methods: analysis of quantitative data Flashcards
(28 cards)
1
Q
what does research that gathers quantitative data produce?
A
- raw scores
- data tables are used to present this data
2
Q
what are the data tables called?
A
- raw score table
- or frequency table
3
Q
why are raw scores summarised?
A
- difficult to understand
- summarised to make it easier to see if trends are being shown and to highlight differences between groups
4
Q
what can the data be summarised using?
A
- descriptive statistics
- measures of central tendency and dispersion
5
Q
define measures of central tendency
A
- descriptive statistic that calculates the average or most typical value in a dataset
6
Q
how can the average score be calculated? (measures of central tendency)
A
- mean
- mode
- median
7
Q
how is the mean calculated?
A
- adding up all values in dataset and diving by number of scores collected
8
Q
when is the mean often used?
A
- when interval/ratio level data is obtained
- it’s the most sensitive and powerful measures of central tendency because all scores in dataset are used in the calculation
- however, it can be affected by extreme values or when there’s a skewed distribution
9
Q
how is the mode calculated?
A
- looking at the most frequent score in dataset
- if there’s 2 most frequent scores (bi-modal), both scores should be reported
- if there’s more than 2, mode is a meaningless measure of central tendency
10
Q
when is the mode used?
A
- when nominal data is obtained and is easy to calculate
- it’s not affected by extreme scores
- however, it’s not a useful measure of tendency on small datasets with frequently occurring same values
11
Q
how is the median calculated?
A
- when values in dataset are placed in rank order (smallest to largest)
- when dataset has odd number of scores, it’s simply the middle score
- if there’s an even number of scores, the mean of two middle scores needs to be calculated
12
Q
when is the median used?
A
- when ordinal level data is obtained
- simple calculation to make and not affected by skewed distribution
- however, it’s less sensitive than the mean and isn’t useful on datasets that have small number of values as it may not represent the typical score
13
Q
define measures of dispersion
A
- descriptive statistic that calculates spread of scores in dataset
- can be misleading without knowing variation between the scores
14
Q
how is measures of dispersion calculated?
A
- range
- standard deviation
15
Q
how is the range calculated?
A
- difference between highest and lowest value
- high range value indicates that scores are spread out and low range value indicates that scores are closer together
16
Q
what is the range affected by?
A
- extreme scores
- may not be useful if there are outliers in the dataset
- also doesn’t indicate if scores are bunched around mean score or more equally distributed around mean
17
Q
how can dataset be calculated if it has extreme scores? (range)
A
- calculate interquartile range
- involves cutting out lowest quarter and highest quarter of values (top and bottom 25%) and calculating range of remaining middle half of scores
18
Q
what is standard deviation?
A
- deviation: distance of each value from the mean
- each score in dataset would have deviation value, so to get single value that represents all deviation scores, the standard deviation needs to be calculated
- SD gives a single value that represents how scores are spread out around the mean
- the higher the SD, the greater the spread of scores around mean value
19
Q
how can data be presented?
A
- summary tables
- graphical representation
20
Q
what do summary tables represent?
A
- measures of central tendency and dispersion
21
Q
how can graphs be used?
A
- to illustrate summary data or data frequencies
- NEVER illustrate raw scores in graph since data should be shown that’s meaningful and summative
22
Q
what are bar charts used for?
A
- to present data from categorical variable eg mean, mode, median
- categorical variable is placed on x-axis, and heigh of bars represents value of that variable
23
Q
what are histograms used for?
A
- used to present distribution of scores by illustrating frequency of dataset
- unlike bar charts where bars are separated by space, bars on histogram are joined to represent continuous data rather than categorical (discrete) data
- possible values are presented on x-axis and height of each bar represent frequency of value
24
Q
why is examining the distribution of data in larger samples important in research?
A
- shows the overall frequency of values in a dataset
- helps identify trends not visible in small samples
- allows estimation of the distribution of scores in the whole population
25
what is a percentage?
- % gives an **overall indication** of relative proportion of people who achieve particular score
- **working out %**: sum of values needs to be calculated and each value divided by sum, total multiplied by 100
26
what happens when the frequency distribution of a population is calculated?
- it can be represented on a **frequency graph**
- if the graph shows a **bell-shaped curve**, the data has a **normal distribution**
27
what are the key characteristics of a normal distribution?
- **symmetrical** around the **midpoint**
- mean, mode, and median are **aligned** at the **center**
- tails never touch the horizontal axis
- **approximate** percentage within SDs:
- 68% fall within ±1 SD each side
- 95% fall within ±2 SDs either side
- SD is calculated from raw scores to determine actual values of these intervals
28
what does it mean when a distribution is skewed, and what causes it?
- skewed distributions are **not symmetrical**
- cased by **nature of the test** or **sample characteristics**
- **negative skew**:
- test is **easy** or sample has **unusual high aptitude**
- most scores are **high**, above the mean
- **positive skew**:
- test is **difficult** or sample has **low aptitude**
- most scores are **low**, below the mean
