A Statistics Refresher PDF

A Statistics Refresher LORESSA JOY D. PAGUTA, MA, RPm LAIRA DEE A. BAROQUILLO, MA, RPm Department of Psychology Sampling and Sampling Techniques Sample vs Population A population is the set of all the individuals of interest in a particular study (Gravetter & Wallnau, 2...

A Statistics Refresher LORESSA JOY D. PAGUTA, MA, RPm LAIRA DEE A. BAROQUILLO, MA, RPm Department of Psychology Sampling and Sampling Techniques Sample vs Population A population is the set of all the individuals of interest in a particular study (Gravetter & Wallnau, 2017). A sample is a set of individuals selected from a population, usually intended to represent the population in a research study (Gravetter & Wallnau, 2017). Sampling is the process of selecting observations (a sample) to provide an adequate description and inferences of the population. 4/28/2023 3 4/28/2023 4 Sampling There are several reasons for researchers to do sampling rather than conducting a census. Four important reasons are as follows: 1. Low cost of sampling 2. Less time consuming in sampling 3. Scope of sampling is high 4. Accuracy of data is high 4/28/2023 5 Census vs Sample Survey Census Sample Survey Census collects information about every Survey collects information from a sample of member of the population. the population. Census takes a long time to complete. Surveys can be done in a shorter period of time compared to a census. Census is generally conducted by the Surveys can be conducted by anyone. government. Census are not conducted frequently. Surveys can be conducted more frequently. 4/28/2023 6 Probability vs nonprobability sampling Probability sampling is a method of selecting a sample wherein each element in the population has a known, nonzero chance of being included in the sample; otherwise, it is nonprobability sampling. Probability sampling techniques: Nonprobability sampling: Simple Random Sampling Convenience Stratified sampling Purposive Cluster sampling Quota Systematic sampling Snowball Multistage Sampling 4/28/2023 7 Simple Random Sampling Simple random sampling is a sampling method wherein all elements of the population have the same probability of inclusion in the selected sample. Strategies: Draw lots (lottery method) Random numbers 4/28/2023 8 Stratified Sampling Stratified sampling is a probability sampling method where we divide the population into nonoverlapping subpopulations or strata, and then randomly pick samples from each stratum. A stratum is a group whose members are of the same characteristics. 4/28/2023 9 4/28/2023 10 Cluster Sampling Cluster sampling is a probability sampling method wherein we divide the population into nonoverlapping groups or clusters, and then randomly select clusters. A cluster is a group whose members are not of the same characteristics. Clusters are also referred as natural groups. 4/28/2023 11 4/28/2023 12 Systematic Sampling Systematic sampling is a probability sampling method in which researchers select members of the population at a regular interval (or k) determined in advance. If the population order is random or random-like (e.g., alphabetical), then this method will give you a representative sample that can be used to draw conclusions about your population of interest. Example: You survey every 20th customer who leaves, every day for a week. 4/28/2023 13 Multistage Sampling In multistage sampling, you draw a sample from a population using smaller and smaller groups (units) at each stage. It’s often used to collect data from a large, geographically spread group of people in national surveys. Multistage cluster sampling: The Multistage random sampling: The researcher divides the population into researcher chooses the samples randomly groups at various stages for better data at each stage. Here, the researcher does collection, management, and interpretation. not create clusters, but he/she narrows These groups are called clusters. down the convenience sample by applying random sampling. 4/28/2023 14 Convenience Sampling Convenience sampling is a non-probability sampling method where units are selected for inclusion in the sample because they are the easiest for the researcher to access. This can be due to geographical proximity, availability at a given time, or willingness to participate in the research. 4/28/2023 15 Snowball Sampling Snowball sampling is a non-probability sampling method where new units are recruited by other units to form part of the sample. Snowball sampling can be a useful way to conduct research about people with specific traits who might otherwise be difficult to identify (e.g., people with a rare disease). 4/28/2023 16 Purposive Sampling This type of sampling, also known as judgement sampling, involves the researcher using their expertise to select a sample that is most useful to the purposes of the research. An effective purposive sample must have clear criteria and rationale for inclusion. 