Module 1 to 3 Statistics, Lecture notes of Statistics

Module 1 to 3 Psychological Statistics notes

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RESEARCH METHODS
BACKGROUND
Introduction to Research
Methods of Knowledge Acquisition
¤ Authority - Knowledge based on
authority may rely upon the reputation
of an individual
¤ Rationalism – The use of reasoning,
alone, to arrive at knowledge
Ex: All statistics professors are
incredible people.
Ms. D is a statistics professor.
Therefore, Ms. D. is an incredible
person.
¤ Intuition Acquiring knowledge
through a sudden insight, the
clarifying idea that springs through
consciousness all at once as a whole.
¤ Scientific Method Uses both
reasoning and intuition for
establishing truth. Relies on objective
assessment.
The Scientific Method
a) Ask a Question
b) Do Background Research
c) Construct a Hypothesis
d) Test Your Hypothesis by Doing
an Experiment
e) Analyze Your Data and Draw a
Conclusion
f) Communicate Your Results
The Research Process
Definition of Terms
¤ Population The complete set of
individuals, objects, or scores, that the
investigator is interested in studying.
¤ Sample A subset of the
population.
¤ Variable - Any property or
characteristic of some event, object,
or person that may have different
values at different times depending on
the conditions.
¤ Independent Variable (IV) - The
independent variable in an experiment
is the variable that is systematically
manipulated by the investigator
¤ Dependent Variable (DV) - The
dependent variable in an experiment
is the variable that the investigator
measures to determine the effect of
the independent variable.
¤ Data - The measurements that are
made on the subjects of an
experiment are called data.
¤ Statistic - A statistic is a number
calculated on sample data that
quantifies a characteristic of the
sample.
¤ Parameter - parameter is a number
calculated on population data that
quantifies a characteristic of the
population.
The only difference is that a statistic is
calculated on a sample and a
parameter is calculated on a
population.
Exercise!
An English teacher conducts an
experiment to determine whether the
mode of presentation affects how well
a lesson material is remembered. For
this experiment, the teacher uses
several words and passages that are
presented visually or auditorily. 100
students are selected from the
undergraduates attending the
university at which the teacher works.
The students are divided into two
groups of 50 students per group. The
first group receives a visual
presentation of the words and
passages, and the second group hears
the words and passages through an
auditory presentation. At the end of
their respective presentations, the
subjects are asked to write down as
much of the material as they can
remember. The average number of
words remembered by each group is
calculated, and the two group
averages are compared to see
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RESEARCH METHODS

BACKGROUND

Introduction to Research

Methods of Knowledge Acquisition ¤ Authority - Knowledge based on authority may rely upon the reputation of an individual ¤ Rationalism – The use of reasoning, alone, to arrive at knowledge Ex : All statistics professors are incredible people. Ms. D is a statistics professor. Therefore, Ms. D. is an incredible person. ¤ Intuition – Acquiring knowledge through a sudden insight, the clarifying idea that springs through consciousness all at once as a whole. ¤ Scientific Method – Uses both reasoning and intuition for establishing truth. Relies on objective assessment. The Scientific Method a) Ask a Question b) Do Background Research c) Construct a Hypothesis d) Test Your Hypothesis by Doing an Experiment e) Analyze Your Data and Draw a Conclusion f) Communicate Your Results The Research Process Definition of Terms ¤ Population – The complete set of individuals, objects, or scores, that the investigator is interested in studying. ¤ Sample – A subset of the population. ¤ Variable - Any property or characteristic of some event, object, or person that may have different values at different times depending on the conditions. ¤ Independent Variable (IV ) - The independent variable in an experiment is the variable that is systematically manipulated by the investigator ¤ Dependent Variable (DV) - The dependent variable in an experiment is the variable that the investigator measures to determine the effect of the independent variable. ¤ Data - The measurements that are made on the subjects of an experiment are called data. ¤ Statistic - A statistic is a number calculated on sample data that quantifies a characteristic of the sample. ¤ Parameter - parameter is a number calculated on population data that quantifies a characteristic of the population. The only difference is that a statistic is calculated on a sample and a parameter is calculated on a population. Exercise! An English teacher conducts an experiment to determine whether the mode of presentation affects how well a lesson material is remembered. For this experiment, the teacher uses several words and passages that are presented visually or auditorily. 100 students are selected from the undergraduates attending the university at which the teacher works. The students are divided into two groups of 50 students per group. The first group receives a visual presentation of the words and passages, and the second group hears the words and passages through an auditory presentation. At the end of their respective presentations, the subjects are asked to write down as much of the material as they can remember. The average number of words remembered by each group is calculated, and the two group averages are compared to see

