for the assignment of numbers to attributes or characteristics of individuals, or things Types of measurement has implications for the type of statistical procedure employed. Some statistical procedures assume a certain level of measurement. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 17. For Broadcasting Mixing your Video Types of Measurement LOGO Three can be distinguished: nominal, ordinal, and scale (includes interval and ratio). Nominal Coarse level of measurement used for identification purposes. Substitutes numbers for other categorical labels. No order of magnitude is implied. Examples: sex (male or female), student classification Do you have a loss of appetite? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 18. For Broadcasting Mixing your Video Types of Measurement LOGO Ordinal.Objects measured on an ordinal scale differ from each other in terms of magnitude, but the units of magnitude are not equal. The objects can be ordered in terms of their magnitude (more or less of an attribute. Examples: socioeconomic status, level of education attained (elementary school, high school, college degree, graduate degree) Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 19. For Broadcasting Mixing your Video Types of Measurement LOGO Scale includes both interval and ratio level scales. Scale measurements yield equal intervals between adjacent scale points. The difference between score of 435 and 445 is the same as the difference between a score of 520 and 530. IQ scores Most scores obtained form achievement tests, aptitude tests, etc. are treated as scaled data Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 20. For Same Variable, Different Broadcasting Mixing your LOGO Video Levels of Measurement Interval level: What is your age in years? Ordinal level:What is your age group? 18 years or younger 19-44 years 45 years or older Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 21. For Mixing your Choosing the Appropriate Broadcasting LOGO Video Statistic Some factors to consider: Research design Number of groups Number of variables Level of measurement (nominal, ordinal, interval/ratio) Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 22. For Broadcasting Mixing your Video Statistical Methods LOGO Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 23. For Broadcasting Mixing your Video Types of Statistics LOGO Descriptive statistics characterize the attributes of a set of measurements. Used to summarize data, to explore patterns of variation, and describe changes over time. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 24. For Broadcasting Mixing your Video Descriptive Statistics LOGO Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 25. For Mixing your Descriptive Statistics Broadcasting LOGO Video • Tabular and Graphical Methods • Qualitative Data • Quantitative Data Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 26. For Tabular and Graphical Broadcasting Mixing your LOGO Video Procedures Data Quantitative Data Qualitative Data Qualitative Data Tabular Graphical Graphical Methods Methods Methods Tabular Methods •Histogram •Frequency •Bar Graph •Frequency •Ogive Distribution Distribution •Pie Chart •Cum. Freq. Dist. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 27. For Mixing your Line Graph Broadcasting LOGO Video • The line graphs are usually drawn to represent the time series data Example: temperature, rainfall, population growth, birth rates and the death rates. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 28. For Mixing your Line Graph Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 29. For Mixing your Polygraph Broadcasting LOGO Video • Polygraph is a line graph in which two or more than two variables are shown on a same diagram by different lines. It helps in comparing the data. Examples which can be shown as polygraph are: The growth rate of different crops like rice, wheat, pulses in one diagram. The birth rates, death rates and life expectancy in one diagram. Sex ratio in different states or countries in one diagram. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 30. For Mixing your Polygraph Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 31. For Broadcasting Mixing your Video Qualitative Data LOGO • Frequency Distribution • Bar Graph • Pie Chart Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 32. For Mixing your Frequency Distribution Broadcasting LOGO Video • A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several non overlapping classes. • The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 33. For Broadcasting Mixing your Bar Graph LOGO Video • A bar graph is a graphical device for depicting qualitative data. • Using a bar of fixed width drawn above each class label, we extend the height appropriately. • The bars are separated to emphasize the fact that each class is a separate category. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 34. For Mixing your Bar Graph Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 35. For Mixing your The simple bar diagram Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 36. For Mixing your Compound bar diagram Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 37. For Mixing your Polybar diagram Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 38. For Mixing your Pie Chart Broadcasting LOGO Video • The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. • First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 39. For Mixing your Pie Chart Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 40. For Mixing your Pie graphs Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 41. For Mixing your Quantitative Data Broadcasting LOGO Video • Frequency Distribution • Histogram • Cumulative Distributions • Ogive Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 42. For Mixing your Frequency Distribution Broadcasting LOGO Video • Selecting Number of Classes Use between 5 and 20 classes. Data sets with a larger number of elements usually require a larger number of classes. Smaller data sets usually require fewer classes. • Selecting Width of Classes Use classes of equal width. Approximate Class Width = Largest Data Value − Smallest Data Value Number of Classes Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 43. For Mixing your Histogram Broadcasting LOGO Video • Another common graphical presentation of quantitative data is a histogram. • A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency • Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 44. For Mixing your Histogram Broadcasting LOGO Video 18 16 14 Frequency 12 10 8 6 4 2 Parts Cost ($) 50 60 70 80 90 100 110 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 45. For Mixing your Ogive Broadcasting LOGO Video • An ogive is a graph of a cumulative distribution.The data values are shown on the horizontal axis. • Shown on the vertical axis are the: cumulative frequencies, • The frequency (one of the above) of each class is plotted as a point. • The plotted points are connected by straight lines. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 46. For Ogive with Broadcasting Mixing your LOGO Video Cumulative Frequencies 100 Cumulative Percent Frequency 80 60 40 20 Parts Cost ($) 50 60 70 80 90 100 110 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 47. For Broadcasting Mixing your Video Types of Statistics LOGO Inferential statistics are designed to allow inference from a statistic measured on sample of cases to a population parameter. Used to test hypotheses about the population as a whole. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 48. For Broadcasting Mixing your Video Inferential Statistics LOGO Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 49. For Mixing your Statistical Tests Broadcasting LOGO Video • Parametric tests Continuous data normally distributed • Non-parametric tests Continuous data not normally distributed Categorical or Ordinal data Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 50. For Broadcasting Mixing your Measures of Central Tendency LOGO Video Level of Statistic Measurement Nominal Mode What is the most frequent value? What is the middle score? Ordinal Median (50% above and 50% below) What is the average? Interval/Ratio Mean (Sum of all scores divided by the number of scores) Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 51. For Mixing your Example of Broadcasting LOGO Video Central Tendency 15,20,21,20,36,15,25,15 15,15,15,20,20,21,25,36 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 52. For Mixing your Example of Mode Broadcasting LOGO Video RACE Race of Respondent Frequency Percent Race of Respondent 1 white 1257 83.8 1400 2 black 168 11.2 1200 3 other 75 5.0 Total 1500 100.0 1000 800 Statistics 600 RACE Race of Respondent N Valid 1500 400 Missing 0 Frequency Mode 1 200 0 w hite black other Race of Respondent Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 53. For Mixing your Example of Median Broadcasting LOGO Video EDUC Education level 10 Cumulative Frequency Percent Percent 4 Some high school 1 4.2 4.2 9 5 Completed high school 6 25.0 29.2 6 Some college 6 25.0 54.2 8 7 Completed college 3 12.5 66.7 8 Some graduate work 4 16.7 83.3 9 A graduate degree 4 16.7 100.0 7 Total 24 100.0 6 Statistics 5 EDUC Education level N Valid 24 Missing 0 4 Median 6.00 3 N= 24 Education level Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 54. For Mixing your Example of Mean Broadcasting LOGO Video Age of Respondent 200 MEAN 100 Std. Dev = 17.42 Mean = 46 0 N = 1495.00 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Age of Respondent Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 55. For Mixing your Mean versus Median Broadcasting LOGO Video • Large sample values tend to inflate the mean. This will happen if the histogram of the data is right-skewed. • The median is not influenced by large sample values and is a better measure of centrality if the distribution is skewed. • Note if mean=median=mode then the data are said to be symmetrical Don’t write anything here Don’t write anything here 55 Don’t write anything here Don’t write anything here
