# Solving-research paper – math problem example

## Solving-Research Paper

2. Define population, sample, parameter and statistic; concepts of population and sample Population refers to the set of all individuals which the researcher wishes to study. Sample is the group of individuals which is a subset of the population who are selected for the study. For the results of the study conducted on the sample to be held true for the entire population, the sample should be a representative sample – that is, it should possess the same characteristics as the entire population, or as close to it as possible. A statistic is a characteristic that describes a sample; a parameter is a characteristic that describes a population. The statistic for a sample usually corresponds in value to its counterpart parameter for the population, but there is typically a small discrepancy between them that is attributable to sampling error. 4. How difference between 2 samples may be due to the treatment tested, and how difference may be due to sampling error. The difference between the two samples would be attributed to the treatment being tested, for as long as the two samples are representative subsets of the same population, or that the samples possess the same attributes as each other and the population they represent. Assuming all other variables are held constant, then the discrepancy may be attributed to the treatment applied. On the other hand, where the samples were not representative of the same population, or if the possessed different attributes than the population and each other, then the discrepancy may be due to sampling error, because the two groups are not identical to each other. The material differences in their attributes introduce other variables than the treatment being tested, and therefore the results are not solely attributable to the treatment. 6. Goal of an experimental research study. Identify two elements necessary for an experiment to achieve its goal. The goal of an experimental study is to arrive at a specific cause and effect relationship between the independent and the dependent variables. The two elements necessary are the variation of only one independent variable in the experimental group, and the control of all other independent variables, such that the resulting difference in outcome is attributable purely to the manipulated independent variable. 10. Experimental and correlational study The caffeine consumption study is an experiment. An experimental study tries to discover relationships between variables by manipulating an independent variable to create different effects in the dependent variable, and the commensurate variables are then compared. On the other hand, the correlational study examines the relationship between two variables; it measures and describes the variables but does not allow the inference of a cause and effect relationship, unlike experimental methods. In the study described, the manipulated (independent, causal) variable is the amount of caffeine given to the experimental group, and denied the control group, while the dependent variable is the level of activity of the children. Any difference between the control and the experimental group would be attributed to the effect caused by the drinking of caffeine. 12. Oxytocin … For this experimental study, identify the independent and the dependent variable In the study, the independent variable was the nature of the inhalant, and the dependent variable was the behaviour of the person who inhaled the substance. When the inhalant was an oxytocin, the resulting behaviour was one of trust (i. e., the incidences of giving money to the a trustee). When the inhalant was a placebo, then the resulting behaviour tended less towards trust. 14. Four scales of measurement: nominal, ordinal, interval, and ratio. a. Additional information from measurements on ordinal scale compared to nominal scale A nominal scale is one wherein the categories are different only in name and offer no other information. An ordinal scale is one where the categories are differentiated in terms of direction as well as name, thereby creating an ordered series, so the added information is the order. b. Additional information from measurement on interval scale compared to ordinal scale. For an interval scale, aside from the order the added information is the magnitude or distance between the categories. c. Additional information obtained from ratio scale compared to interval scale. For the ratio scale, aside from the order and magnitude, the added information is the inclusion of ratios of magnitude, because the zero point indicates none of the variables being measured. 16. Define hypothetical construct. Give example. Explain why operational definitions are needed to define and to measure constructs. Hypothetical constructs refer to variables that are intangible and therefore cannot be observed directly by the senses, but are rather “ constructed” in the mind. Examples of hypothetical constructs are intelligence, self-esteem, or emotion. Because they are intangible, they are not capable of being directly measured or quantified, although there are external manifestations, phenomena, or behaviours that are observable and may be taken as indicative of the hypothetical construct. For this reason, an operational definition is necessary. An operational definition defines the hypothetical construct in terms of externally observable and measurable behaviours. In the behavioural sciences, probably the best known operational definition of a hypothetical construct is an individual’s performance in an IQ examination as a definition of the individual’s intelligence. (By Frederick J. Gravetter, Larry B. Wallnau 2009 Behavioral Sciences, 8th edition, Wadsworth Cengage Learning) 18. X X2 X – 1 6 36 5 1 1 0 3 9 2 4 16 3 2 4 1 Sum 16 66 11 (? X)2 256