3/4/2009 Chia Hui Lai Claire Bode EDUC 5394: Understanding Classroom Research

 Descriptive statistics: summarize data so they can easily be comprehended.  Frequency distribution (f) and percentages are descriptive statistics. EDUC 5394: Understanding Classroom Research

 Inferential Statistics: help researchers draw inferences about the effect of sampling errors on the results that are described with descriptive statistics.  Margin of errors: an inferential statistics widely reported in mass media. For example, the result of public opinion polls; approval of President was 45% ±2. ±2 is the margin of errors.  Samples= statistics; population(census)=parameters. EDUC 5394: Understanding Classroom Research

 Null Hypothesis:  Version A: The observed difference was created by sampling error.  Version B: There is no true difference between the two groups.  True difference is the difference a researcher will find if there were no sampling errors.  Version C: The true difference between the two groups is zero. EDUC 5394: Understanding Classroom Research

 Significant tests: determine the probability that the null hypothesis is true.  If in a significant test, the probability is less than 5 in 100, the hypothesis will be significant. It would be stated as p<.05, where p stands for the word probability.  If the p number is.05 or less such as.01 or.001, the research will reject the null hypothesis.  A researcher has rejected the null hypothesis is to state that the difference is statistically significant.

EDUC 5394: Understanding Classroom Research The Effects of Interactivity on Cross-Channel Communication Effectiveness H2: Consumers' perceived interactivity has a positive impact on their evaluations of products. H5: Online purchase intention has a positive impact on offline purchase intentions. H4: Consumer product evaluation mediates the influence of interactivity on consumer online and offline purchase intention. H1: Consumers' perceived interactivity has a positive impact on their trust in the vendor. H3: Consumer trust mediates the influence of interactivity on consumer online and offline purchase intentions.

 Nominal level: also called “naming level,” in this case participants will respond with words not numbers. For instance: marital status.  Ordinal level: At this level, the measurements place participants in order from high to low.  Interval level: are scores obtained through the use of objective instrument such as attitude scales, multiple choice test.  Ratio level: the highest level, ratio level has absolute zero point; for instance: weight.  Interval level and ratio level have equal distances among the scores they yield. EDUC 5394: Understanding Classroom Research

 A researcher ask each member of a population of 540 teachers which candidate s/he prefers for a school board vacancy, and found that 258 preferred Smith and 282 preferred Jones. The 258 and 282 are frequency and the number of case is 540; usually presented as N=540.  The numbers of cases can be converted to percentages (proportions). EDUC 5394: Understanding Classroom Research

 Uni-variate analysis: the researcher is analyzing how participants vary on only one variable.  Bivariate analysis: researcher conducts a examine on the relationship between two nominal variables. EDUC 5394: Understanding Classroom Research

 Chi-Square: the usual test of the null hypothesis for differences between frequencies (number of cases or n).  Chi-square symbol: X 2  df= degrees of freedom.  X 2 = 4.00, df = 1; not descriptive statistics that a typical consumer of research should attempt to interpret.  This sample is an uni-variate analysis EDUC 5394: Understanding Classroom Research X 2 = 4.00, df = 1, p<.05

 The Chi-square cal also apply in a bivariate analysis.  Type I Error: Rejecting the null hypothesis when it is in fact a correct hypothesis.  Type II Error: Failing to reject the null hypothesis when it is in fact an incorrect hypothesis.  The odd level can be different  5 in 100 =.05, 1 in 100 =.01, 1 in 1000 =.001. EDUC 5394: Understanding Classroom Research X 2 =7.54, df=2, p<.05 X 2 =1.241, df=2, p >.05

 Frequency polygon: a figure which is used to present the data of frequency distribution.  The curve is symmetrical within the high point in the middle and dropping off on the right and left. EDUC 5394: Understanding Classroom Research

 When very large sample are used, the curve often takes on an even smoother shape; the smooth, bell-shaped curve is called the normal curve.  For example, when researcher measure the weights of grants of sand on a beach; the annual amounts of rainfall in most area and so on. EDUC 5394: Understanding Classroom Research

 Some distribution are skewed.  Skewed means the shape has a tail on one side and not the other.  Positive skewed: is skewed to the right; for example: income  Negative skewed: is skewed to the left; for example, test EDUC 5394: Understanding Classroom Research

