Summary Psychological Research Study Notes.

Psychological Research Study Notes. Hypothesis - a relation between constructs specifically targeted for testing. - a rule that associated values of one variable with values of another variable Step 2: Create an OPERATIONAL HYPOTHESIS - Measure the constructs (two or more) - HOW??- Be specific! - Define the population (general/ universal rule) - Decide what design you will use, e.g. Groups. - Your measure (e.g. questionnaire) must be reliable and valid Step 3: Translate the Research Hypothesis into a STATISTICAL HYPOTHESIS 1. Null Hypothesis/ Ho : e.g. Ho: µ = 300 2. Alternative Hypothesis / H1: e.g. H1: µ ≠ 300 (Non directional / two-tailed hypothesis) OR Alternative Hypothesis / H1: e.g. H1 µ › 300 (Directional / One-tailed hypothesis) Step 4: Test your Null Hypothesis using the data you get from your SAMPLE to see if the relationship exists Step 5: CHOOSE between the Null and Alternative Hypothesis and then draw a conclusion regarding your Research / Operational Hypothesis (i.e. accept OR reject H1) H1: Procrastination leads to lower exams scores in UNISA students X- Independent Variable (Causes Y) Relationship (Rule) Y- Dependent Variable (Result of X) Population PYC 6 4. TOPIC 1: OVERVIEW OF THE MAIN CONCEPTS Test THEORIES about HUMAN BEHAVIOUR THEORIES VS HYPOTHESIS: Part of the theory that is tested  Those relations between constructs that are targeted for testing  ALWAYS refers to a POPULATION  Gives us a RULE- about the relationship SAMPLES: Represent the POPULATION  INFERENTIAL STATISTICS: Infer numerical properties of populations FROM sample data GOAL of Research in PYC DEF: Network of postulated theoretical relations between CONSTRUCTS / CONCEPTS / VARIABLES RESEARCH DESIGNS: 1. GROUPS DESIGN: Compare 2 or more POPULATION groups. E.g. Male and Female student IQ scores 2. CORRELATIONAL DESIGN: Look for a relationship between two or more variables in a single sample. E.g. does stress affect your diet? CONSTRUCTS Def: building blocks of theories Construct 1 → Construct 2 ↕ ↕ Construct 3 → Construct 4  Constructs can be abstract/ hypothetical, theoretical E.g. creativity, depression, etc  Created to EXPLAIN certain observations  2 STEPS: From a hypothetical to an OPERATIONAL DEFINITION STEP 1: Specify the OBSERVABLE behaviour: E.g. anxiety- sweaty palms, avoiding stress STEP 2: Formulate a SCORE from the observable behaviour VARIABLES  Can have different values E.g. height, IQ, stress  Can VARY in quantity/ quality  We get dependent (Y) and (X) independent variables  To remember: Kisses (XXX) cause pregnancy (Y- lady with her arms up) 1. Nominal (categorical) 2. Ordinal (rank ordered)  1 and 2 can be grouped into “categorical” 3. Interval, e.g. IQ 4. Ratio, e.g. Score- 0%-100%  3 and 4 can be grouped into “continuous” *Interval and Ratio can be REDUCED to nominal, e.g. Low IQ / High IQ 2 TYPES OF VARIABLES: 1. MANIFEST: behavioural instances, indicators, referents, etc (you can SEE them!) 2. LATENT: hidden variable, intervening, hypothetical, factor (they are HIDDEN!) Levels of Measurement PYC 7 INFORMATION BOX: Levels of Measurement CATEGORICAL: Nominal Scale – Discrete (distinct – either pregnant, or not pregnant) Mutually exclusive (yes, or no i.e. yes, I am male or no, I am not male) Exhaustive (includes all possible categories) E.g. Gender; Yes/No questions Ordinal Scale - Same as nominal but are also ranked in order of importance (strongly agree, agree, neutral, disagree, strongly disagree) Although categories are ranked the interval is not equal, there is no measured degree of difference between strongly agree and agree or disagree and strongly disagree. Often used to measure preferences, behaviour, attitudes and opinions. Includes Likert scales and semantic differential scales. NOT IMPORTANT FOR THIS MODULE! CONTINUOUS: Interval Scale - Same characteristics as nominal but the interval scale can measure the interval between two points. Numbers are meaningful as numbers not just as categories (i.e. thermometer). This scale does not have an absolute zero point, zero is determined arbitrarily (intelligence tests) E.g. IQ scores; anxiety scores; exam results. Ratio Scale - Highest level of measurement: includes all of the above but has an absolute zero point. E.g. Measures weight, length and time. Note: * Nominal and ordinal measurement – have a limited number of categories * Interval and ratio scales can be reduced to nominal or ordinal scales i.e. exam results could be the individual results of each candidate or could just be pass or fail (an ordinance measure) You need to be able to IDENTIFY which scale the variable has been measured on, NOT give a definition of them 4. TOPIC 1: THEORY, HYPOTHESIS AND RESEARCH DESIGNS This is usually the first question in the exam: What is the BASIC GOAL OF RESEARCH? Answer: To test theories about HUMAN BEHAVIOUR Remember we are studying to become a psychologist so all the examples and exam questions will be dealing with some aspect of human behaviour, i.e. memory and IQ, gender and aggression, childhood trauma and current psychological disorders, etc. So how do we go about testing theories? Well it is usually not possible to test a whole theory so we pull out an aspect of a theory that we want to test- called a HYPOTHESIS. This hypothesis is the part of a theory that we are going to test. It contains similar key aspects to a theory- such as RELATIONSHIPS and CONSTRUCTS. What is a construct? These are certain groupings of behaviours that scientist have observed and given specific labels to describe the behaviour- e.g. STRESS, IQ, ANXIETY, CREATIVITY. Please note that you cannot observe (i.e. touch, smell, taste, see, etc) these concepts!! They are HYPOTHETICAL or ABSTRACT in nature. Unobservable or abstract constructs such as anxiety can be measured through their observable behaviours such as sweaty palms, increased heart rate, etc. This is done by giving the concept an operational definition: PYC 8 The operational definition of constructs If you want to carry out a research project then you need to be able to MEASURE your constructs! There are two steps you need to do in order to measure your constructs. Step 1: Specify the observable instances of the construct Step 2: Formulate a SCORE from your observable, i.e. IQ of 100 (this tell you how much of a particular construct the person has) So there are two types of definitions – 1. Theoretical - Dictionary definition – construct defined in terms of other constructs 2. Operational - Defined in terms of observable instances Necessary for measurement Defines what a researcher must DO to measure a construct What are variables? There are different ways to look at variables. 1. Manifest vs Latent: 2. Dependent vs Independent Dependent: If I am dependent it means that I NEED you. So if I am a young child I depend on my mother. We depend on air to live, etc. The symbol for a dependent variable is Y. Independent: If I am independent it means that I don’t need you, I can survive without you. It is also the ‘cause’ of your dependent variable. The symbol for an independent variable is X. What are populations? This is the actual group that we want to study and be able to generalise our findings to. For example: all female nurses between the ages of 25 and 45, or all school going children aged eight in rural areas. Why do we work with samples instead of populations? Most research organisations do not have the budget or the resources to test a whole population, so we draw a sample from the population and get our scores from them. We then INFER back to our population using our sample results, if there is a small change that our sample scores are due to ERROR. This is actually why we need to work with statistics in research, so we can actually calculate how much error we have in our sample! LATENT VARIABLES: E.G. Anxiety Hidden variable Intervening variable Hypothetical variable Factor MANIFEST VARIABLES: E.G. Exam Score Behaviour instances Indicators Referents Observable consequences Observable implications PYC 9 1.4.1 Representing the structure of a theory Psychological theories should be scientific- i.e. observable and testable Scientific theories must specify what observations, made under particular conditions, could disprove this theory. 