whether the mode of presentation had an effect. Practice Problem 1. For the experiment described below, specify the following: the independent variable, the dependent variable(s), the sample, the population, the data, the statistic(s), and the parameter(s). A professor of gynecology at a prominent medical school wants to determine whether an experimental birth control implant has side effects on body weight and depression. A group of 5000 adult women living in a nearby city volunteers for the experiment. The gynecologist selects 100 of these women to participate in the study. Fifty of the women are assigned to group 1 and the other fifty to group 2 such that the mean body weight and the mean depression scores of each group are equal at the beginning of the experiment. Treatment conditions are the same for both groups, except that the women in group 1 are surgically implanted with the experimental birth control device, whereas the women in group 2 receive a placebo implant. Body weight and depressed mood state are measured at the beginning and end of the experiment. A standardized questionnaire designed to measure degree of depression is used for the mood state measurement. The higher the score on this questionnaire is, the more depressed the individual is. The mean body weight and the mean depression scores of each group at the end of the experiment are compared to determine whether the experimental birth control implant had an effect on these variables. To safeguard the women from unwanted pregnancy, another method of birth control that does not interact with the implant is used for the duration of the experiment. SOLUTION Independent variable : The experimental birth control implant versus the placebo. Dependent variables : Body weight and depressed mood state. Sample : 100 women who participated in the experiment. Population : 5000 women who volunteered for the experiment. Data : The individual body weight and depression scores of the 100 women at the beginning and end of the experiment. Statistics : Mean body weight of group 1 at the beginning of the experiment, mean body weight of group 1 at the end of the experiment, mean depression score of group 1 at the beginning of the experiment, mean depression score of group 1 at the end of the experiment, plus the same four statistics for group 2. Parameter : No parameters were given or computed in this experiment. If the gynecologist had measured the body weights of all 5000 volunteers at the beginning of the experiment, the mean of these 5000 weights would be a parameter. Sample and Populations ¤ A sample in a research study is the group on which information is obtained ¤ The larger group to which one hopes to apply the results is called the populations ¤ Unfortunately, the actual population (called the target population ) to which a researcher would really like to generalize is rarely available. ¤ The population to which a researcher is able to generalize, therefore, is the accessible population.

Sampling Methods

¤ Random Sampling - Everyone in the entire target population has an equal chance of being selected.

variables that do not readily lend themselves to experimental manipulation ¤ Descriptive research is a study designed to depict the participants in an accurate way. More simply put, descriptive research is all about describing people who take part in the study. o Observational , defined as a method of viewing and recording the participants o Case study , defined as an in- depth study of an individual or group of individuals o Survey , defined as a brief interview or discussion with an individual about a specific topic

Ethics in Research

¤ Participants  Prospective participants must be given the information they will need to decide to enter a study or not to participate.  Potentially vulnerable participants such as children, the elderly, the mentally ill may be incapable of understanding information that would enable them to make an informed decision about study participation.  Obtain appropriate signed consent.  The participants in research have a right to privacy.  Give the names of people who can answer questions about the research; include the principal investigator.  Always stress the fact that participation is voluntary and that the participant can withdraw at any time  Methodological requirements of the research may demand that the participants remain unaware of the specific hypotheses under investigation. Sample of an Informed Consent I have read the Information Sheet and have had the details of the study explained to me. My questions have been answered to my satisfaction, and I may ask further questions at any time. I understand I have the right to withdraw from the study at any time and decline to answer any particular questions. I agree to provide information to the researcher(s) on the understanding that my name will not be used without my permission. I agree/do not agree to the interview being recorded electronically. I understand that I have the right to ask for the tape to be turned off at any time during the interview. I agree to participate in this study under the conditions set out in the information sheet. Signature – Name - Date ¤ The Researchers  Plagiarism is dishonesty.  Authorship should be based on the intellectual contribution of each author to the study.  NO-NO’s o Gift Authorship o Ghost Authorship

Psychological Statistics

Introduction

Branches of Statistical Methods

¤ Descriptive statistics - procedures for summarizing a group of scores or otherwise making them more understandable ¤ Inferential statistics - procedures for drawing conclusions based on the scores collected in a research study but going beyond them.

Variables, Values, and Scores

Levels of Measurement (Kinds

of Variables)

¤ Nominal Variable - variable with values that are categories (that is, they are names rather than numbers). Also called categorical variable. ◦ Rank-Order Variable - numeric variable in which the values are ranks, such as class standing, or place finished in a race. Also called ordinal variable. Even though we can order these values from lowest to highest, the spacing between the values may not be the same across the levels of the variables. Numeric Variable (Quantitative Variables) ◦ variable whose values are numbers. ¤ Equal-interval variable - variable in which the numbers stand for approximately equal amounts of what is being measured. ¤ Ratio Scale - an equal-interval variable is measured on a ratio scale if it has an absolute zero point , meaning that the value of zero on the variable indicates a complete absence of the variable. ¤ Discrete Variable - variable that has specific values and that cannot have values between these specific values. If you can count a set of items, then it's a discrete variable. ¤ Continuous Variable - If a variable can take on any value between its minimum value and its maximum value. Exercise! What level of measurement are the following variables?

