PSYCHOLOGICAL STATISTICS What is Statistics? - The language of science and data. It is an objective, precise, and powerful tool in science and in everyday life. It involves math and relies upon calculations of numbers. In the broadest sense, “statistics” refers to a range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data. Statistics is how we communicate in science. Statistics provides tools that you need in order to react intelligently to information you hear or read. How to be an intelligent consumer of Statistics? Question the statistics that you encounter, Think about the numbers, their sources, and most importantly, the procedures used to generate them. Variable – is simply a characteristic or feature of things we are interested in understanding. Properties of Scales Independent Variable – manipulated or are changed by researchers and its effects are measured and compared. “Cause” Dependent Variable – changes as a result of the independent variable manipulation. “Effect” Levels of Independent Variable Qualitative Variable – are those that express a qualitative attribute. Do not imply a numerical ordering. Categorical variables. Quantitative Variables – are those variables that are measured in terms of numbers. Numerical variables. Discrete and Continuous Variables Discrete Variable – a variable whose value is obtained by counting and has discrete points on the scale. Can only Nominal Scale – only purpose is to name objects. Ordinal Scale – rank individuals or objects but not to say anything about the meaning of the differences bet ranks. Interval Scale – numerical scales in which intervals have the same interpretation throughout. The difference between the two values is meaningful. Ratio Scale – quantitative scale where there is a true zero and equal intervals between neighboring points. Why is the level of measurement important in Statistics? - - The number of levels of an independent variable is the number of experimental conditions. Qualitative and Quantitative Variables Magnitude – property of “moreness” Equal Interval – difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units. Absolute 0 – nothing of the property being measured exists. Levels of Measurement Types of Variables: take on a finite or countably infinite set of values. Continuous Variable - a variable whose value is obtained by measuring. Having an infinite number of potential values between any two points. It determines the type of statistical analysis that can be conducted, and, therefore, the type of conclusions that can be drawn from the research. Helps determine the appropriate statistical methods and tests that can be used to analyze the data. Collecting Data Data (plural) – measurement or observation. Data Set – collection of measurement or observation. Datum (singular) – a single measurement of observation and is commonly called a score or raw score. Population and Sample Population – is a set of all the individuals of interest in a particular study. Sample – is a set of individuals selected from a population, usually intended to PSYCHOLOGICAL STATISTICS represent the population in a research study. Over-representation – the representation of a group in a category that exceeds our expectations for that group or differs substantially from the representation of others in that category. Sampling Bias – conclusion applies only to the sample and is not generalized to the full population. Parameter vs. Statistic - Sampling Error – the difference between a population parameter and a sample statistic. Sampling errors happen even when you use a random selected sample. This is because random samples are not identical to the population in terms of numerical measures like means and standard deviations. A sample size should be large enough to sufficiently describe the phenomenon of interest and address the research question at hand. But at the same time, a large sample size risks having repetitive data. Reasons for Sampling: Every member of the population to have an equal chance of being selected into the sample. - Systematic Sampling Every member of the population is listed with a number, but instead of randomly generating numbers, individuals are chosen at regular intervals. - Stratified Sampling Dividing the population into subpopulations or “strata” that may differ in important ways. It allows you to draw more precise conclusions by ensuring that every subgroup is properly represented in the sample. - Cluster Sampling Dividing the population into subgroups, but each subgroup should have similar characteristics to the whole sample. Instead of sampling individuals from each subgroup, you randomly select entire subgroups. Parameter – referring to the whole population. Statistic – describes only a sample of the population. Sample Size Matters - Necessity: sometimes it’s simply not possible to study the whole population due to its size or inaccessibility. Practicality: it’s easier and more efficient to collect data from a sample. Cost-effectiveness: there are fewer participant, laboratory, equipment, and researcher costs involved. Manageability: storing and running statistical analyses on smaller datasets is easier and reliable. 