- 56. For Mixing your Measures of Dispersion Broadcasting LOGO Video • Measures of dispersion characterise how spread out the distribution is, i.e., how variable the data are. • Commonly used measures of dispersion include: 1. Range 2. Variance & Standard deviation 3. Coefficient of Variation (or relative standard deviation) 4. Inter-quartile range Don’t write anything here Don’t write anything here 56 Don’t write anything here Don’t write anything here
- 57. For Broadcasting Mixing your Video Measures of Variation LOGO Level of Statistic Measurement Number of How many different values Nominal categories are there? What are the highest and Ordinal Range lowest values? Standard What is the average Interval/Ratio Deviation deviation from the mean? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 58. For Mixing your Curves of Distribution Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 59. For Broadcasting Mixing your LOGO Video Normal Distribution Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 60. For Mixing your Normal Curve Broadcasting LOGO Video Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 61. For Example: Broadcasting Mixing your LOGO Video Number of categories Race of Respondent 1400 RACE Race of Respondent 1200 1000 Frequency Percent 1 white 1257 83.8 800 2 black 168 11.2 600 3 other 75 5.0 Total 1500 100.0 400 Frequency 200 0 w hite black other Race of Respondent Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 62. For Broadcasting Mixing your Video Example of Range LOGO 10 EDUC Education level Cumulative 9 Frequency Percent Percent 4 Some high school 1 4.2 4.2 5 Completed high school 6 25.0 29.2 8 6 Some college 6 25.0 54.2 7 Completed college 3 12.5 66.7 7 8 Some graduate work 4 16.7 83.3 9 A graduate degree 4 16.7 100.0 Total 24 100.0 6 Statistics 5 EDUC Education level N Valid 24 Missing 0 4 Median 6.00 Range 5 3 Minimum 4 N= 24 Maximum 9 Education level Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 63. For Example of Broadcasting Mixing your LOGO Video Standard Deviation Age of Respondent 200 -1 SD MEAN +1 SD 100 Frequency Std. Dev = 17.42 Mean = 46 0 N = 1495.00 20 30 40 50 60 70 80 90 25 35 45 55 65 75 85 Age of Respondent Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 64. For Mixing your Measures of Relationships Broadcasting LOGO Video Level of Statistic Measurement Nominal Phi statistic (φ) Spearman rho (ρ) Ordinal correlation Interval/Ratio Pearson correlation (r) Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 65. For Mixing your Correlation Broadcasting LOGO Video • Assesses the linear relationship between two variables Example: height and weight • Strength of the association is described by a correlation coefficient- r • r = 0 - .2 low, probably meaningless • r = .2 - .4 low, possible importance • r = .4 - .6 moderate correlation • r = .6 - .8 high correlation • r = .8 - 1very high correlation • Can be positive or negative • Pearson’s, Spearman correlation coefficient • Tells nothing about causation Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 66. For Examples of Some Commonly Broadcasting Mixing your LOGO Video Used Statistical Tests Level of Measurement Number of groups Nominal Interval/Ratio t-test of sample mean vs. 1 group χ2 test known population value χ2 test 2 independent groups Independent samples t-test McNemar 2 dependent groups Paired t-test test >2 independent groups χ2 test ANOVA Cochran >2 dependent groups Repeated measures ANOVA Q test Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 67. For Mixing your Non-parametric Tests Broadcasting LOGO Video • Testing proportions (Pearson’s) Chi-Squared (χ2) Test Fisher’s Exact Test • Testing ordinal variables Mann Whiney “U” Test Kruskal-Wallis One-way ANOVA • Testing Ordinal Paired Variables Sign Test Wilcoxon Rank Sum Test Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 68. For Mixing your Use of non-parametric tests Broadcasting LOGO Video • Use for categorical, ordinal or non-normally distributed continuous data • May check both parametric and non- parametric tests to check for congruity • Most non-parametric tests are based on ranks or other non- value related methods • Interpretation: Is the P value significant? