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Psychology 1022 > Week 11 - Summarising Data using Descriptive Statistics > Flashcards

Week 11 - Summarising Data using Descriptive Statistics Flashcards

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1
Q

What are Descriptive Statistics?

A

After collecting raw data, to reduce numbers into meaningful summary is to use “descriptive statistics”. Descriptive statistics allow us to organise, summarise, and simplify raw data so patterns and trends in variables can be seen (ordering chaos!)

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2
Q

What is a descriptive value for a population commonly called?

A

A parameter.

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3
Q

What is a parameter descriptive value symbolised by?

A

A summary value that describes a population. A common example of a parameter is the average score for a population. Greek letters e.g u, o, o2

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4
Q

What is a descriptive value for a sample commonly called?

A

A statistic

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5
Q

What are Inferential Statistics?

A

Methods for using sample data to make general conclusions (or inferences) about populations i.e sample statistics are used as a basis for inferring conclusions about population parameters

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6
Q

We can start to make sense of data by constructing a _____?

A

Frequency distribution

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7
Q

***What is a frequency distribution?

A

Specifies the frequency of occurrence of each possible score (that is, the number of times each score occurred on the scale of measurement)

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8
Q

Which techniques can we use to organise and summarise data?

A

Tabular or graphical techniques (but choose one only)

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9
Q

***What is a frequency table?

A

An organised tabulation showing exactly how many individuals are located in each category on the scale of measurement. e.g 0 1 1 4 2 3 3 5

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10
Q

What does a frequency distribution table consist of?

A

At least two columns - one listing categories on the scale of measurement (X) and another for frequency (f)

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11
Q

In the scale of measurement (X) column for a frequency distribution table, are values listed from highest to lowest?

A

Yes, and none are skipped

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12
Q

In the frequency (f) column for a frequency distribution table, ___ are determined for each value?

A

Tallies. E.g how often each X value occurs in the data set. These tallies are the frequencies for each X value.

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13
Q

What should the sum of the frequencies equal?

A

N

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14
Q

When a frequency distribution table lists all of the individual categories (X values), it is called a _____?

A

Regular frequency distribution table

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15
Q

When there are to many categories to list in the X values column, so a “simple” presentation of data can’t occur, what type of table is used to remedy the situation?

A

A grouper frequency distribution table

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16
Q

In a grouped table, the X column lists groups of scores called ______ as opposed to individual values?

A

Class intervals!

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17
Q

True or false: class intervals don’t have the same width

A

FALSE. They do have the same width. Usually a simple number such as 2, 5, 10 and so on. Each interval begins with a value that is a multiple of the individual width.

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18
Q

What is a “statistic”?

A

A summary value that describes a sample. A common example of a statistic is the average score for a sample.

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19
Q

What are statistics dual purposes?

A
  1. To summarize or describe entire sets of scores 2. Provide info about corresponding summary values for entire populations
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20
Q

What are the corresponding summary values for a population called?

A

Parameters

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21
Q

Most research questions concern population ____?

A

Parameters

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22
Q

Most research data consists of sample ____?

A

Statistics

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23
Q

What is the general purpose for inferential statistical techniques?

A

To use sample statistics as the basis for drawing general conclusions about the corresponding population parameters.

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24
Q

How does descriptive stats organise or summarise a set of scores?

A
  1. Organise entire set of scores into a table or graph 2. Compute one or two summary values (eg the average) that describe entire group
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25
Q

What is the term to describe a set of scores organised into a display showing an entire set?

A

Frequency Distribution

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26
Q

What kind of information does a frequency distribution display?

A
  1. The set of categories that make up the scale of measurement 2. The number of individuals with scores in each of the categories
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27
Q

A frequency distribution can either be a table or a ___?

A

Graph

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28
Q

What are the advantages/disadvantages of a frequency distribution table?

A

Adv: Allows researcher to view entire set of scores Disadv: constructing one without a computer can be tedious with large sets of data

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29
Q

How many columns does a frequency distribution table consist of?

A

Two. One for the scale of measurement (or the set of categories into which individuals have been assigned), and the other for the frequency or number of individuals in each category.

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30
Q

In a frequency distribution graph, on which axis is the scale of measurement (or categories to which individuals have been assigned)?

A

X axis. The Y axis has the frequencies.

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31
Q

As discussed in earlier chapters, how many scales of measurement are there? Hint: it’s an acronym

A

FOUR Nominal Ordinal Interval Ratio

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32
Q

When the measurement scale (Scores) consists of numerical values, what scale of measurement might it be?