2. Non-Probability Sampling Method - Individuals are selected based on nonrandom criteria, and not every individual has a chance of being included. - Used in explanatory & qualitative research. - Aims to develop an initial understanding of a small or under research population. - Convenience Sampling Simply includes the individuals who happen to be most accessible to the researcher. - Voluntary Response Sampling Is mainly based on ease of access. Instead of the researcher choosing participants directly contacting them, people volunteer themselves. - Purposive 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. - Snowball Sampling If the population is hard to access, snowball sampling can be used to recruit participants via other participants. Different Types of Sampling 1. Probability Sampling Method - Gives all members of the population an equal chance to be part of the sample. - Ideal for quantitative studies. Simple Random Sampling Types of Statistical Analyses PSYCHOLOGICAL STATISTICS - - - Descriptive Statistics Numbers that are used to summarize and describe data. Are just descriptive. They do not involve generalizing beyond the data at hand. Inferential Statistics Techniques that allow you to study samples and then make generalizations about the populations from which they were selected. Help you come to conclusions and make predictions based on your data. - Research Design is simply a structural framework of various research methods as well as techniques that are utilized by a researcher. It helps a researcher to pursue their journey into the unknown but with a systematic approach. Quasi-Experimental Experimental Non-Experimental Research Design Types of Research Design - - Descriptive Design – seeks to describe the current status of an identified variable. Correlational Design – attempts to determine the extent of a relationship between two variable using statistical data. Correlational Studies Direction or Types Positive Correlation – both variables change in the same direction. Negative Correlation – the variables change in opposite directions. Zero Correlation – there is no relationship between the variables. Experimental Research Design 1. Qualitative Research Design True Experiment – uses the scientific method to establish the cause-effect relationship among a group of variables that make up a study. Three Features: Phenomenological – researchers describe the lived experiences of individuals about a phenomenon as described by participants. Ethnographic – researchers studies the shared patterns of behaviors, language, and actions of an intact cultural group. Grounded – involves the collection and analysis of data to support theoretical explanation. Historical – analyze the meaning of past events in an attempt to interpret the facts and explain the cause of events and their effects in the present event. Action Research – an approach in which the researcher and client collaborate in the diagnosis of the problem and the development of its solution. Case Study – an inquiry design found in many fields especially evaluation in which the researcher develops an indepth analysis of a case. Manipulation Either of the two: Randomization Two Groups Statistical/Mathematical Notation Raw Score – are the original, unchanged scores obtained in the study. - Scores for a particular variable are represented by the letter X. The letter N is used to specify how many scores are in a set. An uppercase letter N identifies the number of scores in a population and lowercase letter N identifies the number of scores in a sample. Summation Non-Experimental: Descriptive Co-relational Experimental: Quasi-Experiment – involves getting as close as possible to the conditions of a true experiment but cannot meet all requirements. Two Features: Types of Quantitative Research - Manipulation Randomization Two Groups PSYCHOLOGICAL STATISTICS - The Greek letter sigma, or Σ, is used to stand for summation. The expression ΣX means to add all the scores for variable X. The summation sign, Σ, can be read as “the sum of.” Thus, ΣX is read as “the sum of the scores.” To use summation notation correctly, keep in mind the following two points: 1. The summation sign, Σ, is always followed by a symbol or mathematical expression. The symbol or expression identifies exactly which values are to be added. To compute ΣX, for example, the symbol following the summation is X, and the task is to find the sum of the X values. On the other hand, to compute 𝛴(𝑋 − 1)2, the summation sign is followed by a relatively complex mathematical expression, so your first task is to calculate all of the (𝑋 − 1)2 values and then add the results. 2. The summation process is often included with several other mathematical operations, such as multiplication or squaring. To obtain the correct answer, it is essential that the different operations be done in the correct sequence. Following is a list showing the correct order of operations for performing mathematical operations. Most of this list should be familiar, but you should note that we have inserted the summation process as the fourth operation in the list. Order of Mathematical Operations: 1. Any calculation contained within parentheses is done first. 2. Squaring (or raising to other exponents) is done second. 3. Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right. 4. Summation using the notation is done next. 5. Finally, any other addition and/or subtraction is done.