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 69. For Mixing your Chi-Squared (χ2) Test Broadcasting LOGO Video • Used to compare observed proportions of an event compared to expected. • Used with nominal data (better/ worse; dead/alive) • If there is a substantial difference between observed and expected, then it is likely that the null hypothesis is rejected. • Often presented graphically as a 2 X 2 Table Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 70. For Mixing your Analysis of Variance Broadcasting LOGO Video • Used to determine if two or more samples are from the same population- the null hypothesis. If two samples, is the same as the T test. Usually used for 3 or more samples. • If it appears they are not from same population, can’t tell which sample is different. Would need to do pair-wise tests. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 71. For Broadcasting Mixing your Video Tests of Hypotheses – LOGO Tests of Significance Designed experiment - only two explanations for a negative answer, difference is due to the applied treatments or a chance effect Survey is silent in distinguishing between various possible causes for the difference, merely noting that it exists. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 72. For Broadcasting Mixing your Video Tests of Hypotheses LOGO - Tests of Significance Survey: Are the observed differences between groups compatible with a view that there are no differences between the populations from which the samples of values are drawn? Designed experiments: Are observed differences between treatment means compatible with a view that there are no differences between treatments? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 73. For Mixing your Standard Error Broadcasting LOGO Video • Standard error of the mean Standard deviation / square root of (sample size) • (if sample greater than 60) • Standard error of the proportion Square root of (proportion X 1 - proportion) / n) • Important: dependent on sample size Larger the sample, the smaller the standard error. Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 74. For Mixing your Errors Broadcasting LOGO Video • Type I error Claiming a difference between two samples when in fact there is none. Also called the α error. Typically 0.05 is used Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 75. For Mixing your Errors Broadcasting LOGO Video • Type II error Claiming there is no difference between two samples when in fact there is. Also called a β error. The probability of not making a Type II error is 1 - β, Hidden error because can’t be detected without a proper analysis Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 76. For Hypothesis Testing Broadcasting Mixing your LOGO Video Decision Chart Reality Null Hypothesis (H0 ) is true Alternative Hypothesis (H1) is true Decision Type I error Correct decision Reject (H0 ) (α) (Power = 1 - β) typically .05 or .01 typically .80 Correct decision Type II error Don’t reject (H0 ) (1 - α) (β) typically .95 or .99 typically .20 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 77. For Difference between two group Broadcasting Mixing your LOGO Video means: The independent samples t-test Males and females are asked a question that is measured on a five-point Likert scale: To what extent do you feel that regular exercise contributes to your overall health? 1 Strongly agree 2 Agree 3 Neither agree nor disagree 4 Disagree 5 Strongly disagree Do males and females differ in their response to this question? Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 78. For Mixing your Comparison of 2 Broadcasting LOGO Video Sample Means • Student’s T test Assumes normally distributed continuous data. T value = difference between means standard error of difference T value then looked up in Table to determine significance Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 79. For Broadcasting Mixing your LOGO Video 25 males and 25 females answered our question. Here is how they responded: 1 1 males 1 females 1 2 3 4 5 meanmales=2.5 meanfemales=3.2 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
- 80. For Mixing your Video Student t test Broadcasting LOGO Group Statistics Std. Error GENDER N Mean Std. Deviation Mean EXERCISE 1 male 25 2.56 1.158 .232 2 female 25 3.24 1.012 .202 The t-test reveals a significant difference between males & females: Independent Samples Test t-test for Equality of Means Mean t df Sig. (2-tailed) Difference EXERCISE -2.212 48 .032 -.68 Don’t write anything here Don’t write anything here Don’t write anything here Don’t write anything here
Editor's Notes
- #5: Give examples of each