 Mean (M): the balance point in a distribution and the most frequently used average.  The symbol preferred by statisticians is: X, which is pronounced “X- bar.”  The deviation sum has to be zero or the statistic is not the mean.  The drawback is that it is drawn in the direction of extreme scores.  When the distribution is highly skewed, research will use a different average. EDUC 5394: Understanding Classroom Research Scores of Group A: 1, 1, 1, 2, 3, 6, 7, 8, 8, Mean=4.11 Scores of Group B: 1, 2, 2, 3, 4, 7, 9, 25, 32 Mean=9.44

 Median: the middle of score. To get an approximate median, put the scores in order from low to high.  An important use of the median is to describe the averages of skewed distributions.  Mode: the most frequently occurring score.  The mode can have more than one value.  Scores of Group A: 1, 1, 1, 2, 3, 6, 7, 8, 8,  Scores of Group B: 1, 2, 2, 3, 4, 7, 9, 25, 32  What is the median in group A ?  What is the median in group B ?  What is the mode in group A ?  What is the mode in group B ? EDUC 5394: Understanding Classroom Research

 Because there is more than one type of average; therefore, the researchers indicate the specific type of average being reported with statement such as the mean is  Average = measures of central tendency. EDUC 5394: Understanding Classroom Research

 Is a margin of error a “descriptive” or an “inferential” statistic ?  Does the sample error refer to random error or to bias ?  The expression p<.05 stands for what words ?  Which scale of measurement has an absolute zero ?  Which scale of measurement is at the lowest level?  If a researcher found that a chi-square test of a difference yield a p less than 5 in 100, on the basis of conventional wisdom, what should the researcher conclude about the null hypothesis ?  What is the name of the error researchers make when they reject the null hypothesis when, in fact, it is an incorrect hypothesis ?  What is the name of the curve that is symmetrical ?  Which average is defined as the most frequently occurring score?  Which average is defined as the balance point in a distribution ?  Which average is defined as the middle score ? EDUC 5394: Understanding Classroom Research

 Mean: Average  Standard Deviation:  S or SD, s or sd  Describe its variability  Variability: Amount by which participants vary or differ from one another. EDUC 5394: Understanding Classroom Research

 Median: The middle score in a distribution  Used when distribution is highly skewed  Used when data is ordinal  Range: Highest score minus the lowest score  Inter quartile range: Range of the middle two quarters Describes the variability of the average scores. EDUC 5394: Understanding Classroom Research

102, 104, 105, 107, 108, 109, 110, 112, 115, 118, 118  Median (middle number) is 109.  Using the set of numbers to the left of 109, the median is 105.  Using the set of numbers to the right of 109, the median is 115.  The width of the inter quartile range is = 10. EDUC 5394: Understanding Classroom Research

 Examines relationship between two quantitative sets of scores.  A statistic representing how closely two variables co- vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1.  Indicates the strength and direction of a linear relationship between two random variables.  Could be used to determine relation between pre-test/post-test EDUC 5394: Understanding Classroom Research

 Often used to test null hypothesis regarding observed differences between two means.  Assesses whether the means of two groups are statistically different from each other.  Only value of interest is p.  Example: Find the difference between mean scores of boys and girls on a timed basic facts test.

 Analysis of variance called ANOVA  Only one independent variable is being considered  Can compare a number of means  Indicates whether a set of differences is significant overall.  Testing differences between more than two groups or treatment. EDUC 5394: Understanding Classroom Research

 An extension of the one-way analysis of variance  Two independent variables  The investigator can take into account simultaneously the effects of two factors on an outcome of interest. (say age, gender, and IQ)  Additionally, the investigator can test for interaction, if any, between the two factors. EDUC 5394: Understanding Classroom Research

 Statistical Significance-Whether a difference is reliable in light of random errors.  Practical Significance ◦ Cost-benefit analysis ◦ Crucial difference ◦ Client acceptability ◦ Public and political acceptability ◦ Ethical and legal implications EDUC 5394: Understanding Classroom Research

 Robertniles.Com available from Robertniles.Com available from  Answers.com available from Answers.com available from  Socialresearchmethosd.net available from Socialresearchmethosd.net available from  Childrens-mercy.org available from mercy.org/stats/definitions/iqr.htm Childrens-mercy.org available from mercy.org/stats/definitions/iqr.htm  Mste.uiuc.edu available from Mste.uiuc.edu available from  Answers.yahoo.com available from Answers.yahoo.com available from  Jaid.org available from Jaid.org available from  Roscoe, J. T. (1969). Fundamental Research Statistics. New York, NY: Holt, Rinehart and Winston, Inc.  Patten, M. L. (2009). Understanding Research Methods. Glendale, CA: Pyrczak Publishing. EDUC 5394: Understanding Classroom Research