1.4.2 The Hypothesis as a relationship between two variables DEFINITIONS: 1. Hypothesis – a postulated relation (or absence of a relationship) between two or more constructs that is specifically targeted for testing in a particular research project. The nature of the relation is a rule that associates values of one variable with values of another variable. (The correct definition is often worded like this in the exam!) 2. Variable – anything that can take on different values i.e. age, IQ, height, weight, etc - as people can be different ages, intelligence, anxiety etc 3. Dependent Variable – the variable that is influenced or changed (symbol is: Y) 4. Independent Variable – the variable that does the influencing (symbol is: X) 5. Intervening Variable – a variable that is the effect of one variable and the cause of another NOTE: All the unknown variables can be lumped together to be called ONE unknown variable. (U) When testing a hypothesis we cannot state that a rule exists without taking into account that more than just one independent variable might be influencing the dependent variable. E.g. gender (the independent variable) influences “attitude to AIDS” (the dependent variable) in the women and men have a different “attitude to AIDS”. Attitude to AIDS is, however dependent on other variables as well, not just gender. Apart from X, Y is also influenced by U. So to overcome this problem we take all the male scores and get and average and all the female scores and get an average. If we assume the average U effect on Y is zero we can use this as a basis for working out the other scores. This is easier said than done as it is never possible to test an entire population (I.e. all the employees everywhere). Because it is unlikely that we will ever know the exact average score we tend to hypothesise that something is ‘more likely’ to happen or one gender would be ‘more positive’ than the other, simply because we cannot know the exact score. 1.4.2 The Hypothesis as a statement which is widely true The postulated relation is claimed to be as generally (widely) true as possible i.e. the relation holds true for each person in the population in a wide range of situations. A hypothesis provides a rule that associates values of one variable with those of another, and also includes the population that relates to the relation. 1.4.3 Operational forms of the Hypothesis Theoretical hypothesis – the variables cannot be directly observed Research or Operational hypothesis – variables are measurable and can be directly observed. The variables imply how they can be measured. 1.4.5 Comparisons of group designs with correlation designs Group design Correlation Design The researcher can define a population of subjects for each of the values of the independent variable. The researcher has control over the size of the sample, selects a random sample of the desired size from the population and plans how the two can be compared. A single sample is selected from the research population and it is then noted how many belong to each category i.e. male and female. It could be that there are NO females in the sample… this is typical of a correlation design. Construct 1 → Construct 2 ↕ ↕ Construct 3 → Construct 4 PYC 10 5. TOPIC 2: PROBABILITY 5.1 OVERVIEW OF THE RESEARCH PROCESS: WHERE DOES PROBABILITY FIT IN? THEORY HYPOTHESIS POPULATION (e.g. 10 000 students) Inferential statistics SAMPLE (e.g. 100 students) TESTED PROBABILITY (p-value) Ultimately we want to Prove / Disprove Accept / Don’t accept the theory Test for a relationship- identify the Dependent Variable (Y) and the Independent Variable (X) Translate your research hypothesis into your statistical hypothesis: Ho and H1. Can we infer from our sample back to our population??? We need to look at Sampling ERROR first before we can decide- this is the reason we use PROBABILITY Results Scores, e.g. Means/ Averages E.g. score 72% for research exam A test statistic, e.g. tc, td, zx, tx, etc will give you an associated p-value. You DON’T calculate it!!! Note the p-value is 0 ≤ p ≤ 1 * can NEVER be negative or more than 1 We can also use Normal Distributions and the Z-Table to get p-values. PYC 11 DEFINITIONS: 1. Probability – a measure of uncertainty – the likelihood of an event (something happening) occurring where various outcomes are possible. i.e. if you flip a coin (event) what is the probability it will land on heads (outcome) Probability is measured by dividing the number of times the event occurs by the number of possible outcomes i.e. you flip a coin once you can have heads (1 outcome) or tails (2 outcomes) so the probability of the event occurring is 1 divided by 