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Based on your reading and study, what are some of the concerns a researcher who used a quantitative designs should address?   https://youtu.be/cwU8as9ZNlA QUANTITATIVE RESEARCH METHODOLOGIES Strategies for Analyzing Quantitative Data Chapter Eleven Analyzing the Quantitative Data  Questions to ask  What do the data mean?  What message to the data communicate? Analyzing the Quantitative Data  Before employing any statistical procedure consider how to organize the data set  Computer spreadsheets are good tools for organizing data  Choose the appropriate statistics Functions of Statistics  Statistics have two major functions (a) to describe what the data look like and (b) to allow us to draw inferences about the data  Descriptive statistics – describe the data  Inferential statistics – allow us to draw inferences Statistics as Estimates of Population Parameters  When statistics are used to draw inferences about a population from which a research sample has been drawn, we are using them as estimates of population parameters  A parameter is a characteristic or quality of a population that, in concept, is a constant; however, its value is variable  Within the context of quantitative data analysis, a parameter is a particular characteristic of the entire population – which is sometimes called a universe- about which we draw conclusions  Any calculation we perform for the sample rather than the population is called a statistic Considering the Nature of the Data  Consider whether the data  Have been collected for a single group or, instead, for two or more groups  Involve continuous or discrete variables  Represent nominal, ordinal, interval, or ratio scales  Reflect a normal or non-normal distribution Considering the Nature of the Data  Single-group vs Multi-group data require different statistical techniques  A Variable is a quality or characteristic in a research investigation that has two or more possible values  A continuous variable reflects an infinite number of possible values falling along a particular continuum  A discrete variable has a finite and small number of possible values Considering the Nature of the Data  Four different scales of measurement  Nominal Data  Ordinal Data  Interval Data  Ratio Data Considering the Nature of Data  Normal and Non-Normal Distributions  Many theorists have proposed that many characteristics of living populations reflect a particular pattern that is called the normal distribution or normal curve or bell curve Normal Distribution Sometimes called a normal curve or a bell curve  It is horizontally symmetrical  Its highest point is at the midpoint – in statistical terms, three widely used measures of central tendency – the mode, the median, and the mean – are equivalent  Predictable percentages of the population lie within any given portion of the curve Non-Normal Distribution Sometimes the variable doesn’t fall in a normal distribution  The distribution may be skewed  It is positively skewed if the peak of the distribution lies to the left of the midpoint  It is negatively skewed if the peak of the distribution lies to the right of the midpoint  Kurtosis is an unusually peaked, or pointy, distribution reflecting a leptokurtic curve  An unusually flat curve is a platykurtic curve  Percentile ranks form a flat distribution Choosing Between Parametric and Nonparametric Statistics  Parametric statistics are based on certain assumptions bout the nature of the population in question  Two of the most common assumptions are (a) the data reflect an interval or ration scale and (b) the data fall in a normal distribution  Nonparametric statistics are not based on assumptions Descriptive Statistics  Measures of Central Tendency  This refers to the techniques for finding a point around which the data revolve  Three commonly used measures of central tendency are the mode, the median, and the mean Measures of Central Tendency 3 measures Mode Median Mean  Mode is the number that occurs most frequently  Median is the numerical center of a set of data  Mean is the arithmetic average of the scores within the data set Measures of Variability: Dispersion and Deviation  The farther the data are dispersed from the central axis, the greater the margin of error becomes  To derive meaning from the data it is important to not only determine their central tendency, but also their spread – and it helps to explain their spread in terms of one or more quantitative values  The simplest measure of variability is the range, which indicates the spread of the data from lowest to highest value Measures of Variability: Dispersion and Deviation  The range is easy to compute but has limited usefulness as a measure of variability  Other measures of variability use the median or mean as a starting point. One measure is the interquartile range which divides the distribution into four equal parts  Because quartiles are associated with the median, any researcher employing the median as a measure of central tendency should also consider the quartile deviation as a possible statistical measure for variability Measures of Variability: Dispersion and Deviation  If the mean is used as a starting point, then we calculate the difference between each score and the mean score – this is called the deviation  If we add all the differences (ignoring plus and minus) and then divide the sum by the number of scores, we get an average of the differences between any score and the mean. This number is sometimes called the average deviation (it is a little used value) Measures of Variability: Dispersion and Deviation  The standard deviation is the measure of variability most commonly used in statistical procedures Using the Mean and Standard Deviation Raw score Norm- referenced scores Percentile rank Standard score Standard deviation Stanine  Raw score is the number of correct answers on a test  Norm-referenced scores are scores that reflect where each person is positioned relative to other members of the person’s group  A percentile rank is an example of a norm- referenced score  A standard score tells us how far an individual’s performance is from the mean with respect to standard deviation units  Stanines are a commonly used standard-score scale. They have a mean of 5 and a standard deviation of 2 Measures of Association: Correlation  Statistical process by which we discover whether two or more variables are in some way associated with one another is called correlation  The resulting statistic is called a correlation coefficient (a number between negative 1 and positive 1)  The most widely used statistic for determining correlation is the Pearson product moment correlation What Correlation Coefficients Tell Us Direction & Strength  Direction (either positive or negative)  Strength (perfect, strong, weak, moderate) How Validity and Reliability Affect Correlation Coefficients  Beginning researchers should be aware that the extent to which one finds a statistical correlation between two characteristics depends, in part, on how well those characteristics have been measured  The researcher will find substantial correlations between two characteristics only if both characteristics are measured with a reasonable degree of validity and reliability  Remember that correlation does not indicate causation Inferential Statistics  Inferential statistics have two main functions  To estimate a population parameter from a random sample  To test statistically based hypotheses Statistical Techniques for Testing Hypotheses These are some of the more common tests  ANOVA  ANCOVA  T-test  Regression  SEM  Mann-Whitney U  Chi-square Interpreting the Data Generalizatio ns  Relate the findings to the original research problem and to the specific research questions and hypotheses  Relate the findings to pre-existing literature, concepts, theories, and research studies  Determine whether the findings have practical significance as well as statistical significance  Identifying limitations of the study