Descriptive Statistics- Graphs Flashcards
What do descriptive statistics present?
An overview of collected information (data)
What do descriptive statistics make coherent & easily digestible?
Large sets of information
What do descriptive statistics avoid?
Distorting the data
What do descriptive statistics suggest?
The appropriate inferential test to use.
How many parts are involved in the presentation of descriptive statistics?
3
What are the 3 parts involved in the presentation of descriptive statistics?
Graphical presentation (figures), numbers (often in table format), & verbal description (written in a report).
What do descriptive statistics provide?
An integrated, coherent & concise summary of data that can be related back to any question being asked.
What do we aim to do with collected data?
Get a visual summary of it (by transferring numbers into a graphical presentation).
How many levels of measurement are there?
4
What levels of measurement are there?
Nominal (measuring name-based data), ordinal (measuring order-based data), interval (measuring numerical data with no real zero point), & ratio (measuring numerical data with a true zero point) levels.
What are examples of nominal data?
Eye colours, car models, & favourite colours.
What are examples of ordinal data?
Rankings & rating scales
What are examples of interval data?
Times of the day & temperatures.
What are examples of ratio data?
Heights, weights, reaction times, & exam scores.
Which mathematical notation can be applied to nominal data?
”=” & “≠”
Which mathematical notation can be applied to ordinal data?
”=”, “≠”, “>”, & “<”
Which mathematical notation can be applied to interval data?
”=”, “≠”, “>”, “<”, “+”, & “-“
Which mathematical notation can be applied to ratio data?
”=”, “≠”, “>”, “<”, “+”, “-“, “x”, & “÷”
In which order does each level of measurement increase in complexity & informativity?
Nominal data, then ordinal data, then interval data, then ratio data.
What limits the choice of statistical test that can be applied to data?
The mathematical notation that can be applied to each data’s level of measurement.
Which levels of measurement are discrete?
Nominal & ordinal levels.
Which levels of measurement are continuous?
Interval & ratio levels.
What is the aim of displaying the frequencies from categorical data?
To display it in the simplest way that conveys all the relevant bits of information.
What do we present if we want to create a visual summary (or plot) of nominal data?
A bar chart of frequencies.
When visually summarising nominal data, how do we indicate that we do not have a continuous scale on the x-axis?
By placing spaces in between each bar.
If you show 10 people a face & ask them to judge the age of the face shown, how many responses will you get?
10 (N = 10)
If you show 10 people a face & ask them to judge the age of the face shown, what responses might you get?
52, 49, 52, 61, 57, 57, 56, 54, 55, & 59
What does N = 50 mean?
You have 50 scores.
What must we do to make sense of continuous (interval & ratio) data?
Organise it
Once our data has been divided into (meaningful) intervals, what do we graph to assess frequency distribution?
The number of items in each interval.
How can we divide data into intervals?
By determining the smallest & largest score in our data set, & counting how many times these scores and every score in between are present.
What does a frequency table look like?
It has the dependent variable (e.g. “Score”) and the independent variable (e.g. “Frequency”) in separate cells at the top of the table, then 2 rows of numbers underneath each of these headings.
What does a frequency histogram look like?
It has the independent variable (e.g. “Age Scores”) on the x-axis, and the dependent variable (e.g. “Frequency”) on the y-axis, with bars representing each independent variable in the middle.
How do you group data in order to create a frequency histogram?
By locating your minimum & maximum values (e.g. a minimum score of 57 & a maximum score of 96), & identifying how many intermediate values you have (e.g. 40).
How do you create a frequency histogram?
By using a frequency table.
What is an example of data that could be grouped & transformed into a frequency histogram?
The frequency of scores (in percentages) on a statistics test.
If you have scattered & sparse data that have not been grouped, what will its frequency histogram look like?
It will have the independent variable (e.g. “Score) along the x-axis, and the dependent variable (e.g. “Frequency Count”) along the y-axis, with clusters of bars of varying lengths in the middle.
What is an example of a range of scores & their frequencies that could be grouped together in a frequency histogram?
Scores of 57, 58, 59, & 60, with frequencies of 1, 2, 1, & 0.
How would you represent scores of 61, 62, 63, and 64 with frequencies of 1, 1, 0, & 0, in a frequency table for use in a frequency histogram?
Under the heading “Scores”, you would put “61-64”, and under the heading “Frequency”, you would put “2”.
What does a histogram of grouped data look like?
It has the independent variable (e.g. “Score”) on the x-axis, & the dependent variable (e.g. “Frequency Count”) on the y-axis, with several bars all joined together in the centre.
What is the advantage of presenting grouped data in a histogram?
It means that the data has not been changed, but that the shape of the histogram is clear.
What tells you the number of times an individual score appears (along the y-axis) in a histogram?
The height of each bar
What tells you what each score is (along the x-axis) in a histogram?
The position of each bar.
What are we interested in when creating a histogram?
The range of our values.
What do the tails of a histogram look like?
They are short assorted purple bars, either side of a bump in the middle.
What does the centre of a histogram look like?
An array of thin bars of different heights.
What are some possible differences that could be present between 2 histograms?
Their shapes (they could have 1 or 2 centres), their location on the graphs, & the colour of their bars.
What does a histogram with a negative skew look like?
It has 1 centre (towards the right) & 1 tail (towards the left), each located in the middle of the graph.
What does a histogram with a positive skew look like?
It has 1 centre (towards the left) & 1 tail (towards the right), each located in the middle of the graph.
