Intro to Psychological Statistics (lecture notes) PDF

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STATISTICS NOTES LECTURE + BOOK Methods of Knowing 1. Authority – when used, something is considered true because of tradition/ some person of distinction says it is. 2. Rationalism – uses reasoning alone to arrive at knowledge 3. Intuition – sudden insight 4. Scientific Method – uses both reasoning and intuition, has built to safeguard the truth - Reliance on objective assessment - Scientific experiments What is statistics? – Refers to a set of mathematical procedure for organizing, summarizing, and interpreting information Nature of Statistics – it is the science of collecting, organizing, presenting, analyzing data to assist in making more effective decisions. Purpose of Statistics  Organize and summarize information  Answer the questions in research Goals of Statistics 1. Help ensure that the info or observations are presented and interpreted in an accurate and informative way. 2. Provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific community. Population – the set of all individuals of interest in a particular study. Sample – set of individuals selected from a population usually intended to represent the population in a study Sampling A sample should have the same characteristics as the population it is representing. Sampling can be:  

With replacement – a member of the population may be chosen more than once (e.g. picking the candy from the bowl) Without replacement – a member of the population may be chosen only once (lottery ticket)

Sampling methods  Random – each member of the population has an equal chance of being selected  Nonrandom The actual process of sampling causes sampling errors. For example, the sample may not be

large enough or representative of the population. Factors not related to the sampling process cause nonsampling errors. A detective counting device can cause a nonsampling error. 

Sampling Error – the discrepancy between a sample statistic and its population parameter

Random Sampling Methods  Simple random sample – each sample of the same size has an equal chance of being selected  Stratified sample – divide the population into groups called strata and then take a sample for each strata  Cluster sample – divide the population intro strata and then randomly select some of the strata. All the members from these strata are in the cluster sample.  Systematic sample – randomly select a starting point and take every n-th piece of data from a listing of a population. Parameter – a value that describes a population Statistic – a value that describes a sample Types of Statistics  Descriptive – statistical procedures used to summarize, organize, and simplify data. (e .g tables/graphs are used to organize data). Descriptive values such as the average score are used to summarize data.  Inferential – methods for using sample data to make a general conclusion (inference) about populations. Because a sample is typically only a part of a population, sample data provide only limited info about the population. As a result, sample statistics are generally imperfect representatives of the corresponding population parameters. Variable and Data Variable is a characteristic or condition that changes or has different values for different individuals.  

Independent Variable – systematically manipulated by investigator. Dependent Variable – (DV) investigators measures to determine effect of the IV

(IV) the the the

Data are measurements of observations. Data sets a collection of measurements or observations.

Datum is a single measurement (score/raw score)  Qualitative – generally described by words or letters.  Dichotomic ; if it takes the form of a word with two options (e.g gender: male/female)  Polynomic ; if it take the form of a word with more than two options (education: primary school, secondary school, and university)  Quantitative – always numbers, they are the result of counting or measuring attributes of a population.  Discrete ; if it is the result of counting, usually whole number  Continuous; if it is the result of measuring (e.g distance travelled, weight)

4 TYPES OF MEASUREMENT SCALES 1. Nominal Scale is an unordered set of categories identified only by name. Nominal measurements only permit you to determine whether two individuals are the same or different 2. Ordinal Scale is an ordered set of categories. Ordinal measurements tell you the direction of difference between two individuals. 3. Interval scale is an ordered series of equal-sized categories. Interval measurements identify the direction and magnitude of different. The zero point is located arbitrarily on an interval scale. 4. Ratio scale is an interval scale where a value of zero indicated none of the variable. Ratio measurements identify the direction and magnitude of differences and allow ratio comparisons of measurements.

FREQUENCY DISTRIBUTIONS A frequency distribution is an organized tabulation showing exactly how many individuals are located in each category on the scale of measurement. A frequency distribution presents

an organized picture of the entire set of scores, and it shows where each individual is located relative to others in the distribution. 

Regular Frequency Distribution is when a frequency distribution lists all of the individual categories (X values)

Constructing a Frequency Distribution of Grouped Scores The steps for constructing a frequency distribution of grouped scores are as follows: 1. Find the range of the scores 2. Determine the width of each class interval (i) - The width of each class interval should a relatively simple number. For example 2, 5, 10, or 20 would be a good choice for the interval width. Notice that it is easy for to count by 5s or 10s. These numbers are easy to understand and make it possible for someone to see quickly how you have divided the range of scores. 3. List the limits of each class interval, placing the interval containing the lowest score value at the bottom. a. The lower limit of this interval must be such that the interval contains the lowest score b. It is customary to make the lower limit of this interval evenly divisible by i 4. Tally the raw score intro the appropriate class intervals. 5. Add the tallies for each interval to obtain the interval frequency. Frequency Distribution Graphs The score categories (x values) are listed on the X axis and the frequencies are listed on the Y axis. When the score categories consist of numerical scores from an interval or ratio scale, the group should be either a histogram or a polygon. Histograms In a histogram, a bar is centered above each score (or class interval) so that the height of the bar corresponds to the frequency and the width extends to the real limits, so that adjacent bars touch. The score is progression/continuum, it is not a different content Histograms represent a progression of numbers Polygons / Polygon Graphs In a polygon, a dot is centered above each score so that the height of the dot corresponds to the frequency. The dots are then connected by

straight lines. An additional line is drawn at each to bring the graph back to a zero frequency. - The graph starts with zero and ends with zero - The data needs to be adjacent to each other Bar Graphs Bar graphs are used to present nominal data. Smooth Curve If the scores in the population are measured on an interval or ration scale, it is customary to present the distribution as a smooth curve rather than a jagged histogram or polygon. - The smooth curve emphasizes the fact that the distribution is not showing the exact frequency for each category. Shape A graph shows the shape of distribution.  A distribution is symmetrical is the left side of the graph is roughly a mirror image of the right side. V - One example of a symmetrical distribution is the bell-shaped normal function  On the other hand, distributions are skewed when scores pile up on one side of the distribution, leaving a “tail” of a few extreme values on the other side. Positively and Negatively Skewed Distributions In a positively skewed distribution the scores tend to pile up on the left side of the distribution with the tail tapering off to the right. In a negatively skewed distribution the scores tend to pile up on the right side of the distribution and the tail points to the left....