2 FORMULA: P (E) = Number of favourable events Number of possible outcomes Where (E) is the Event EXAMPLE: So the probability of a coin landing heads up is: P (Heads) = 1 2 This only works when there is a specific number of events and a specific number of possible outcomes. Where we do not know the frequency (f) of events or possible outcomes we use a different formula: P (E) = Number of observations of E________ = f (E) Number of times the experiment was performed N This is called RELATIVE FREQUENCY (another term for probability!) Statistical experiment – broad term in statistics to cover everything from counting the number of times a coin lands heads up to predicting trends in the economy, or the probability of possible causes of a disease. The more times you carry out the same statistical experiment the closer you will come to the theoretical probability of your results, as opposed to the relative frequency which is an approximation of the event occurring. Events are independent if the result of one has no bearing on the result of the next. i.e. your last flip of the coin will not determine your next flip of the coin. Events are mutually exclusive if either one or the other can occur, but not both. i.e. you can either get heads or tails with one coin, it cannot land both sides up! Sample space – all possible outcomes of a statistical experiment. Denoted as S. Also called a population. i.e. S = {heads, tails} as there are only two possible outcomes of one flip of a coin or S = {(heads, tails) (heads, heads) (tails, heads) (tails, tails) for flipping the coin twice The law of large numbers – If an experiment is done repeatedly, and the results are independent of each other, the observed proportion (frequency) of favourable occurrences of an event will approach its theoretical probability. If you flip a coin 100 times it is unlikely that you will get heads 50 times but if you flip it a million times you will be much closer to getting heads exactly half the time. Some characteristics and rules of probability  P- value – the probability value (the chances of an event happening). The outcome that we’re interested in is called an EVENT. An event is a specific outcome (like choosing a girl out of a group of students) when there are many possible outcomes (e.g. 700 students, with 300 girls and 400 boys)  P-values can be expressed as a percentage, fraction or decimal (proportions are better).  A p-value represents a proportion (proportion of outcomes supporting an event.) PYC 12  Proportion – a decimal number between 0 and 1  A p-value range is 0 ≤ p ≤ 1 (Between 0 and 1; included 0 and 1)  If p = 0 – the event definitely will NOT happen; If p = 1 – the event definitely WILL happen  The probability of an even NOT occurring: 1 – P(E)  The sum of all probability in a sample space (also called the area under the curve) = 1 S: All possible outcome of a statistical experiment = sample space (or the POPULATION). E.g. S = [heads, tails]. Sum of S (sample space) = 1 so if we know the probability of an event occurring we can work out the probability of an event NOT occurring. [1 – P (E)] See the example of Zanier cards in the U.S.G. pg. 32 RULES FOR COMBINING PROBABLITY: when dealing with independent events (know these for the exam!): 1. Additive Rule – P (A or B) = P (A) + P (B) simple rule used when events are mutually exclusive and signalled by the word OR. Either A or B can happen but not both. E.g. what is the probability that I will draw an ACE or a JACK? There are 4 aces in a deck and 4 Jacks. P (ACE) or P (Jack) = 4/52 + 4/52 = 8/52 = 0.15 (there is a 15% chance of drawing either an ace or a Jack) P (A or B) = P (A) + P(B) – P(A and B) – use if the events are NOT mutually exclusive P(A and B) takes into account the possible overlap in probabilities. See example [p (ace or heart] in U.S.G. Top of pg. 35 2. Multiplicative Rule – P (A and B) = P (A) x P (B) used to determine the product of two or more probabilities and is indicated by the word AND. i.e. the probability of A and B occurring. 