4/28/2023 17 Quota Sampling Sampling is done until a specific number of units (quotas) for various subpopulations have been selected. Quota sampling is a means for satisfying sample size objectives for the subpopulations. In probability sampling, the units are selected randomly while in quota sampling a non- random method is used—it is usually left up to the interviewer to decide who is sampled. 4/28/2023 18 A Statistics Refresher  Inferential statistics are methods used to make Descriptive inferences statistics are methods used from observations of a small to provide a concise group of people known as a description of a collection of sample to a larger group quantitative information. of individuals known as a population. 4/28/2023 20 Scales of Measurement and their Properties 4/28/2023 21 Frequency Distribution A frequency table is an ordered listing of number of individuals having each of the different values for a particular variable. A frequency distribution shows the pattern of frequencies over the various values. 4/28/2023 22 Three kinds of graphs are used to illustrate frequency distributions are the histogram (a), the bar graph (b), and the frequency polygon (c). 4/28/2023 23 Frequency Distribution 4/28/2023 24 Frequency Distribution 4/28/2023 25  skewed distribution - distribution in which the scores pile up on one side Skewness of the middle and are spread out on the other side; distribution that is not symmetrical. 4/28/2023 26 Frequency Distribution floor effect situation in which many scores pile up at the low end of a distribution (creating skewness to the right) because it is not possible to have any lower score. 4/28/2023 27 Frequency Distribution ceiling effect situation in which many scores pile up at the high end of a distribution (creating skewness to the left) because it is not possible to have a higher score. 4/28/2023 28 Kurtosis The term testing professionals use to refer to the steepness of a distribution in its center is kurtosis. 4/28/2023 29 Measures of Central Tendency The central tendency of a distribution refers to the middle of the group of scores. Measures of central tendency refers to the set of measures that reflect where on the scale the distribution is centered. Three measures of central tendency: mean, mode, and median. 4/28/2023 30 Measures of Central Tendency 4/28/2023 31 Measures of Central Tendency 4/28/2023 32 Measures of Variability (Dispersion) Variability is an indication of how scores in a distribution are scattered or dispersed. Statistics that describe the amount of variation in a distribution are referred to as measures of variability. Some measures of variability include the range, the standard deviation, and the variance. 4/28/2023 33 4/28/2023 34 Range The descriptive statistic that indicates the distance between the two most extreme scores in a distribution is called the range. Range = Highest score – Lowest score We usually use the range as our sole measure of variability only with nominal or ordinal data. 4/28/2023 35 Variance The variance is the average of each score’s squared difference from the mean. The more spread out the distribution has a larger variance because being spread out makes the deviation scores bigger. If the deviation scores are bigger, the squared deviation scores and the average of the squared deviation scores (the variance) are also bigger. 4/28/2023 36 Standard Deviation The most widely used number to describe the spread of a group of scores is the standard deviation. The standard deviation is simply the square root of the variance. The standard deviation indicates the “average deviation” from the mean, the consistency in the scores, and how far scores are spread out around the mean. 4/28/2023 37 Normal Curve Normal curve. specific, mathematically defined, bell-shaped frequency distribution that is symmetrical and unimodal; distributions observed in nature and in research commonly approximate it. 4/28/2023 38 Standard Scores A standard score is a raw score that has been Z Scores (zero plus or minus one scale) T Scores (fifty plus or minus ten scale) converted from one scale to Stanine another scale, where the A Scores latter scale has some IQ Scores arbitrarily set mean and Percentile Ranks standard deviation. 4/28/2023 39 4/28/2023 40 4/28/2023 41 Correlation Correlation is an expression of the degree and direction of correspondence between two things. The coefficient of correlation is the numerical index that expresses this relationship: It tells us the extent to which X and Y are “co-related.” 4/28/2023 42 Correlation If two variables simultaneously increase or simultaneously decrease, then those two variables are said to be positively (or directly) correlated. A negative (or inverse) correlation occurs when one variable increases while the other variable decreases. 4/28/2023 43 4/28/2023 44 A Statistics Refresher Cohen, R. J. & Swerdlik, M. E. (2018). Psychological Testing & Assessment, 9th edition. McGraw-Hill Education, New York Kaplan, R. M. & Saccuzzo, D. P. (2018). Psychological Testing : Principles, Applications, & Issues, 9th edition. Cengage Learning, Boston, MA