A

Interval or Ratio

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33
Q

How can we graph the frequency of a measurement scale with numerical values?

A

In a histogram OR polygon graph

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34
Q

What does a histogram graph look like?

A

It shows a bar above each score so that the height of the bar indicates the frequency of occurrence for that particular score

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35
Q

What does a polygon graph look like?

A

It shows a point abve each score so that the height of the point indicates the frequency. Straight lines connect the points.

36
Q

When the measurement scale (Scores) consists of no numerical values, what scale of measurement might it be?

A

Nominal OR Ordinal

37
Q

When categories on the scale of measurement are not numerical values, the frequency distribution must be presented as a ____ graph?

A

Bar graph

38
Q

What is a bar graph?

A

It is like a histogram except a space is left between adjacent bars.

39
Q

Are frequency distributions considered a final statistical analysis?

A

No. It is a preliminary method and is rarely included in published research reports.

40
Q

What is the most commonly used descriptive statistic that is more simple than a frequency distribution scale?

A

Measuring the central tendency (or average). So locating the center of the distribution scores by finding a single score that represents the entire set.

41
Q

What is the central tendency?

A

Is a statistical measure that identifies a single score that defines the center of a distribution. The goal of central tendency is to identify the value that is most typical or most representative of the entire group.

42
Q

When the scores consist of numerical values from an interval or ratio scale of measurement, what is the most commonly used descriptive values?

A

The mean and the standard deviation

43
Q

What does the MEAN do?

A

Measures the central tendency

44
Q

What does the standard deviation do?

A

Describes the variability of the scores

45
Q

What is the symbol X commonly used for in statistics textbooks?

A

To represent the sample mean.

46
Q

In research reports, the convention is to use the letter ___ to represent the sample mean?

A

M

47
Q

What is the mean?

A

The mean is a measure of central tendency obtained by adding the individual scores, then dividing the sum by the number of scores. The mean is the arithmetic average.

48
Q

What is the median?

A

The median measures central tendency by identifying the score that divides the distribution in half. If the scores are listed in order, 50% of the individuals have scores at or below the median.

49
Q

What is the mode?

A

The mode measures central tendency by identifying the most frequently occurring score in the distribution

50
Q

What is the standard deviation?

A

Standard deviation is the square root of the variance and provides a measure of variability by describing the average distance from the mean. The standard deviation uses the mean of the distribution as a reference point and describes the variability of the scores by measuring the distance between each score and the mean. Conceptually, standard deviation measures the average distance from the mean.

51
Q

As a general rule, __% of the scores in a distribution are within a distance of one standard deviation of the mean, and roughly ___% of the scores are within two standard deviations..?

A

70 and 95%

52
Q

What is the “variance”?

A

Variance measures the variability of the scores by computing the average squared distance from the mean. First, measure the distance from the mean for each score, then square the distances and find the sum of the squared distances. Next, for a sample, the average squared distance is computed by dividing the sum of the squared distances by n - 1.

53
Q

What is the term to describe measuring the distance away from the mean?

A

Deviation For example, if the mean is 80 and you have a score of 84, then the distance (or deviation) is 4 points.

54
Q

What is the process of calculating the variance?

A

First, measure the distance of EACH score away from the “mean” [so the mean is calculated by adding up EACH score and diving by the number of scores in total] Then, square each of these distances and compute the average of the squared distances (aka variance). [e.g 4 squared + 2 squared + 8 squared + 9 squared DIVIDED BY 4 (the number of scores in total) = Variance However, NOTE that when dividing the sum of the average squared distances, divide it by the SUM of the numbers of scores in total, MINUS 1 (n - 1 formula). This is confusing but minusing 1 will produce a variance for a sample that is ACCURATE and UNBIASED to represent the population variance. Finally, to then calculate the standard deviation, square root the standard deviation sum. [aka Standard deviation = the square root of the variance total

55
Q

What is the value of n - 1 known as?

A

Degrees of freedom

56
Q

Why is the degrees of freedom (df) a necessary adjustment?

A

To ensure sample variance provides an accurate representation of its population variance. Otherwise, the sample variance tends to underestimate the actual variance of the population.

57
Q

To compute the median, what is the first step?

A

List the scores in order, from smallest to largest.

58
Q

What is the most frequently occurring score called?

A

The mode

59
Q

What is the sum of the squared deviations called?

A

Variance

60
Q

In addressing the shape of the distributions, what is a “normal distribution” and when plotted as a frequency polygon, what pattern does it form?

A

A normal distribution is a theoretical frequency distribution that has certain special characteristics. A “normal curve” pattern is formed - a symmetrical, bell-shaped frequency polygon representing a normal distribution.