3. Conditional Probability – P (A | B) the probability of event A occurring depends on event B also occurring. The Probability Model This indicates the chance of a possible outcome of an event, rather than choosing one outcome and testing that. So: Either heads or tails has an equal chance of occurring: P (heads) = P (tails) = ½ = 0.5- NB: this is the THEORETICAL PROBABLITY of this event occurring! Example 2: Normal die have 6 possible outcomes so the chance of each one occurring is the same: P (1) = P (2) = P (3) = P (4) = P (5) = P (6) = 1/6 PYC 13 UNISA Study Unit 2.3 Probability distributions and the normal curve How we go from normal distributions to probability? Work through the example in the UNISA guide from p. 46 A. Sample: 36 kids - each kid has a score out of 15 e.g. 9/15 B. What is the probability of getting a score of 9/15? 4 kids got this score P (9/15) = f/p = 4/ 36 = 0.11 = 11% of getting a score of 9/15 on the memory test! C. What is the probability of getting a score of 9/15 or MORE, i.e. 10/15, 11/15, etc? Add up ALL the probabilities for each score above 9/15 = 4/36 + 3/36 + 2/36 + 1/36 = 10/36 = 0.277 = 0.28 = 28% of getting a score of 9/15 or MORE We call this CUMULATIVE PROBABILITY D. If you plot the 36 kids score on a bar graph you will see it makes a bell-shaped curve (p.48) Cumulative probability is the probability of a number of possible events falling into a certain category i.e. probability of something equal to or greater than a certain point. The data can be interpreted as ‘under a curve’ if a curve is drawn over the top of the histogram. Continuous variable – such as age it can be measured in years, months, days, hours, minutes and seconds so the data is continuous. (As opposed to discrete variables which are measured in whole numbers) Continuous variables depend on an infinite number of possibilities so: P (number of 30 year olds)/infinity = 0 Thus the probability of any value in a continuous variable is 0. So the normal rule for probability does not work! The Normal distribution – was constructed specifically to deal with continuous variables Real data rarely offers exact sameness of the lower and higher end scores with the middle score always the highest. Statisticians however, do say that it is a very good abstract model for distribution and that ‘normally’ the majority clusters around the centre with a certain amount of tapering at the start and finish. This is why this is called ‘normal’ distribution and is represented by the ‘normal’ curve. PYC 14 The family of normal curves 2 variables: mean (µ) and standard deviation (σ), the rest of the terms are constants All normal curves are bell shaped distributions but the height and spread depend on the mean and standard deviation Taken from: Anything to the left of the mean is –ve and anything to the right is +ve. We only have to work out the values to the right as, by logic, we can work out that the values to the left are the same only negative.  Total area under the curve gives a probability of -∞ and +∞ and is equal to + 1 ** See Appendix D in the UNISA Study Guide The Normal Curve The more data included in the sample population the smoother the curve will be based on the law of large numbers. Most normal curves are not as smooth as the one illustrated as the data is not perfectly symmetrical. Most psychological and educational data are distributed approximately normally so that the normal curve can be used as a theoretical model of interpreting the distribution of that data. The normal curve is very useful in practice as many kinds of statistical tests can be derived from normal distributions and many psychological tests work if the data is approx. normally distributed as well as with wide deviations. 4 key properties 1. They are bell shaped, most observations occur at the midpoint of the curve 2. They are symmetrical 3. They are continuous, theoretically there are an infinite number of values so the curve is smooth 4. The curves are asymptotic: the two tails NEVER touch the horizontal axis as there is always some probability of a more extreme result. (Most common exam question) PYC 15 The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be converted to a Standard Normal Distribution using the z-score formula as follows: Formula: Z = X - µ σ The measures on the x axis of the Normal Curve are called z-scores Z-scores can be derived from any data provided we know the mean and standard deviation of the scores. When dealing with samples or test data, rather than populations the formula becomes _ Z = X – X S Z-scores – always reflect the number