- #52: The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. For example, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, consider the test score values: 15, 20, 21, 20, 36, 15, 25, 15 The sum of these 8 values is 167, so the mean is 167/8 = 20.875. The Median is the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. For example, if there are 500 scores in the list, score #250 would be the median. If we order the 8 scores shown above, we would get: 15,15,15,20,20,21,25,36 There are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores are 20, the median is 20. If the two middle scores had different values, you would have to interpolate to determine the median. The mode is the most frequently occurring value in the set of scores. To determine the mode, you might again order the scores as shown above, and then count each one. The most frequently occurring value is the mode. In our example, the value 15 occurs three times and is the model. In some distributions there is more than one modal value. For instance, in a bimodal distribution there are two values that occur most frequently. Notice that for the same set of 8 scores we got three different values -- 20.875, 20, and 15 -- for the mean, median and mode respectively. If the distribution is truly normal (i.e., bell-shaped), the mean, median and mode are all equal to each other. Dispersion. Dispersion refers to the spread of the values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. In our example distribution, the high value is 36 and the low is 15, so the range is 36 - 15 = 21. The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range (as was true in this example where the single outlier value of 36 stands apart from the rest of the values. The Standard Deviation shows the relation that set of scores has to the mean of the sample. Again lets take the set of scores: 15,20,21,20,36,15,25,15 to compute the standard deviation, we first find the distance between each value and the mean. We know from above that the mean is 20.875. So, the differences from the mean are: 15 - 20.875 = -5.875 20 - 20.875 = -0.875 21 - 20.875 = +0.125 20 - 20.875 = -0.875 36 - 20.875 = 15.125 15 - 20.875 = -5.875 25 - 20.875 = +4.125 15 - 20.875 = -5.875 Notice that values that are below the mean have negative discrepancies and values above it have positive ones. Next, we square each discrepancy: -5.875 * -5.875 = 34.515625 -0.875 * -0.875 = 0.765625 +0.125 * +0.125 = 0.015625 -0.875 * -0.875 = 0.765625 15.125 * 15.125 = 228.765625 -5.875 * -5.875 = 34.515625 +4.125 * +4.125 = 17.015625 -5.875 * -5.875 = 34.515625 Now, we take these "squares" and sum them to get the Sum of Squares (SS) value. Here, the sum is 350.875. Next, we divide this sum by the number of scores minus 1. Here, the result is 350.875 / 7 = 50.125. This value is known as the variance . To get the standard deviation, we take the square root of the variance (remember that we squared the deviations earlier). This would be SQRT(50.125) = 7.079901129253. Although this computation may seem convoluted, it's actually quite simple. To see this, consider the formula for the standard deviation:
- #60: Theorists propose that many characteristics of human populations reflect a particular pattern. The pattern has several distinguishing characteristics: It is horizontally symmetrical Its highest point is at the midpoint: more people are located at the midpoint than at any other point along the curve. The mode, median, and the mean are the same. Predictable percentages of the population lie within any given portion of the curve. Approximately 68% of the population lies between the mean and + or – one standard deviation 28% lies +- two standard deviation 4% lies +- < two standard deviation
- #61: http://www.psy.pdx.edu/PsiCafe/Overheads/NormCurve.htm
- #64: The most accepted index of dispersion in modern statistical practice.
- #77: Statistical hypothesis testing involves the decision as to whether or not to reject a null hypothesis (H 0 ) and accept an alternative hypothesis (H 1 ). The decision constitutes an inference made about a population, based upon a study sample. The null hypothesis typically asserts no difference between groups being compared, or no relationship among variables being analyzed. Not rejecting H 0 when it is in fact true or rejecting H 0 when it is in fact false is a correct decision (not an error). Rejecting the null hypothesis when it is in fact true is call Type I error ( ). For example, we commit this type of error when we assert that a treatment group differs from a control group when in the population there really is no discernable difference. We want the probability of a to be small, e.g., .05 Failing to reject the null hypothesis when it is in fact false constitutes a Type II error ( ). We commit this type of error when we assert there is no difference between a treatment group and a control group when there is in fact a difference in the population. The probability of rejecting H 0 when H 1 is true is 1- . This is what we mean by the power of a statistical test. We want this probability to be large, e.g., .80.