# PSYB01H3 Lecture Notes - Level Of Measurement, Central Tendency, Frequency Distribution

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Chapter 12 - Understanding research results: description and correlation

•Stats are used for describing data and making inferences on sample data

Scales of Measurement: a review

•Levels of a variable can be decribed by 4 scales

oNominal: no numerical, quantitative properties

oOrdinal: rank order

oInterval: quantitative properties, no absolute 0

oRatio: quantitative properties, has an absolute 0

Analyzing the results if research investigation

•Depending on the way the variables are studied there are 3 basic ways of describing the

results

oComparing group percentages

oCorrelating scores of individuals on two variables

oComparing group means

Comparing group percentages

•Example: studying if which females or males like traveling more

oLets say out of 50 females and 50 males

•80% of females like to travel

•60% of males like to travel

oNeed to focus on % because of variable of liking travel or disliking travel is

nominal

Correlating individual scores

•Used when you do not have distinct subject groups

•Individuals are measured on 2 variables

oEach variable has a range of numerical values

•Example: do people who sit near the front receive higher grades?

Comparing group means

•Example: studying effect of exposure to an aggressive adult on children's play

oOn average how many aggressive acts did the children perform during play in both

groups?

•Aggression is a ratio scale variable because there is a true zero and equal intervals

Frequency distributions

•When analyzing results it is useful to start by making a frequency distribution of the data

•Frequency Distribution: indicates the number of individuals that receive each possible

score on a variable

oUseful to look at this in terms of %s

•Example: how many students in a class received a specific score on an exam

Graphing frequency Distributions

•Pie Charts: divide a whole circle or pie into slices that represent relative percentages

oUseful when representing nominal scale information

•Bar graphs: use a separate and distinct bar for each piece of information

oX-axis is the independent variable

oy-axis is the dependent variable

•Frequency polygons: use a line to represent frequencies

oUseful when representing interval or ratio scales

oCan have more then one line to represent more then one group

•Histograms: uses bars to display a frequency distribution for a quantitative variable

oScale values are continuous and show increasing amounts on a variable such as age,

blood pressure or stress

oBars are drawn next to each other since values are continuous

•Looking at frequency distributions allows you to directly observe how your participants

responded

oCan look at what scores are most frequent and the shape of the distribution of

scores

oFind "outliers" or unusual, unexpected scores

Descriptive statistics

•Descriptive statistics allow researchers to make precise statements about the data

oTwo statistics are needed to describe the data

oOne number can be used to describe the central tendency or how participants scored

overall while another number describes the variability or how widely the distribution of

scores is spread

•These 2 numbers summarize the information contained in a frequency

distribution

Central tendency

•Central tendency: a central tendency statistic tells us what the sample as a whole or on the

average is like

oThree measures of central tendency:

•Mean: the average

Abbreviated as "M"

Indicator of central tendency only when scores are measured on an

interval or ratio scale

•Median: the score that divides the group in half

Abbreviated as "Mdn"

Indicator of central tendency only when scores are measured on an

ordinal scale

Also useful with interval and ratio scale variables

•Mode: the most frequent score

Only measure of central tendency that is appropriate if a nominal

scale is used

oThe median or mode can be a better indicator of central tendency than the mean if a

few unusual scores bias the mean

## Document Summary

Chapter 12 - understanding research results: description and correlation: stats are used for describing data and making inferences on sample data. Scales of measurement: a review: levels of a variable can be decribed by 4 scales, nominal: no numerical, quantitative properties, ordinal: rank order o. Interval: quantitative properties, no absolute 0: ratio: quantitative properties, has an absolute 0. Analyzing the results if research investigation: depending on the way the variables are studied there are 3 basic ways of describing the results, comparing group percentages, correlating scores of individuals on two variables, comparing group means. Comparing group percentages: example: studying if which females or males like traveling more, lets say out of 50 females and 50 males. 60% of males like to travel: need to focus on % because of variable of liking travel or disliking travel is nominal. These 2 numbers summarize the information contained in a frequency distribution.