of standard deviations that a particular score lies above or below the mean. All distributions of z-scores have a mean of 0 and a standard deviation of 1- AS THEY ARE STANDARD NORMAL DISTRIBUTIONS! Can be used to compare an individual across different distributions, each with a different mean and a different deviation BENEFIT: Standardised distribution allows us to compare variables with different mean, standard deviation and scores expressed in differing original units 1. EXAMPLE: How to calculate a z-score: 1. Student A scores 56% on a cognitive psychology exam (X) 2. The class average is 52 % (X) 3. The standard deviation is 4 (s) Step 1: Write out your Formula: _ Z = X – X S Step 2: Fill in the correct values and do the calculation: Z = 56–52 4 Z = 4 4 Z = 1 (A z-score of 1 = 1 standard deviation above the mean) X = raw score/ individual score µ = population mean σ = standard deviation of the population Step 3: Plot your z score on you X-axis and see where it cuts the curve Step 4: Go to your z-tables and look up your z-score with its smaller and larger portion pvalues Write the values under your heading Step 5: Look at the question: Do they want to know the probability of getting her score or HIGHER then use the Smaller Portion value. Do they want to know the probability of getting her score or LOWER? Then use the Larger Portion p-value. Larger Portion p= 0.84 Smaller Portion p= 0.16 X = raw score/ individual score ͞x-bar = sample mean s = standard deviation of the sample PYC 16 1. EXAMPLE: How to calculate a z-score: 1. Student A scores 56% on a cognitive psychology exam (X) 2. The class average is 65 % (X) 3. The standard deviation is 6 (s) Step 1: Write out your Formula: _ Z = X – X S Step 2: Fill in the correct values and do the calculation: Z = 56–65 6 Z = -9 6 Z = -1.5 Step 3: Plot your z score on your X-axis and see where it cuts the curve Step 4: Go to your z-tables find your z-score and your smaller and larger portion p-values Write the values under your heading NB: If your z-score is NEGATIVE use the positive z-score value!! Step 5: Look at the question: Do they want to know the probability of getting her score or HIGHER then use the Larger Portion value. Do they want to know the probability of getting her score or LOWER? Then use the Smaller Portion p-value. Larger Portion Smaller Portion p= 0.93 p= 0.067 PYC 17 TOPIC 2: Z-SCORE SUMMARY 1. Any NORMAL DISTRIBUTION can be transformed into a STANDARD NORMAL DISTRIBUTION (Z-Score) 2. Using this Formula Z = X - µ – Population values σ _ Z = X – X – Sample values S 3. Once you have a Z-score look it up in your Z-TABLES 4. Find your SMALLER PORTION and LARGER PORTION VALUES (P-VALUES) 5. Plot them on your Standard Normal Curve 6. Advantage of using z-scores: Compare variables with different means, standard deviations and units of measurement * A Z-Score tells you how many standard deviations YOUR score lies above or below the µ mean (0). X = variable µ = population mean σ = standard deviation of the population Raw score- Average Score Standard Deviation INFORMATION BOX Frequency distribution – table or graph indicating how observations are distributed Frequency distribution table:  Column 1: ordered list of all possible scores or categories  Column 2: number of times each score occurs – tally marks used to help counting but not included in final table  Column 3: total frequency  Sum of the frequencies should be the same as the number of cases in the sample  Categories should be mutually exclusive  Sufficient categories so that each case can be classified into one of the available categories Cumulative frequency – number of scores below or above a certain frequency Frequency graph – X axis: categories or scores, Y axis: frequency Bar Chart – frequency distribution of categorical data (bars do not touch) Histogram – frequency distribution of successive scores or class intervals (numerical data and bars are touching) Frequency polygon – points are joined with straight lines PYC 18 Study Unit 2.3.1 Sampling and sampling distributions- Overview WHAT ARE SAMPLING DISTRIBUTIONS? Sampling distributions are needed in order to estimate POPULATION values- remember that we NEVER actually know the population value (e.g. mean score) so we rely on sampling distributions as our BEST GUESS for population values.