61
Q

In a “normal curve” pattern, where is the mean, median, and mode positioned?

A

At the center of the distribution

62
Q

What is “kurtosis”?

A

How flat or peaked a normal distribution is. In other words, kurtosis refers to the degree of dispersion among the scores or whether the distribution is tall and skinny or short and fat.

63
Q

What is a “mesokurtic” normal curve?

A

Mesokurtic (pronounced me-zˉo kur-tik) curves have peaks of medium height, and the distributions are moderate in breadth. Meso means MIDDLE.

64
Q

What is a “leptokurtic” normal curve?

A

Leptokurtic (pronounced lep-tuh-kur-tik) curves are tall and thin, with only a few scores in the middle of the distribution having a high frequency. Lepto means THIN.

65
Q

What is a “platykurtic” normal curve?

A

Platykurtic (pronounced plat-i-kur-tik) curves are short and more dispersed (broader). In a platykurtic curve, there are many scores around the middle score that all have a similar frequency. Platy means BROAD or FLAT.

66
Q

True or false: most distributions do not approximate a normal or bell-shaped curve

A

TRUE. They are usually skewed or lopsided.

67
Q

What is a positively skewed distribution?

A

A distribution in which the peak is to the left of the center point, and the tail extends toward the right, or in the positive direction. The mode—the score with the highest frequency—is the high point on the distribution. The median divides the dis-tribution in half. The mean is pulled in the direction of the tail of the distribu-tion; that is, the few extreme scores pull the mean toward them and inflate it.

68
Q

What is a negatively skewed distribution?

A

A distribution in which the peak is to the right of the center point, and the tail extends toward the left, or in the negative direction. In a negatively skewed distribution, the mean is pulled toward the left by the few extremely low scores in the distri-bution. As in all distributions, the median divides the distribution in half, and the mode is the most frequently occurring score in the distribution.

69
Q

If your exam score could be positively or negatively skewed, which one is preferable for higher scores?

A

A negatively skewed distribution

70
Q

What is a “z” score (or standard score)?

A

A number that indicates how many standard deviation units a raw score is above or below the mean of a distribution. It tells us whether an individual raw score is above the mean (positive z score) or below the mean (negative z score). Z scores are a way of transforming raw scores to standard scores for purposes of comparison in both normal and skewed distributions.

71
Q

What is the formula to calculate a Z score?

A

z (z score) = X (the raw score) - X/ (the sample mean) DIVIDED BY S (the standard deviation)

72
Q

If the distribution of scores for which you are calculating z scores is normal (symmetrical or unimodal), then it is referred to as….?

A

The standard normal distribution

73
Q

What is the standard normal distribution?

A

A normal distribution with a mean of 0 and a standard deviation of 1.

74
Q

True or false: it is very unusual for a normally distributed population of scores to include z-scores larger than 4.0

A

TRUE. The range will usually be -4.00 to +4.00

75
Q

What is the percentile rank?

A

A score that indicates the percentage of people who scored at or below a given raw score.

76
Q

A distribution can have more than one ____ but can have only one _____.​

A

mode; median or mean

77
Q

What is probability?

A

Both the study of likelihood and uncertainty and the number of ways a particular outcome can occur divided by the total number of outcomes

78
Q

How do we calculate the percentile rank?

A

We need the z score. The formula is :

79
Q

What is the range?

A

The range is the total distance covered by the distribution, from the highest score to the lowest score. It is completely determined by the most extreme values - it therefore ignores all other scores in the distribution. Only the highest and lowest score are considered

80
Q

What does a frequency distribution tell us about?

A

Central tendency (where do most scores fall) Variability (what is the spread of scores) Shape of the distribution (symmetrical or skewed)

81
Q

***What type of statistic is the central tendency?

A

Descriptive statistic

82
Q

****Why would a distribution not be “normal”?

A

When a mode does not fall in the middle of a distribution If the scores are not bellshaped or symmetrical If scores do not cluster around the centre of the distribution

83
Q

***** What does the μ represent?

A

The mean

84
Q

******What is standard normal distribution and how does it occur?

A

When we transform RAW scores into Z scores. It is when the U (mean) = 0, and the standard deviation (σ) is 1.

85
Q

****** What does σ represent?

A

Standard deviation

86
Q

*******When the σ is 1 and the μ is 0 what does that mean?

A

We have standard normal distribution (bell curve shape)

87
Q

****** What is this formula? x - μ / σ

A

The formula used to calculate the z score

Psychology 1022 (12 decks)

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