  1. Position in the top 40
  2. Height
  3. Health rating (1 = Poor, 2 = OK, 3 = Good)
  4. Shoe color (1 = Black, 2 = Brown, 3 = Blue, 4 = Other)
  5. Ordering of top five contestants in a speech contest
  6. Temperature in Celsius
  7. Age
  8. Scores on levels of academic burnout

Describing Data

We carry out a study and collect the data. We then want to describe the data that we have collected. The first thing to describe is the distribution of the data, to show the kinds of numbers that we have.

Frequency Tables

How to Make a Frequency Table There are four steps in making a frequency table. ❶ Make a list down the page of each possible value, from lowest to highest. The list goes from the lowest possible rating, up the highest possible rating. Note that even if one of the ratings between the lowest and highest is not used, you still include that value in the listing, showing it as having a frequency of 0. For example, if no one gave a stress rating of 2, you still include 2 as one of the values on the frequency table. ❷ Go one by one through the scores, making a mark for each next to its value on your list.

How to Make a Histogram There are four steps in making a histogram. ❶ Make a frequency table (or grouped frequency table).Put the values along the bottom of the page, from left to right, from lowest to highest. If you are making a histogram from a grouped frequency table, the values you put along the bottom of the page are the interval midpoints. The midpoint of an interval is halfway between the start of that interval and the start of the next highest interval. ❸ Make a scale of frequencies along the left edge of the page that goes from 0 at the bottom to the highest frequency for any value.Make a bar above each value with a height for the frequency of that value. For each bar, make sure that the middle of the bar is above its value.

Shapes of Frequency

Distributions

¤ Frequency distribution - pattern of frequencies over the various values; what a frequency table, histogram, or frequency polygon describes. ¤ Unimodal distribution - Frequency distribution with one value clearly having a larger frequency than any other bimodal distribution frequency ¤ Bimodal distribution - frequency distribution with two approximately equal frequencies, each clearly larger than any of the others. ¤ Multimodal distribution - frequency distribution with two or more high frequencies separated by a lower frequency. ¤ Rectangular distribution - frequency distribution in which all values have approximately the same frequency.

Symmetrical and Skewed

Distributions

¤ Symmetrical distribution - distribution in which the pattern of frequencies on the left and right side are mirror images of each other. ¤ Skewed distribution - distribution in which the scores pile up on one side of the middle and are spread out on the other side; distribution that is not symmetrical. ¤ 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. ¤ 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. Normal and Kurtotic Distributions ¤ Normal Curve - specific, mathematically defined, bell-shaped frequency distribution that is symmetrical and unimodal; distributions observed in nature and in research commonly approximate it. ¤ Kurtosis - extent to which a frequency distribution deviates from a normal curve in terms of whether its curve in the middle is more peaked or flat than the normal curve.

Central Tendency and

Variability

Central Tendency - the central tendency of a group of scores (a distribution) refers to the middle of the group of scores.  Mean  Mode  Median ¤ Mean – an arithmetic average of a group of scores; sum of the scores divided by the number of scores.

  • Balancing point for the distribution of scores. M – mean Σ – “sum of”; add up all the scores following this symbol. X – scores in the distribution of the variable X. N – stands for number – the number of scores in a distribution. Exercise! Ex 1: Figure out the mean… 12, 10, 8, 6, 4, 2 Answer : 42/6 = 7
  1. Square each of these deviation scores (multiply each by itself)
  2. Add up the squared deviation scores. This total is called the sum of squared deviations
  3. Divide the sum of squared deviations by the number of scores. ¤ The Standard Deviation - Square root of the average of the squared deviations from the mean.
  • The most common descriptive statistic for variation. 1. Figure the variance. 2. Take the square root.
  • The standard deviation is, basically, the average amount that scores differ from the mean. ¤ The Variance SD2 - variance. SD - standard deviation. sum of squares ( SS ) - sum of squared deviations. ¤ The Importance of Variability in Psychology Research Without studying variability:  You will not know whether the data are close to the average or whether the data are spread out over a wide range.  You can’t compare two data sets effectively. Exercise!
  1. Calculate the SD for the following sample set of scores: 2.2, 2.4, 3.3, 3.1,

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